Tanta University Faculty of Engineering Computer and Control Engineering Department Adapitve Neuro-Fuzzy Controller Design Tuned by an Immune Genetic Algorithm By Eng. Saad Mohame

Tanta University Faculty of Engineering

Computer and Control Engineering Department

Adapitve Neuro-Fuzzy Controller Design Tuned by an Immune

Genetic Algorithm

By

Eng. Saad Mohamed Hafez Hewaidy M. Sc., Electrical Engineering (Automatic Control Engineering)

A Ph.D Thesis

Electrical Engineering

(Computer and Control Engineering)

Under the Supervision of

Prof. Dr. Mahmoud M. Fahmy Computer and Control Engineering Department,

Faculty of Engineering, Tanta University

Prof. Dr. Mohamed T. Faheem Computer and Control Engineering Department,


Ass. Prof. Dr. Tarek E. El-Tobely Computer and Control Engineering Department,


2013

Tanta University Faculty of Engineering

Computer and Control Engineering Department

Adapitve Neuro-Fuzzy Controller Design Tuned by an Immune

Genetic Algorithm A Thesis

Submitted for the Requirements of the Degree of Doctor of Philosophy of Science in Electrical Engineering

(Computer and Control Engineering) By

Eng. Saad Mohamed Hafez Hewaidy M. Sc., Electrical Engineering (Automatic Control Engineering)

Under the Supervision of



Prof. Dr. Mohamed T. Faheem Computer and Control Engineering Department,




2013

Viva Voce

Date :January 3, 2013

Place: Faculty of Engineering, Tanta University

Committee



Prof. Dr. Mohamed M. Sharaf Industrial Electronics and Automatic Control Department,

Faculty of Eelectonic Engineering, Menofia University

Ass. Prof. Dr. Elsayed A. Sallam Computer and Control Engineering Department,




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بسم هللا الرحمن الرحیم

من عمل صالحا من ذكر أو أنثى وهو مؤمن فـلنحيينه حيـاة طيبة ولنجزينهم

أجرهم بأحسن ما كانوا يعملون صدق اهللا العظيم

)٩٧( اآلیة: سورة النحل

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The thesis at a glance Multivariable ANFIS (MV-ANFIS) controller that consider the interactions between the variables of the controlled process are introduced in this thesis. To overcome the dimensionality problem of a complex model of fuzzy rules, the cascaded distributed multi-variable ANFIS (CD-MV-ANFIS) controller is also proposed. These controllers are tuned by an Immune Genetic Algorithm (IGA) and implemented on drum boiler turbine units and greenhouse system (GH).

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Acknowledgment

A thesis does not just 'happen'. Apart from the researcher's interest and effort, the guidance and support of the supervisors together with many other kind people are indispensable. I have been truly fortunate in this regard. I would like to acknowledge my indebtedness to my principal supervisor Prof. Dr. Mahmoud M. Fahmy Computer and Control Engineering Department, Faculty of Engineering, Tanta University. Prof. Fahmy is the one who suggested that my Ph.D. thesis be in the area of ANFIS application. He at the outset lent me some books about the field of research. I am likewise indebted to Prof. Fahmy for his expert directives, and generous dignified in his office at the college hosted. My indebtedness extends to my co-supervisor Prof. Dr. Mohammed T. Faheem, Taif Universit, Faculty of Engineering, Dept. of Electrical Engineering, Taif, KSA, on leave from Tanta University, Faculty of Engineering, Dept. of Computer and Control Engineering, Tanta, Egypt". I am indebted to Prof. Fahim for his expert directives, generous assistance, and continuous encouragement throughout the development of this research work. My indebtedness extends also to my co-supervisor Ass. Prof D. Tarek E. EL-Tobely, Assistance Professor at the Computer and Control Engineering Department, Faculty of Engineering, Tanta University. Dr. El-Tobely is the one who drew my attention to the interesting application of ANFIS for the field of industrial processes. His motivational ideas, witty observations, and constructive criticisms are gratefully appreciated. Heartfelt thanks should go to my parents for their help me by invocation to god, also brother, and sisters for providing me with their affection sincere love. Thankfulness for my cousin Sabria. I also sincerely wish to thank my wife, Eman, for her understanding, patience, and tolerance. Without her help, this work would not have been completed. Sincere wishes of health and wellness and a bright future for my children Mohammed and Abdel Rahman.

Dedication My Ph.D. thesis is dedicated with affection to my mother, whose sympathy and affection disease.

Feedback It will be a great pleasure for me to receive comments and enquiries regarding the different aspects of this thesis. Interested readers and researchers are gently requested to contact me personally, by e-mail, or through the work, and I promise to respond promptly to each and every correspondence.

Saad. M. Hewaidy

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ABSTRACT

This thesis aims at introducing an adaptive neuro-fuzzy inference

(ANFIS) controller for non-linear dynamical systems. To achieve this goal,

two proposed schemes that take into consideration the interactions between

the variables of the controlled process are proposed. Indeed, these types of

controllers are more complicated than the simple multi-input multi-output

(MIMO) ANFIS controllers. The first proposed scheme is a multivariable

ANFIS (MV-ANFIS) controller, which consists of a set of control loops each

one is a single-input single-output (SISO) ANFIS controller with three fuzzy

sets.

The second proposed scheme is a cascaded distributed multi-variable

ANFIS (CD-MV-ANFIS) controller that can overcome the dimensionality

problem of complex fuzzy rules model. The cascading process in this scheme

reduces the complexity of the fuzzy rules model by dividing the controlling

system into groups of cascaded sub-systems each one has a multi-input

single-output (MISO) ANFIS, which by turn reduces 70% of the fuzzy rules.

To enhance the performance of the proposed controllers, the

controllers' parameters are tuned by an artificial immune system (AIS),

afterwards these controllers are tested and implemented on two different non-

linear control processes: the drum boiler turbine units and the greenhouse

system.

The pressure, power and drum water level are chosen as controlled

parameters in the non-linear drum boiler turbine units, due to their strong

effect on the output response of the system, where the 3rd and 7th orders

models are implemented, while in the greenhouse (GH) system the

temperature and humidity are the selected control parameters.

Simulation results revealed that the two proposed controllers were

capable of closely reproducing the optimal performance.

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The comparison of the performances of two proposed controllers

(MV-ANFIS and CD-MV-ANFIS) on two types of drum boiler turbine units

and greenhouse (GH) system was made. The results showed that the

performance of two controller are much close to each other, besides the

reduction of tuning parameters as well as the consuming time for CD-MV-

ANFIS controller was achieved.

Also, the comparison studies for different controllers [27] , [37] [43],[58]

and [36] emphasize that the proposed controllers have capability to handle

any variation on grid demand over a wide range operations without any effect

on safety of valves.

The results are also compared for greenhouse (GH) system to the recent

published paper [87] in this field. In this paper the PID controller tuned by a

hybrid genetic algorithm that combines both (AIS) and (GA) system.

Another comparison was made with the nonlinear MIMO plant model

controlled by simplified (ANFIS) controller [76].

These comparisons show that the second proposed controller in this thesis

outperforms the results presented in these papers in both accuracy and speed.

Keywords: MIMO Controllers; Multivariable ANFIS Controllers; Cascaded

multivariable controllers; Drum-boiler-models; Greenhouse system.

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Contents

Page xi List of Figures xxi List of Tables xxv List of Abbreviations 1 1 Introduction and Review of Earlier Work 1 1.1 Introductio 1 1 2 2 2 2 3 3

1.2 Overview 1.2.1 Definition of Neural Networks 1.2.2 Definition of Fuzzy System 1.2.3 Definition of Fuzzy Neural Networks 1.2.4 Definition of Neuro-Fuzzy Inference systems 1.2.5 Definition of Neuro-Fuzzy systems 1.2.6 Definition of Adaptive Neuro-Fuzzy Inference System 1.2.7 Definition of Genetic Algorithm (GA)

3 1.3 Review of Earlier Work on NN, Fuzzy and NF systems 3 1.3.1 Neural networks research 4 1.3.2 Fuzzy systems research 6 9

1.3.3 Neuro fuzzy system research 1.3.4 Genetic and Immune Genetic algorithm (IGA)

11 1.4 Statement of the Problem under Study 11 1.5 Contribution of Thesis 13 1.6 Simulation and data discussion 14 1.7 Organization of Thesis 16 2 Multivariable ANFIS (MV-ANFIS) with Immune Genetic

Algorithm: Proposed Approach 1 16 2.1 Introduction 17 2.2 Generic Structure of an FIS 18 2.3 Neuro-fuzzy paradigm 20 2.3.1 ANFIS Methodology

20 2.4 Network Representation of Proposed MV-ANFIS System

22 2.4.1 Learning procedure of adaptive components 26 2.5 Parameter Tuning 26 2.5.1 Tuning by Genetic Algorithm (GA) 26 2.5.2 The Artificial Immune System(AIS) 26 2.5.3 Pattern recognition in the immune system

x

27 2.5.4 Shape-space model and affinities 28 2.6 MV-ANFIS Controller for SISO Plant 32 2.6.1 Simulation results 36 2.7 Modeling linear and nonlinear plants 36 2.7.1 modeling Task 1 37 2.7.2 modeling Task 2 37 2.7.3 Modeling Task 3 37 2.7.4 ANFIS partitioning 38 2.7.4.1 MV-ANFIS network in modeling 42 2.7.4.2 Discussion of ANFIS and AMLPs networks 43 2.8 Case study: Multi-input Multi-output Modeling of drum boiler 44 2.8.1 Modeling using Multivariable ANFIS (MV-ANFIS) 47 2.8.2 Comparison of NN and MV-ANFIS models. 48 2.9 Summary 49 3 Cascaded Distributed Multivariable ANFIS CD-(MV-ANFIS)

with Immune Genetic Algorithm: Proposed Approach 2 49 3.1 Design of (CD-MV-ANFIS) Controller 53 3.1.1 Feedback fuzzy controller 54 3.1.2 Fuzzy Control Rules 55 3.2 Immune Genetic Algorithm (IGA) 57 3.2.1 Generation the initial antibodies: 57 3.2.2 Calculating the fitness: 58 3.2.3 Calculation of affinities 58 3.2.4 Crossover and Mutation 60 3.3 ANFIS as a Controller 62 3.4 ANFIS Controller for SISO Plant 67 3.4.1 Simulation results 71 3.5 Summary 72 ٤ Application of Proposed Approaches 1and 2 to Drum Boiler

turbine units 72 4.1 Introduction 74 4.2 Non-linear Models of drum boiler-turbine unit 76 4.2.1 Mathematical of third order drum boiler-turbine model

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77 4.2.2 Mathematical of seven order drum boiler-turbine model 80 4.3 Multivariable ANFIS Controller for drum boiler turbine unit 80 4.3.1 Neuro-Fuzzy Feedforward Controller 85 4.3.2 Neural-network supervisory designer

87 4.4 Design of Neuro-Fuzzy Controllers. 87 4.4.1 Case studies 91 4.4.2 Effectiveness of Membership Function Number and

Tuning epochs

93 4.4.3 Feedforward Controller 99 4.5 Control loop Interaction and Tuning 100 4.6 Performance of drum boiler- turbine unit based on MV-ANFIS

controller

100 4.6.1 Step load response of third order drum boiler model 104 4.6.2 Ramp Response for third order drum boiler model 106 4.6.3 Step load response of seven order drum boiler model 110 4.7 Effect of Immune genetic algorithm for tuning 112 4.8 Application of Cascaded Distributed Multivariable ANFIS

(CD-MV-ANFIS)for drum boiler turbine units

112 4.8.1 Controller third and seven order Drum Boiler processes 115 4.8.2 Effectiveness of Membership Function Number and

Tuning Type

121 4.8.3 Comparison between two approaches 123 4.9 Comparing results with other controllers. 130 4.10 Summary 132 5 Application of Proposed Approach 1and 2 to greenhouse(GH)

system 132 5.1 Introduction 133 5.2 Fault detection and isolation systems 134 5.3 Hierarchical decomposition of greenhouse climate management 135 5.3.1.Greenhouse crop production process 137 5.3.2. Greenhouse dynamical model 139 5.4 Control of the greenhouse ventilation model 139 5.4.1. Control model 140 5.4.2. Feedback-Feedforward linearization and decoupling 143 5.5 Simulation Results 144 5.5.1 Performance of a greenhouse system based on M-ANFIS 150 5.5.2 Comparing the Performance the M-ANFIS controller to

other controllers.

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155 5.6 Cascaded distributed multivariable (CD-MV-ANFIS) controller.

157 5.6.1 Controller of a greenhouse(GH) climate system 159 5.6.2 Blend Immune Genetic Algorithm (BIGA) 159 5.6.2.1 Algorithm of Blend Immune Genetic Algorithm 162 5.7 Simulation results for greenhouse (GH) system 163 5.7.1Comparing the performance of greenhouse system by

using two approaches

166 5.7.2 Comparing the performance (CD-MV-ANFIS) with other controllers

182 5.8 Summary 183 6. Conclusions and Trends for Relevant Future Work 184 6.1 Summary and conclusion 183 6.2 Contributions 184 6.3 discussions 192 6.4 Future work Appendix 193 Appendix A 199 Appendix B 203 Appendix C 204 References

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List of Figures

Page

Figure (2.1) Takagi-Sugeno Fuzzy Inference System 19

Figure (2.2) MV-ANFIS Architecture with n rules ٢١ Figure (2.3) ANFIS learning using hybrid technique ٢٣

Figure (2.4) antigen epitope is recognized by an antibody ٢٧ Figure (2.5) The complementarily relation between the antigen and

antibody ٢٧

Figure (2.6) ANFIS Architecture with nine rules ٢٩

Figure (2.7) Case1:The simulation result of the proposed controller with change of set point ±.9

٣٤

Figure (2.8) Case1:Initial and final coefficient of consequent parameters with 3 fuzzy sets

٣٤

Figure (2.9) Case2:The simulation result of the proposed controller with change of set point ±1.8

٣٥


٣٥

Figure (2.11) Case3:The simulation result of the proposed controller with change of set point ±1.8

35


٣٥

Figure (2.13) (a) Modeling of the linear dynamic system using the MV-ANFIS with 7 fuzzy sets (b) Mean squares errors corresponding to each model

٣٩

Figure (2.14) (a) modeling of the Non-linear dynamic system using the ANFIS with 7 fuzzy set (b) Mean squares errors corresponding to each model

٤٠

Figure (2.15) Membership function of Non-linear dynamic system using the ANFIS with 3 fuzzy sets for all modeling takes (a) Initial membership function (b) final membership

41

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Figure (2.16) Two-output MV-ANFIS architecture with two rules per output.

44

Figure (2.17) Response between actual and desired output values in developed MV-ANFIS model with 3,5, and 7 member ship function (a) pressure (b) power (c) density

45

Figure (2.18) Membership function using ANFIS with 3 fuzzy sets (a) Initial membership function (b) final membership

46

Figure (2.19) Root mean square error value in case of MV-ANFIS & NN modeling

47

Figure (3.1) ANFIS Architecture for n inputs 50 Figure (3.2) A (CD-MVANFIS) controller 51

Figure (3.3) (a) A two-input first-order sugeno fuzzy model with two rules; (b) Equivalent ANFIS architecture

53

Figure (3.4) Applied membership function 54 Figure (3.5) Feedback fuzzy controller tuned by Immune Genetic

algorithm 56

Figure (3.6) Immune Genetic Algorithm 57

Figure (3.7) Two-point crossover 59 Figure (3.8) Mutation in binary 59

Figure (3.9 Learning phase of the Inverse Learning 61 Figure (3.10) Application phase of the Inverse Learning 61

Figure (3.11) Specialized Learning 62 Figure (3.12) ANFIS Architecture with nine rules 63

Figure (3.13) Case 1: The simulation result of the proposed controller with changes of set point ±3.5 and ±1.5

68

Figure (3.14) Case 1: Initial and final coefficient of consequent parameters with 3 fuzzy sets

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Figure (3.16) Case 2: The simulation result of the proposed controller with changes of set point ±5 and ±8 using 3fuzzy sets

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Figure (3.18) Case 3: Initial and final coefficient of consequent 70

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parameters with 5 fuzzy sets Figure (3.19) Case 3: Initial and final coefficient of consequent

parameters with 5 fuzzy sets 71

Figure (4.1) Multivariable ANFIS controller 73

Figure (4.2) Feedforward ANFIS controller 73 Figure (4.3) Schematic diagram of the Drum- boiler-turbine unit 75

Figure (4.4) The main outputs of boiler and its input ٧٥ Figure (4.5) Neural network structure of feedforward fuzzy

controller. ٨٤

Figure (4.6) Input-output steady-state data for upper-pressure limit case.

89

Figure (4.7) Input-output steady-state data for constant-pressure case.

٨٩

Figure (4.8) Input-output steady-state data for sliding-pressure case. ٩٠

Figure (4.9) Input-output steady-state data for lower-pressure limit case.

٩٠

Figure (4.10) Rsme for sliding-pressure case, 3, 5 and 7 mf, 20 epochs.

٩٢

Figure (4.11) FISU1 membership functions for sliding-pressure case, 3 mf, 20 epochs.

٩٢

Figure (4.12) FISU1 power membership functions. 93 Figure (4.13) FISU1 pressure membership ٩٤

Figure (4.14) FISU1 fuzzy inference surfaces. 95 Figure (4.15) FISU2 fuzzy inference surfaces. 96

Figure (4.16) FISU3 fuzzy inference surfaces. ٩٦ Figure (4.17) System response to changes in the pressure, power

&drum level 12 Bar, (± 55 Mw, ±0.75 Mm) 102

Figure (4.18) System response to changes in the pressure, power &drum level (From low-to full load)

103

Figure (4.19) System response to changes in the pressure, power &drum level (From full -to low load) at different fuzzy sets

١٠٣

Figure (4.20) Ramp load tracking with tuned controller parameters ١٠٥ Figure (4.21) Ramp load tracking with tuned controller parameters 105

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from low to full load.. Figure (4.22) System response to changes in the pressure, power

&drum level (± 4 Bar, ± 15 MW, ±65 mm) ١٠٧

Figure (4.23) System response to changes in the pressure, power &drum level(± 7 Bar, (± 35 Mw, ±.85 Mm)

١٠٧

Figure (4.24) System response to changes in the pressure, power &drum level (± 12 Bar, (± 15 Mw, ±85 Mm)

١٠٨

Figure (4.25) System response to changes in the pressure, power &drum level (From low-to full load)

108

Figure (4.26) System response at low load with and without (IGA) 111

Figure (4.27) System response at high load with and without (IGA) ١١١ Figure (4.28) The proposed (CD-MVANFIS) control scheme for

boiler systems 113

Figure (4.29) Initial and final values of consequent parameters within 5 fuzzy sets (a) for pressure loop (b) for power loop (c) for drum level loop

١١٤

Figure (4.30) Performance of proposed controller based on Immune Genetic Algorithm using different fuzzy sets at low load for third order model

115

Figure (4.31) Performance of proposed controller based on immune genetic algorithm using different fuzzy sets at low load 7order model

117

Figure (4.32) Performance of proposed controller based on genetic and an immune genetic algorithm using for 3rd order model

١١٧

Figure (4.33) System response to changes in the pressure, power &drum level (± 32 Bar, (± 65 Mw, ±1 Mm) for third order model

119

Figure (4.34) System response to changes in the pressure, power &drum level (± 7 Bar, (± 15 Mw, ±35 Mm) for seven order model

120

Figure (4.35) MSE for drum boiler using proposed controller based on tuning type left column for three order model, right column seven order model

121

Figure (4.36) Compare system response under LQR, fuzzy, and ANFIS controller, where drum pressure and power changes from 90 to 125, and from 45 to 100 respectively

١٢٤

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Figure (4.37) Compare system response under LQR, fuzzy, and ANFIS controller, in case of equal drum water level deviation equal zero

124

Figure (4.38) Controlling inputs for u1 (fuel flow rate) using ANFIS, LQR, and fuzzy controllers.

١٢٥

Figure (4.39) Controlling inputs for u2 (throttle valve position) using ANFIS, LQR, and fuzzy controllers.

125

Figure (4.40) Controlling inputs for u3 (feedwater floow) using ANFIS, LQR, and fuzzy controllers.

126

Figure (4.41) Comparison between the proposed ANFIS controller with adaptable nonlinear, effective feedback, and fuzzy controllers for third order model

128

Figure (4.42) Comparing MSE for using (ANFIS, adaptable nonlinear, effective feedback, and fuzzy) controllers for third order model

١٢٨

Figure (4.43) Comparing MSES for all outputs using the proposed MV-ANFIS, and fuzzy) controllers for seven order model

١٢٩

Figure (5.1) A schematic diagram of the greenhouse crop production process.

١٣٦

Figure (5.2) A schematic diagram of the greenhouse climate control process.

140

Figure (5.3) Overall control strategy in case of small delays and/or a slow desired time response where RT and RW are the temperature and humidity ratio set value respectively.

143

Figure (5.4) Greenhouse: (a) indoor air temperature (upper) and indoor air humidity ratio (bottom), (b) internal control signals: Ventilation (upper) and water capacity ratio (bottom).Using different fuzzy sets

145

Figure (5.5) Greenhouse outputs: indoor air temperature (upper) and indoor air humidity ratio (bottom) for all day operation, example1.

١٤٦

Figure (5.6) Greenhouse internal control signals: Ventilation (upper) and water capacity ratio (bottom).

١٤٦

Figure (5.7) Greenhouse control signals: ventilation rate (upper),water capacity of fog system (middle), heat transfer (bottom).

147

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Figure (5.8) Greenhouse disturbances: output temperature (upper),absolute humidity (middle), and solar radiation energy (bottom).

148

Figure (5.9) Greenhouse outputs: indoor air temperature (upper) and indoor air humidity ratio (bottom) example2.

١٤٩

Figure (5.10) Greenhouse control signals: Ventilation (upper) and water capacity ratio (bottom).

150

Figure (5.11) Case 1 Greenhouse outputs: indoor air temperature, red line (IGA-ANFIS) and dash blue(ANFIS)

151

Figure (5.12) Case2 Greenhouse outputs: indoor air temperature, red line (IGA-ANFIS) and dash blue(ANFIS)

152

Figure (5.13) Case3 (1) Greenhouse outputs: indoor air temperature, red line (IGA-ANFIS) and dash blue(ANFIS)

152

Figure (5.14) Case3 (2) Greenhouse outputs: indoor air temperature, red line (IGA-ANFIS) and dash blue(ANFIS)

١٥٢

Figure (5.15) E of Temperature using MV-ANFIS controller tuned by Immune genetic compared to other controller

154

Figure (5.16) E of Humidity using MV-ANFIS controller tuned by Immune genetic compared to other controller

١٥٤

Figure (5.17) ANFIS Architecture for 2 inputs ١٥٦

Figure (5.18) A(CD-MVANFIS) controller 157 Figure (5.19) The proposed (CD-MVANFIS) control scheme for

greenhouse (GH) system ١٥٨

Figure (5.20) Genetic Algorithm 160

Figure (5.21) Blend Immune Genetic Algorithm (BIGA) ١٦١ Figure (5.22) Compare a greenhouse outputs using CD-MV-ANFIS,

based on genetic algorithm: indoor air temperature (upper) and indoor air humidity ratio (bottom) for all day operation

162

Figure (5.23) Response of temperature at first 30 minute for cascade (CD-MV-ANFISs), and (MV-ANFIS) tuned by genetic

163

Figure (5.24) Response of humidity at first 10 minute for cascade (CD-MV-ANFISs), and (MV-ANFIS) tuned by Immune genetic algorithm

164

Figure (5.25) MSE of temperature for both (CD-MV-ANFISs), and ١٦٤

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(MV-ANFIS) based on tuning type. Figure (5.26) MSE of humidity for both (CD-MV-ANFISs), and (MV-

ANFIS) based on tuning type 165

Figure (5.27) Response of (CD-MV ANFIS) controller optimized by GA method at different performance criteria.

١٦٨

Figure (5.28) Response of (CD-MV ANFIS) controller optimized by AIS method at different performance criteria.

١٦٩

Figure (5.29) Response of (CD-MV ANFIS) controller optimized by AISIGA)-GA(B method at different performance criteria.

١٧٠

Figure (5.30) Comparison between PID and ANFIS controller optimized by GA method at different performance.

172

Figure (5.31) Comparison between PID and ANFIS controller optimized by AIS method at different performance.

173

Figure (5.32) Comparison between PID and ANFIS controller optimized by AIS-GA(BIGA) method at different performance.

١٧٤

Figure (5.33) Comparison the performance criteria between PID and ANFIS controller optimized by GA method (a) ITAE (b) IAE (c) ISE (d) MSE

175

Figure (5.34) Comparison the performance criteria between PID and ANFIS controller optimized by AIS method (a) ITAE (b) IAE (c) ISE (d) MSE

١٧٦

Figure (5.35) Comparison the performance criteria between PID and ANFIS controller optimized by AIS-GA (BIGA) method (a) ITAE (b) IAE (c) ISE (d) MSE

١٧٧

Figure (5.36) Comparison between output responses for using CD-MV-ANFIS and simplified ANFIS controllers (a)and (b) output results in both controllers. (c),and (d) control signals.

١٨٠

Figure (5.37) MSES for both CD-MV-ANFIS and simplified ANFIS controllers

١٨٠

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List of Tables

Page

Table 2.1 values associated for different fuzzy set in each case

33

Table 2.2 Initial FIS in case1 using 3 fuzzy set 33

Table 2.3 Final FIS in case1 using 3 fuzzy set 33

Table 2.4 errors in modeling linear dynamic system using ANFIS with different fuzzy sets

39

Table 2.5 RMS errors in modeling Non-linear dynamic system using ANFIS with different fuzzy sets 40

Table 2.6 Average RMS error for different fuzzy sets in modeling Non- linear dynamic system using ANFIS.

41

Table 2.7 Comparison between ANFIS and AMLPs networks(Modeling task 1)

42


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Table 2.9 Comparison between ANFIS and AMLPs networks (Modeling task 3)

43

Table 3.1 Total number of parameters to be tuned for different fuzzy sets

66

Table 3.2 RMS values associated for different fuzzy set in each case

70

Table 4.1 Rated operating conditions of 3rd order model 77

Table 4.2 Rated operating conditions of 7th order model 80

Table 4.3 Constant Pressure Equilibrium Points 87

Table 4.4 Sliding Pressure Equilibrium Points 88

Table 4.5 Upper Pressure Limit Equilibrium Points 88

Table 4.6 Lower Pressure Limit Equilibrium Points 88

Table 4.7 MSES based on the number of fuzzy sets 95

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Table 4.8 FISU1 KNOWLEDGE BASE FOR SLIDING-PRESSURE: CASE WITH 3 MF

97


98

Table 4.10 FISU3 KNOWLEDGE BASE FOR SLIDING-PRESSURE: CASE WITH 3 MF 99

Table 4.11 MSES& percentage of errors 3 order model with tuned parameters

102

Table 4.12 MSES& percentage of errors for seven order model

109

Table 4.13 MSES for seven order model based on number of membership function

109

Table 4.14 Scaling factors of (FF/FB) of proposed controller 109

Table 4.15 Effectiveness of fuzzy set on performance accuracy for two models 116

Table 4.16 MSES and % of errors with different cases based on tuning tools

116

Table 4.17 MSES& percentage of errors for third order using CD-MVANFIS controller

118

Table 4.18 MSES& percentage of errors for 7th order using CD-MVANFIS controller

119

Table 4.19 Comparison of performance accuracy between MV-ANFIS and CD-MV-ANFIS controller for third order model

122

Table 4.20 Comparison of performance accuracy between MV-ANFIS and CD-MV-ANFIS controller for seven order model

122

Table 4.21 Compared MSES of the proposed controller with different controllers at different ranges of operation

126

Table 5.1 A hierarchical decomposition of greenhouse climate management

135

Table 5.2 RMS values for different controllers 153

Table 5.3. Normalized values tuned by immune genetic 154

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algorithm Table. 5.4 MSES for Green house system based on number of

membership function 154

Table 5.5 Comparison of performance accuracy between MV-ANFIS and CD-MV-ANFIS controller for Greenhouse system based on tuning type

167

Table.5.6 The performance of ANFIS controller optimized by GA, AIS, and (BIGA) method based on performance criteria

169

Table 5.7 The performance of the proposed controller compared to PID at different criteria in case of GA, AIS, AIS-GA

180

Table 5.8 Comparing the proposed controller to other controllers

161

Table 6.1 RMS and errors reduction for ANFIS and AMLPs networks

185

Table 6.2 Root mean square error value in case of MV-ANFIS & NN modeling

185

Table 6.3 The average Mean square errors for different set-point changes using Multi-loop ANFIS and fuzzy controller for third order model

186

Table 6.4 The average Mean square errors for different set-point changes using Multi-loop ANFIS and fuzzy controller for third order model.

186

Table 6.5 Mean square errors for different set-point changes using Multi-loop ANFIS and fuzzy controller for seven order model.

187

Table 6.6 The average Mean square errors for different set-point changes using Multi-loop ANFIS and fuzzy controller for seven order model.

188

Table 6.7 The average MSES of the proposed controller with different controllers at different ranges of operation

188

Table 6.8 Average MSES and % of errors for two model based on tuning algorithm

189

Table 6.9 Comparison the performance between PID and CD-MV-ANFIS controller optimized by GA, AIS, AND (BIGA) method based on minimum error for common performance criteria

191

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List of Abbreviations

Adaptive neuro-fuzzy inference system ANFIS

Neural network NN

Fuzzy systems FS

Neuro-fuzzy NF

Fuzzy Logic FL

Artificial Neural Network ANN

Fuzzy Inference System FIS

Single-input Single-output SISO

Multiple-input Multiple-ouput MIMO

fossil fueled power plant FFPP

Pseudo Random Binary Sequence PRBS

Fuzzy Logic Control FLC

Proportional integral derivative PID

Serial distributed multivariable SDM

Gain scheduled proportional and integral FGPI

Genetic Algorithm GA

Adaptive Fuzzy Controller AFC

Fuzzy neural network FNN

Proportional integral PI

Least Square Error LSE

Co-active neuro-fuzzy inference system CANFIS

Multi-Layer Perception MLP

Multi-loop ANFIS controller MANFIS

Multi-variable ANFIS controller MV-ANFIS

Cascaded distributed ANFIS control scheme CD-MV-ANFIS

Back-propagation learning algorithm BPLA

Takagi-Sugeno TS

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Adaptive Multi-Layer Perception AMLP

Radial basis function neural network RBFNN

learning vector quantization LVQ

Multiple-Input Single-output MISO

knowledge base KB

Adaptive Multi-Layer Perception Network AMLP

Membership function MF

Nonlinear autoregressive with exogenous input NARX

Mmulti-layer neural network MNN

shape memory alloy SMA

Linear correlation coefficient Lcc

Fuzzy inference surface for pressure FIS-y1

Fuzzy inference surface for power FIS-y2

fuzzy inference surface for density ρ FIS-ρ

Model Predictive Control MPC

time constant associated with state x1 TC1

time constant associated with state x2 TC2

Fossil Fuel Power Unit FFPU

Feedforward and feedback FF/FB

Takagi-Sugeno Fuzzy TSF

fuzzy inference surfaces for u1 FISU1



Scaling factor for deviation of pressure Scalf-P

Scaling factor for deviation of power Scalf-E

Scaling factor for deviation of level Scalf-L

Artificial immune system AIS

Blend Immune Genetic Algorithm BIGA

Average mean squared errords AMSE

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Ventilation rate VR

Integral absolute error IAE

Integral time absolute error ITAE

Integral square error ISE

Mean square error MSE

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Published papers

1. Fahmy, M.M., Fahiem, T. M., Eltobely,T.E.,and Hewaidy,S.M. "Aplication of Adaptive-Neuro-Fuzzy inference system on modeling and controling Power Plant" the 2nd International Conference on Advanced Computer Theory and Engineering (ICACTE 2009), September 25 - 27,, Cairo, Egypt, 2009.

2. Fahmy, M.M., Fahiem, T. M., Eltobely,T.E.,and Hewaidy,S.M

"Multivariable ANFIS Controller for drum boiler models tuned by genetic algorithm" Ain Shams Journal of Electrical Engineering (ASJEE),2010.

3. Hewaidy,S.M.,Fahmy,M.M.,Fahiem,T. M., and Eltobely,T.E.,"A

Cascaded Distributed Multi-variable ANFIS Controller Tuned by an Immune Genetic Algorithm", Accepted on International Journal of Emerging Technologies of Sciences and Engineering" Paper id 373,2012.

Chapter 1 Introduction and Review of Earlier Work

In this introductory chapter, we briefly present the problem of modeling and controlling non-linear dynamical systems. The contributions of relevant intelligent systems for solving this problem are presented. An overview and earlier research works on neural networks (NNs), Fuzzy systems (FS) and Neuro-fuzzy (NF) systems are introduced in sections 1.2 and 1.3. The research point of this thesis which is namely based on Adaptive neuro-fuzzy inference systems (ANFIS) is defined in section 1.5 while our contribution is illustrated in section 1.5. The simulations results are described in section 1.6. Finally the organization of the thesis is provided in section 1.7. 1.1 Introduction

Recently, the current trend in intelligent systems or soft computing research is concerned with the integration of artificial intelligent tools [48] (neural networks, fuzzy technology, evolutionary algorithms…) in a complementary hybrid framework for solving complex problems. In most literature works, it is noted that the control of nonlinear systems is difficult to be studied specially in the absence of a systematic procedure as compared to those available for linear systems. It is noted that more commonly available methods are heuristic in nature and the fuzzy logic and neuro-fuzzy can reduce the arbitrariness in the design of a controller to a great extent. In most recent design control processes, neuro-fuzzy is used. This neuro-fuzzy system that has been emerged from the fusions of neural and fuzzy, and form a popular ANFIS are involved in solving real world problems [108].

1.2 Overview An intelligence system is a system that is able to make decisions that would be regarded as intelligent if it was done by humans. Intelligence systems adapt themselves using some example situations (inputs of a system) and they correct decisions automatically for future situations. Neural networks (NNs), Fuzzy systems, and Neuro-Fuzzy systems are the examples of artificial intelligence systems. In this section we introduce some concepts related to intelligent control tools which can be summarized as follows.

1.2.1 Definition of Neural Networks (NNs) The NNs are a data processing system consisting of a large number of simple, highly interconnected processing elements (artificial neurons) in an architecture inspired by the structure of the cerebral cortex of the brain [91]

Chapter 1: Introduction and Review of Earlier Work

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& [80].They are useful empirical modeling tools that have been used for process estimation and control since 1950’s.

1.2.2 Definition of Fuzzy System (FS) The Fuzzy systems provide a unified framework for taking into account the gradual or flexible nature of variables, and representation of incomplete information [81]. This is an alternative to a classical approach and is based on the observations that humans think using linguistic terms such as “small” or “large” and others rather than numbers. The concept is described in a natural language; by Zadeh using fuzzy sets introduced by him self in 1965. The essence of fuzzy systems is conditional if-then rules, which use fuzzy sets as linguistic terms in antecedent and conclusion parts. A collection of these fuzzy if then rules can be determined from human experts or alternatively can be generated from observed data (examples). For this reason, NNs were incorporated into fuzzy systems, which can acquire knowledge automatically by learning algorithms of NNs. These systems are called Neuro-Fuzzy systems and have advantages over fuzzy systems, i.e., acquired knowledge is easy to understand. Like in NNs, knowledge is saved in connection weights, but can also be easily interpreted as fuzzy if then rules.

1.2.3 Definition of Fuzzy Neural Networks Fuzzy neural networks are connectionists models that are trained as neural networks, but their structure can be interpreted as a set of fuzzy rules.

1.2.4 Definition of Neuro-Fuzzy Inference systems Neuro-fuzzy inference systems consist of a set of rules and an inference method that are embodied or combined with a connectionist structure for a better adaptation, that is will be used in this work

1.2.5 Definition of Neuro-Fuzzy systems Neuro-Fuzzy systems are the systems that neural networks (NN) are incorporated in fuzzy systems, which can use knowledge automatically by learning algorithms of NNs, and can be viewed as a mixture of local experts (rules operate dominantly in each fuzzy region) and their parameters are updated using gradient and least squares optimization methods. The most frequently used NNs in Neuro-Fuzzy systems are radial basis function networks (RBFN) that is introduced by [22] and [57]. Their popularity is due to the simplicity of structure, well-established theoretical basis, and faster learning than in other types of NNs.


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1.2.6 Definition of Adaptive Neuro-Fuzzy Inference System (ANFIS):

ANFIS is one of the examples of Neuro Fuzzy systems in which a fuzzy system is implemented in the framework of adaptive networks, that first proposed by [47]. ANFIS constructs an input output mapping based both on human knowledge (in the form of fuzzy if then rules) and on generated input output data pairs by using a hybrid algorithm that is the combination of the gradient descent and least square estimates. ANFIS is not a black box model and works well with optimization techniques, which is computationally efficient and is also well suited to mathematical analysis. Therefore, it can be used in modeling and controlling studies, and also for estimation purposes.

1.2.7 Definition of Genetic Algorithm (GA) The genetic algorithm (GA) method is a global search technique based on an analogy with biology in which a group of solutions evolves through natural selection and survival of the fittest [38].

1.3 Review of Earlier Work on NN, Fuzzy, NF, and Genetic Algorithm: The literature survey on Neural Network (NN), Fuzzy Logic (FL) and Neuro-Fuzzy (NF) systems are given here, In the first section, studies on NNs, in the second section cases in which fuzzy systems were applied are presented. In the last two sections, studies on NF, and GA development and implementation are given .

1.3.1 Neural Networks Research

The formal realization that the brain in some way performs information processing tasks was first spelt out by [43]. They represented the activity of individual neurons using simple threshold logic elements, and showed how networks made out of many of these units interconnected could perform the logical operations. Rosenblat [83] developed the concept of perceptions, a generalization of the McCulloch and Pitts concept of the functioning of the brain, by adding learning [61]. These studies were the initiations of NNs. Ghaffari, K. et al [36] presented a comprehensive model of a fossil fueled power plant (FFPP) that proposed in order to evaluate the performance of a newly designed turbine follower controller. Considering the drawbacks of previous works, an overall model was developed to minimize the error between each subsystem model output and the experimental data obtained at the actual power plant.


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Station is the most commonly found valve problem in the process industry. Valve stiction may cause oscillations in control loops which increases variability in product quality, accelerates equipment wear and tear, or leads to system instability. Zabiri and Samyudia [105], they present a new approach in control valve in modeling using Recurrent Neural-Network with NARX structure. It was shown that the performance of the developed model was comparable to other models reported in literature.

Labview is a graphical programming language that has its roots in automation control and data acquisition, Fernandez, et al [34], they have utilized this platform to provide a powerful toolset for process identification and control of nonlinear systems based on artificial neural networks (ANN). This tool has been applied to the monitoring and control of a lab-scale distillation column DELTALAB DC-SP. The proposed control scheme offers high speed of response for changes in set points and null stationary error for dual composition control and shows robustness in presence of externally imposed disturbance. Czajkowski and Patan [21] proposed a paper to deal with the general information about using state space neural network models for purpose of the fault detection as an example of the boiler unit. The work presented deals with problems such as selecting proper threshold for compromising both fault sensitivity and early fault detection, designing proper neural network structure or calculating performance indices. All simulation data used in experiments are collected from simulator of the boiler unit implemented in Matlab/Simulink.

1.3.2 Fuzzy Systems Research As the complexity of a system increases, our ability to make precision and yet significant statements about the behavior diminishes until a threshold is reached beyond which precise and significance become almost mutually exclusive characteristics [106].

The concept of fuzziness was first proposed by Zadeh [106]. He aimed to describe complex and complicated systems using fuzzy approximation and introduced fuzzy sets. “Generally, fuzzy logic can be considered as a logical system that provide a model for modes of human reasoning that are approximations rather than exact”[85]. Fuzzy logic systems had found successful applications in wide variety of

fields such as: automatic control, pattern recognition, signal processing, expert systems, communication, system identification and time series prediction [22]. In chemical engineering systems, they have been generally used in control studies. Since Fuzzy Logic Control (FLC) does not require a


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model and the control is based on expertise human reasoning, they have been applied in many control schemes. Also, they are used extensively in modeling.

Kwang [55] presents an application of an online self-organizing fuzzy logic controller to a boiler-turbine system of fossil power plant. The control rules and the membership functions of the proposed fuzzy logic controller are generated automatically without using a plant model. A boiler-turbine system is described as a multi-input multi-output (MIMO) nonlinear system in this paper. Then, three single-loop fuzzy logic controllers are designed independently. Simulation shows robust results for various kinds of electric load demand changes and parameter variations of boiler-turbine system.

Hewaidy, et al. [43] introduced a multivariable fuzzy logic controller, to deal with multivariable control processes. Unlike, the decomposition of multivariable control rules, the proposed scheme integrates the input-output fuzzy variables in a relation that describes the interaction between variables of the physical system. Because of expertise’s limitation to generate fuzzy rule for complex multivariable controllers, Wang’s and Mendl’s method was employed to obtain the initial fuzzy rules of the proposed controller. Boiler is a non-linear, time varying multi-input multi-output (MIMO) system whose states generally vary with operating conditions. The proposed scheme was tested on a 160 MW oil-fired nonlinear drum boiler-turbine process. Simulation results showed that controlling the boiler-turbine processes best achieved using the proposed multivariable fuzzy controllers compared with multi-loop controllers. Hewaidy and Hamdi [42 ], introduced fuzzy controller named serial distributed multivariable (SDM) fuzzy controller for Boilers systems, where it is nonlinear, time varying, multi-input multi-output (MIMO) systems, whose states generally vary with operating conditions. The major problem in controlling such non-linear boilers with Shrink/Swell phenomena is that their drum water level dynamics include an integrator that results a critically stable behavior. Having the non-linearity, the Shrink/Swell phenomena, and the integration problems in boiler systems requires an effective multi-purposes controller. The proposed controller has three notable features, transparency, adaptability, and less dimensionality. Cengiz [20] proposed a fuzzy logic-based control technique to regulate the power and enthalpy outputs in a boiler of a 765 MW coal-fired thermal power plant was carried out. For comparison, a conventional proportional, integral and derivative (PID), a fuzzy logic (FL) and a fuzzy gain scheduled proportional and integral (FGPI) controllers have been applied to the power plant model. The simulation results show that the FGPI controller developed


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in this study performs better than the other controllers on the settling time and overshoot of power and enthalpy outputs. The proportional integral derivative (PID) controller is the most widely used control strategy in industry. The popularity of PID controllers can be attributed partly to their robust performance in a wide range of operating conditions and partly to their functional simplicity. Vaishnav and Khan [92] presented a paper for designing PID controller using Ziegler-Nichols (ZN) technique for higher order system. A Fuzzy logic controller using simple approach with smaller rule set was proposed. Simulation results were demonstrated. Performance analysis shows the effectiveness of the proposed Fuzzy logic controller as compared to the ZN tuned PID controller with fine tuned PID controller. Vikram, et al [95] proposed Adaptive Fuzzy Controller (AFC) to regulate the room temperature over a wide range. This fuzzy controller automatically detects the changes in the outside temperatures and correspondingly maintains the inside temperature to a grand value. The simulations are performed in MATLAB and are verified with standard system data.

1.3.3 Neuro Fuzzy System Research

In most fuzzy systems, fuzzy rules were obtained from the human expert. However, every expert does not want to share his knowledge and there is no standard method that exists to utilize expert knowledge. As a result, ANNs were incorporated into fuzzy systems to be able to acquire knowledge automatically by learning algorithms. The learning capability of the NNs was used for automatic fuzzy if then rules generation [22]. The connection of fuzzy systems with an ANN is called neuro-fuzzy, NF, systems. Like in NNs where knowledge is saved in connection weights, it is interpreted as fuzzy if then rules in NF systems. The most frequently used NN in NF systems is radial basis function neural network, RBFNN in which each node has radial basis function such as Gaussian and Ellipsoidal. Their popularity is due to the simplicity of structure, well-established theoretical basis and faster learning than in other types of NNs. Also, there are many developed fuzzy neural networks (FNN) as NF algorithms in literature. Adaptive network based fuzzy inference system, ANFIS, is one of them. It is type of RBFNN. Jang and Mizutani [48] proposed to use the ANFIS architecture to improve the performance of the fuzzy controllers. The performance of the fuzzy controller relies on two important factors: knowledge acquisition and the availability of human experts. For the first problem, Jang[49] proposed the ANFIS to solve the automatic elicitation of the knowledge in the form of


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fuzzy if then rules. For the second problem, that is how the fuzzy controller is constructed without using human experts, a learning method based on a special form of gradient descent (backpropagation) was used. The proposed architecture identified the near optimal membership functions and the other parameters of a controller rule base for achieving a desired input-output mapping. The backpropagation type gradient descent method was applied to propagate the error signals through different time stages to control the plant trajectory. The inverted pendulum system was employed to show the effectiveness and robustness of the proposed controller.

Faisel, et al [31] discussed the properties of the TSK/Mamdani approaches and neuro-fuzzy (NF) fault diagnosis within an application study of an electro-pneumatic valve actuator in a sugar factory. System shutdown, breakdown and even catastrophes involving human fatalities and material damage. Computational intelligence techniques are being investigated as extension of the traditional fault diagnosis methods.

Khosravi [53] developed a new method to model occurred faults in different parts of nonlinear systems. Using an Adaptive Neuro-Fuzzy Inference System (ANFIS) they build a model for faultless plant which is used in the procedure of fault modeling. The considered model for fault is again an ANFIS system and its parameters are adjusted in an indirect way using difference between actual output and output of plant model. Simulation results on a nonlinear system are shown in this paper and they clearly demonstrate the capability of the proposed method for fault modeling.

Denai [26] attempted in the proposed work to illustrate the utility and effectiveness of soft computing approaches in handling the modeling and control of complex systems. The present work will concentrate on the pioneering neuro-fuzzy system, Adaptive Neuro-Fuzzy Inference System (ANFIS). ANFIS is first used to model non-linear knee-joint dynamics from recorded clinical data. The established model is then used to predict the behavior of the underlying system and for the design and evaluation of various intelligent control strategies.

Mehrabian [66] presented a model based on the recurrent neurofuzzy networks and subtractive clustering for a superheating system of a 325MW steam power plant. The experimental data are obtained from a complete set of field experiments under various operating conditions. Nine neuro-fuzzy models are constructed and trained for seven subsystems of the superheating unit. Then, these nine fuzzy models are put together merging series and parallel units according to the real power plant subsystems, to obtain the global model of the superheating process. Comparing the time response of the nonlinear neuro-fuzzy model of a subsystem with the time response of its


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linear model based on the Least Square Error (LSE) method, indicates that the nonlinear neurofuzzy model is more accurate and reliable than the linear model in the sense that its response is closer to the response of the actual superheating system. Nguyen and Afzulpurkar [73] presented a comparative study using ANNs and co-active neuro-fuzzy inference system (CANFIS) in modeling a real, complicated multi-input–multi-output (MIMO) nonlinear temperature process of roller kiln used in ceramic tile manufacturing line. Using this study, we prove that CANFIS is better suited for modeling the temperature process in control phase. After that, a neural network (NN) controller has been developed to control the above mentioned temperature process due to a feedback control diagram. The designed controller performance is tested by a Visual C++ project and the resulting numerical data shows that this controller can work accurately and reliably when the roller kiln set-point temperature set changes.

Ahmed [4] presented an application of adaptive (ANFIS) control for switched reluctance motor (SRM) speed. The ANFIS has the advantages of expert knowledge of the fuzzy inference system and the learning capability of neural networks. An adaptive neuro-fuzzy controller of the motor speed is then designed and simulated. Digital simulation results show that the designed ANFIS speed controller realizes a good dynamic behaviour of the motor, a perfect speed tracking with no overshoot and a good rejection of impact loads disturbance.

The results of applying the adaptive neuro-fuzzy controller to a SRM give better performance and high robustness than those obtained by the application of a proportional integral (PI) controller. Ayyoub and Aghil [12] presented paper to focus on the application of ANFIS in the modeling of nonlinear behavior of the shape memory alloy actuators (SMA). Although SMA actuators have attracted much attention for applications in several areas such as miniature robots they have not been widely employed for motion control applications due to their nonlinear behaviors and control difficulties. Because of their ability in the nonlinear learning and adaptation, ANFIS architectures are suitable tools in modeling and control of nonlinear systems. The experimental test bed includes SMA wire, a force sensor, data acquisition system and a power amplifier. Results demonstrate the ability of ANFIS in modeling of shape memory alloy behavior and successful force control of the SMA wire. The early detection of faults (just beginning and still developing) can help avoid. There are four criteria required to indicate the student’s performance and efficiency level which are scores earned, time spent, number of attempts and


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help needed. A fuzzy rule base model that has been proposed in previous work is found to be insufficient in deciding all possible conditions. To deal with this problem, Norazah [74] focused on the Adaptive Neuro-Fuzzy Inference System (ANFIS) approach in determining the possible conditions in order to form a fuzzy rule based system of a student model. The backpropagation is utilized as the learning mechanism for the neural network to solve the incompleteness in the decision made by human experts. By training the neural network with 18 human decisions that are certain, the neural network has successfully derived other decisions to form a complete fuzzy rule base and able to adjust its parameter by learning mechanism. However, some of the decisions are found illogically.

Liquid tank systems play an important role in industrial application such as in food processing, beverage, dairy, filtration, effluent treatment, pharmaceutical industry, water purification system industrial chemical processing and spray coating. A typical situation is one that requires fluid to be supplied to a chemical reactor at a constant rate. An upper tank can be used for filtering the variations in the upstream supply flow. Many times the liquid will be processed by chemical or mixing treatment in the tanks, but always the level of the fluid in the tanks must be controlled. In order to achieve high performance, Nawi [72] proposed hybrid PI-NN hybrid GA-AIS to improve coupled tank Liquid Levels System. The performances of proposed method also compared with GA and Artificial Immune System (AIS) alone, it was shown that hybrid PI-NN hybrid GA-AIS have superior features. Omar [76] presented a simplified adaptive neuro-fuzzy inference system (ANFIS) controller to control nonlinear multi-input multi-output (MIMO) systems. This controller uses only few rules to provide the control actions, instead of the full combination of all possible rules. Consequently, the proposed controller possesses several advantages over the conventional ANFIS controller especially the reduction in execution time, and hence, it is more appropriate for real time control.

1.3.4 Genetic and Immune Genetic algorithm (IGA) During the last three decades there has been a growing interest in algorithms which rely on analogies to natural phenomena such as evolution, heredity, and immunity. The emergence of massively parallel computers made these algorithms of practical interest. The genetic algorithm (GA) belongs to one category of these best known algorithms, whose beginnings can be traced back to the early 1950s when several biologists used computers for simulations of biological systems [90]. However, the work done in the late 1960s and the early 1970s at the University of Michigan under the


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direction of John Holland led to GA as it is known today [67]. With the characteristics of easier application, greater robustness and better parallel processing than most classical methods of optimization, GA has been widely used for combinatorial optimization [102], [51], structural designing [50],and machine learning rule-based classifier systems [79] [109] and other engineering problems [8], [10], and [32]. The range of power system problems to which GAs have been applied is broad. Areas of application include most of power system analysis, planning and operation [93],[85], and [65]. It is well known that GA pertains to searching algorithms with an iteration of generation-and-test [3]. The conceptualisation of GA in current form is generally attributed to Holland. However, particularly in the last ten years, substantial research effort has been applied to the investigation and development of genetic algorithms. Goldberg gives an excellent introductory discussion on Ghaffari [37] as well as some more advanced topics. Genetic algorithm is a derivative-free and stochastic optimization method - [99]. Its orientation comes from ideas borrowed from natural selection as well as the evolutionary process. As a general purpose solution to demanding problems, it has the distinguishing feature of parallel search and global optimization. In addition, genetic algorithm needs less prior information about the problems to be solved than the conventional optimization schemes [46] and [91]. The ship routing problem (SRP) is a special variant of the classical vehicle routing problems (VRPs), which is different from the VRP with backhauls (VRPB). The VRPB and its variant have attracted the attention of researchers to develop exact and approximate procedures. Toth and Vigo [90] and Mingozzi [67] presented LP formulations for the VRPB and developed branch and bound algorithms. Yano [102] developed a set cover based exact algorithm for a practical VRPB application. It is well known that all VRPs belong to the class of NP-hard combinatorial optimization problems. Therefore it is impossible to find exact solutions of real-life problems with a reasonable computational effort. Thus most researches in the literature have concentrated on the development of approximate algorithms. All of these contributions to VRPBTW were under the assumption that all delivery must be made on each route before any pickup [50]. As to ship routing problem, Jin [51] presented a MIP formulation for container ship routing problem (CSRP) and proposed variable neighbor search and taboo search heuristic algorithms. Yano [102] proposed a new immune genetic algorithm for the large scale SRP. The backhaul and time window constraints are also considered. The


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immune GA is innovated based on the classic GA and it can improve the general search ability and fight the premature convergence effectively. Numerical experiments indicate the proposed method is effective and competitive in reducing both the total shipping cost and the needed ship numbers. An immune genetic based algorithm (IGA) for random test pattern generation was proposed by [13]. In the proposed algorithm, some of the main characteristics of the immune system were used to enhance the GA algorithm. As a result, a new random-based test pattern generation technique based on the immune genetic algorithm (IGA) was presented. Experimental results showed that the proposed algorithm improved the ability of global search, avoided dropping into the local optimal solutions and increased the speed of computation convergence with respect to previously proposed non-immune GA algorithms 1.4 Statement of the Problem Under Study Recent publications in the area of industrial non-linear systems study multiple outputs when being merely juxtaposed evidently these are a constraint which is not applicable for the majority of practical control schemes, besides a set of limitations, e.g. empirical tuning of their parameters when the operating conditions of the controlled process are changed. To achieve our goals, two proposed schemes to control the dynamical systems are introduced. The first one comprises a set of control loops each of which is a single-input single-output (SISO) ANFIS controller. The second one takes into consideration the interactions between the variables of the controlled process by developing (MV-ANFIS) control schemes. The thesis also proposes a cascade distributed multi-variable ANFIS (CD-MV-ANFIS) controller to overcome the dimensionality problem of complex model of fuzzy rules.

1.5 Contribution of the Thesis The general aim of this thesis is to design and applying of ANFIS controller. This thesis is concerned with modeling, simulation, and design of ANFIS controller's for non-linear system. The adaptive-neuro-fuzzy-inference-system (ANFIS) is presented in this thesis as a tool to handle imprecise and highly non-linear behaviors of drum- boiler systems, and greenhouse (GH) system outputs. The proposed ANFIS is shown to be effective to successfully handle the problem carried out from shrink/swell phenomena associated with changing of drum water level among changing of grid load, also avoids the change of pressure above admissible limit. Also the introduced controller proved its ability to control the (GH) system due to


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changes of climate temperature and humidity over a wide range of operation. This contribution was achieved as follows.

Development of multi-input multi-output modeling based on ANFIS systems:

The single-input single-output ANFIS is designed and tested by applying in the SISO linear and non-linear plant, then to test the soundness of the proposed system, modeling, a multi-input multi-output ANFIS is proposed for 3rd order drum boiler-turbine unit. The proposed SISO and MIMO ANFIS system is compared to modeling with a Multi-Layer Perception (MLP) neural network.

Development of multi-variable ANFIS controllers with immune genetic algorithm for drum-boiler-turbine-unit:

This thesis develops a MIMO ANFIS control scheme to consider the interactions between the control variables of the two processes be controlled. Constructing the rule base is the corner stone in developing such control scheme. The modeling method is employed to obtain the initial fuzzy rules of the proposed MIMO ANFIS controller.

By combining ANFIS with traditional soft computing techniques such as immune genetic algorithms, we build a powerful hybrid intelligent control system that can use the advantages that each technique offers. The process operating window is partitioned to take into account the process nonlinear characteristics, and tuning is carried out by an immune genetic algorithm at the points of interest in the partitions.

Development multi-variable ANFIS (MV-ANFIS) controller with immune genetic algorithm for a greenhouse system.

The control process is divided into two distinct control loops, one maintaining the temperature by adjusting the ventilation rate, and the other maintaining the humidity ratio by adjusting the water capacity of the fog system. Several types of conventional control structures are employed to control the greenhouse environments; however, their parameters should be tuned if the operating conditions are changed. An Immune Genetic Algorithm (IGA) is used to give adaptability to the fuzzy system to adapt to changing situations. In addition, it provides the system with an aid to show how much uncertainty is incorporated in the system. Simulation results showed that the simplified architecture is able to cope with the complexity of the plant and has the ability to handle measurement


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and modeling uncertainties. Best results were achieved using the proposed IGA-ANFIA controllers compared with the other conventional controller.

Development a Cascaded distributed ANFIS (CD-MV-ANFIS) control scheme with immune genetic algorithm for a non-linear system

A conventional ANFIS Controller previously depicted would consist of one ANFIS block with input vector, X and output vector Y. All inputs are involved in fuzzy rules of which comprising several AND-conditions. For large problems, however, the conventional approach to the development of ANFIS systems becomes impractical, since the number of rules increases exponentially with the number of inputs. This thesis extends a process modeling idea, by [35] to a process control. The former replaces the process be modeled by a set of sub-models, while the latter replaces the MIMO conventional controller by a set of sub controllers. Conventional MIMO ANFIS controller mentioned above have a set of limitations, e.g. empirical tuning of their parameters when the operating conditions of the process are controlled is changed. Besides a huge numbers of fuzzy rules that are required to cover a wide range of the operating conditions of the processes be controlled, since the number of rules increases exponentially with the number of inputs. The proposed scheme decomposes a complex controller with input vector, XRn into cascade distributed architecture of sub ANFIS models each of which has input vector XR2 that reduces the number of fuzzy rules drastically. The proposed controller has three notable features, transparency, adaptability, and less dimensionality. Developing the proposed controller based on that idea needs fewer rules than that required for the conventional MIMO control scheme. The proposed control scheme considers a promising scheme for controlling real time MIMO non-linear systems with ease. The performance of proposed controller compared with different earlier works.

1.6 Simulation results

The simulation contains the major inputs and outputs. Specialized learning algorithm for proposed controller is used for drum-boiler-systems to see the performance of the ANFIS as a controller. Therefore, ANFIS controller is designed and implemented in adaptive closed loop control scheme. The performance of the ANFIS controller is also compared with that of earlier work for the cases under study. In this work to show the effectiveness and ANFIS controller, it is applied on five different non-linear models. The first and second model is (third and seven order drum-boiler-turbine-unit) [16], the third to fourth is the (GH) system, [41], and nonlinear MIMO plants.


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The GA was employed to determine the input and output scaling factors for the proposed controller, instead of the widely used trial and error method. This controller uses only few rules to provide the control actions, instead of the full combination of all possible rules. Consequently, the proposed controller possesses several advantages over the conventional ANFIS controller especially the reduction in execution time, and hence, it is more appropriate for real time control. The results obtained from the controller based on the new proposed developed schemes using genetic algorithm (GA), artificial immune system (AIS) have been obtained for both (third and seven orders) of non-linear drum boiler turbine units. To support the usefulness of our work, the hybrid genetic algorithm (AIS-GA) which is a combination of both (AIS) and (GA) is used for comparing the results obtained from the proposed controller with those obtained by PID controller introduced in [72] for a greenhouse (GH) system. These results show that the performance of the proposed controller introduced in our work is faster 20 times more than those obtained by PID controller base on Integral absolute error (IAE). Meanwhile, in case of using Mean square error (MSE), Integral square error (ISE), and Integral time absolute error (ITAE).The results show that the responses obtained by proposed controller are improved by about 35 percent with respect to those obtained by the PID technique at the same conditions. Another comparison with the nonlinear MIMO plant model controlled by simplified (ANFIS) controller by [76]. Although the simplified (ANFIS) controller used zero order sugeno fuzzy models, the proposed cascaded ANFIS controller required less number of parameters; in terms of premise and consequent parameters. The number of tuned parameters in our controller is smaller than that given by above controller by 87 parameter; this is due to the minimizing of used rules. Comparing results of our controller shows the capability to track the set points without overshoot, while the overshoot reaches 25 percent using a simplified ANFIS controller. Finally, it is shown that the proposed controller has a great improvement on the output responses for all wide ranges of operations.

1.7 Organization of the Thesis

This thesis is organized in six chapters. In addition to the present chapter, the designation of Multivariable ANFIS (MV-ANFIS) and Cascaded Distributed Multivariable ANFIS CD-(MV-ANFIS) Controllers are detailed in chapters 2 and chapter 3. Controlling non-linear plants are explained in details in chapters 4 and chapter 5 using two proposed schemes. The Immune genetic algorithm (IGA) was used for tuning parameters of two schemes.


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Chapter 2: Multivariable ANFIS (MV-ANFIS) with Immune Genetic Algorithm: Proposed Approach 1 is discussed here.

Chapter 3: Cascaded Distributed Multivariable ANFIS CD-(MV-ANFIS) Controller with Immune Genetic Algorithm: Proposed Approach 2 is explained here. Chapter 4: Application of the two proposed schemes Multivariable ANFIS (MV-ANFIS) and Cascaded Distributed Multivariable ANFIS CD-(MV-ANFIS) for controlling (third and seven orders) drum-boiler-turbine units is discussed here. Immune Genetic algorithms are employed to enhance the performance of the proposed controllers. Comparing the performance of the proposed controllers for the drum boilers turbine units with different earlier works also presented.

Chapter 5: Application of the two proposed schemes Multivariable ANFIS (MV-ANFIS) and Cascaded Distributed Multivariable ANFIS CD-(MV-ANFIS) for controlling a greenhouse system (GH) is discussed here. Immune Genetic algorithms are employed to enhance the performance of the proposed controllers. Comparing the performance of the proposed controllers for the drum boilers turbine units with different earlier works also presented.

Chapter 6: Concludes the thesis by summarizing the contributions made and presenting suggestions for future work.

The thesis ends with a list of 109 references arranged in alphabetical order of the names of authors and with serial numbers in square brackets. If more than one reference happens to be for the same authors, this subset of references is arranged in chronological order: first published, first cited. Book titles, in particular, are written between single quotes.

Chapter 2 Multivariable ANFIS with Immune Genetic Algorithm:

Proposed Approach 1

In this chapter the neuro-fuzzy paradigm and ANFIS methodology are explained in section 2.3.The Network representation of the proposed MV-ANFIS and learning procedure of the adaptive component is detailed in section 2.4. The parameters tuning using the Immune Genetic Algorithm (IGA) are briefly described in section 2.5. The application of the introduced scheme for modeling and controlling simple examples of linear and non-linear plant are studied in last section 2.6 and section 2.7 respectively. 2.1 Introduction

ANFIS is a hybrid of two intelligent systems: Artificial Neural Networks (ANNs) and Fuzzy Inference Systems (FISs). ANNs map an input space to an output space through a collection of layered processing elements called neurons that are interconnected in parallel by synaptic junctions [88]. ANNs are developed by continuously passing real world system data from its input to the output layer. For each pass of data, signals propagate from the input to output layer to produce an output which is compared to the desired output. The difference between these values is then used to adjust the synaptic connections so that the ANN can mimic the system the data represents. This procedure gives ANNs the capability of looking for patterns in the information presented to it, thus providing it with the advantage of learning about systems. FISs are based on fuzzy logic (a continuous range of truth values from 0 to 1), IF-THEN fuzzy rules and fuzzy reasoning (which can be likened to human reasoning through linguistic variables such as small, medium, large). These features of FIS allow it to make inferences using the rules and known facts to derive reasonable decisions [10,11]. Thus the combination of ANNs and FISs to form ANFIS, integrates the benefits of the individual intelligent systems to form a superior technique that can optimally model and control the dynamics of difficult systems. Artificial Neural Networks (ANNs) and neuro-fuzzy systems (NFSs) have been widely used in modeling and control of many practical industrial processes. However, most of them have concentrated on single-output systems only. Our proposed MV-ANFIS sachem covered complicated multiple inputs multiple outputs non-linear (MIMO) industrial processes.

Chapter 2: Multivariable ANFIS (MV-ANFIS) with Immune Genetic Algorithm

١٧

2.2 Generic Structure of ANFIS The generic structure of an FIS consists of four main components. The knowledge base (KB) stores the available knowledge about the problem in the form of Fuzzy “IF-THEN” rules. The other three components compose the Fuzzy inference engine that puts into effect the inference process on the system inputs by means of the Fuzzy rules. The fuzzification interface establishes a mapping between crisp values in the input domain (U) and Fuzzy sets defined in the same universe of discourse. The defuzzification interface realizes the opposite operation by establishing a mapping between Fuzzy sets defined in the output domain (V) and crisp values defined in the same universe. Further details and analysis on each of the above four components of FIS are presented in [96]. Mamdani and Takagi-Sugeno-Kang (TSK)[63]and[88] proposed the fuzzy systems as examples of fuzzy inference systems. Mamdani fuzzy inference system was first used to control a steam engine and boiler combination by a set of linguistic rules obtained from human operators [63], with respect to the format of the procedural knowledge rules, fuzzy systems may be classified in two types: Mandani fuzzy systems [63], the knowledge rules are of the form: IF 1x is rx1 and and … and nx is r

nx

THEN ru is rU (2.1) where the xi, for i=1,2,…,n, are the system inputs, and r

ix are fuzzy sets, ur

is the rule output, ur is an output fuzzy set, and r=1,2,…,N, is the rule number index. Both, the antecedent and the consequent of the knowledge rules are fuzzy propositions. The dynamic behavior of an FIS is characterized by a set of linguistic description rules based on expert knowledge. This expert knowledge is explained in [44], since the antecedents and the consequent of the IF-THEN rules are associated with fuzzy concepts (linguistic terms), they are often called fuzzy conditional statements, Lee [56]. In TSK fuzzy systems, the antecedent of the knowledge rules is a fuzzy proposition, and the consequent is a crisp relation. For first order systems the rule output is calculated as a linear function of the inputs: IF 1x is rx1 and … and nx is r

nx

THEN ru = nrn

rr xcxcc 110 (2.2)


١٨

where ric are constants. Given input values x1, …, xn, the total output, u, of

the TSK fuzzy system[88] is a weighted average of the individual rule

outputs:

r

rr

rr

w

uwu (2.3)

n

ixr r

iw

1

(2.4)

where the weights rw are calculated as the product of the input membership values: The two rules TSK fuzzy system described in Figure (2.1).In retrospective, TSK fuzzy systems are a combination of fuzzy and non-fuzzy models. They integrate qualitative knowledge representation with precise quantitative data expressions. The major advantage of TSK fuzzy systems consists on being universal approximators. They allow the representation of complex nonlinear mappings with simpler linear relations. The knowledge rules set an approximation of a nonlinear input-output mapping, X1×X2×..... Xn → R, by a piecewise linear function. The rule antecedents define a decomposition of the input space into a set of overlapping partitions, and establish a switching function that selects, given the actual input values, the appropriate linear functions needed for approximation. Then, the approximated output value is produced by one or interpolated by the combination of two or more relations in the rule consequents, as defined by the inference mechanism of the TSK system. 2.3 Neuro-Fuzzy Paradigm There are several types of neural network such that, Adaptive Multi-Layer Perception (AMLP) networks adaptive network, radial basis function neural network (RBFNN), the learning vector quantization (LVQ) network, and the group-method of data handling network (GMDH) can be given the examples of feedforward networks, these types are summarized in [86] and[101]. The NFS approximates an n-dimensional, usually unknown, function that is partially defined by a set of input-output data. The NFS is a fuzzy system whose knowledge rules represent the relation among samples of the given data. The components of the NFS are determined using neural network learning algorithms applied to the given data. For the purpose of learning, the fuzzy system may be represented by a three-layer feedforward neural


١٩

network. The first layer represents the input variables, the middle layer represents the fuzzy rules, the third layer represents the output variables, and the connection weights are given specified with fuzzy sets. In general, the neural network representation vividly illustrates the parallel nature of fuzzy systems. The learning procedure is a data-driven process. The learning procedure operates on local information, and causes only local modifications in the underlying fuzzy system. The learning procedure takes into account the properties of the associated fuzzy system, thus constraining the possible modifications of the system’s parameters. Since the NFS is always a fuzzy system at any stage of the learning process, the learning procedure can be initialized specifying the components of a fuzzy system. Consequently, the NFS paradigm may be used to build a fuzzy system from data or to enhance an existing one by learning from examples. In order for an FIS to be mature and well established so that it can work appropriately in prediction mode, its initial structure and parameters (linear and non-linear) need to be tuned or adapted through a learning process using a sufficient input-output pattern of data. One of the most commonly used learning systems for adapting the linear and non-linear parameters of an FIS, particularly TS type, is the ANFIS. The proposed MV-ANFIS approach 1 and the main concepts and algorithms adopted during its learning process are described hereafter.

x y B1

A2 B2

w1

w2

Z1 =p1*x+q1*y+r1

Z =

Z2 =p2*x+q2*y+r2

A1

w1+w2

w1*Z1+w2*Z2

Figure (2.1) Takagi-Sugeno Fuzzy Inference System


٢٠

2.3.1 ANFIS Methodology

The ANFIS method allows the design of Sugeno-type fuzzy systems [88] with rules of the form: Rj: IF x1 is LXj

1 ^ x2 is LXj2 ^ ……^ xn is LXj

n

THEN nj

njjjj xcxcxccy 22110

(2.5)

where j=1,2,…,N is the rule number, the LXji , for i=1,2,…,n, are the linguistic terms (membership functions) of the input variables xi, in the antecedent of the j-th rule,and the c jk , for k=0,1,…,n, are the input weighting coefficients to calculate the output yj in the consequent of the j-th rule. Given arbitrary initial knowledge rules, the ANFIS method adjusts the membership functions, LXji, and the coefficients, c jk, in the consequent of all the rules. The output of each rule can be a linear combination of input variables plus a constant term or can be only a constant term. The final output is the weighted average of each rule’s output. To do so, the Sugeno-type fuzzy system is represented as a feedforward neural network, for which its components are refined through standard learning procedures to fit the input-output behavior of the fuzzy system 2.4 Network Representation of Proposed MV-ANFIS System

In the introduced MV-ANFIS method, a fuzzy system with n inputs and N rules is represented by a five-layer feedforward network structure with N neural processing units in layers L1, L2, L3, and L4, and 1 unit in L5. Layer L0 with n distribution units is not considered a neural processing layer. The architecture of the proposed MV-ANFIS is depicted in Figure (2.2). In gross terms, L1 constitutes an input fuzzification stage, then each row across L2, L3, and L4 evaluates a knowledge rule, and finally L5 computes the final output value. Neural units in L1 and L4 are adaptive; their parameters are learned during training. Neural units in L2, L3, and L5 are fixed; their parameters are not modified during training. The exact representation and operation of the network is as follows. Layer 1 (L1). Each node receives a single system input and fuzzifies its value, that is, calculates its degree of membership to the linguistic term (fuzzy set) represented by the neural unit. Each node defines a bell-shaped membership function for the associated linguistic term:

b

i

i

acx

x

2)(

1

1)( (2.6)


٢١

where xi is a system input variable, a, b, and c are the trainable parameters, and (.) is the membership value. Layer 2 (L2). Each neural unit in L2 is connected to those nodes in L1 that form the antecedent of the corresponding rule, thus the inputs to the nodes in L2 are degrees of membership. By multiplying all incoming values, each node calculates the degree of fulfillment, r , of the corresponding rule:

)(1 ir

n

ir x r = 1, 2, ….., N (2.7)

Layer 3 (L3). Each neural unit in L3 is connected to all units in L2. Each unit calculates a relative degree of fulfillment of the corresponding rule by

Figure (2.2) MV-ANFIS Architecture with n rules

x1

x2

x3

xn

X 2 X 3

X 1 X n

1

2

3

4

5

n-1

n

∑

yi

x1


٢٢

normalizing its degree of fulfillment with respect to the degrees of fulfillment of all the rules:

n

ir

rr

1

(2.8)

Layer 4 (L4). Each neural unit in L4 is connected to one unit in L3 and to all the system inputs. Each node calculates the consequent of the corresponding rule weighted by its relative degree of fulfillment:

nrn

rrrrrr xcxcxccyy 22110( (2.9)

where the, ric for i=0,1,2,…,n, are trainable parameters.

Layer 5 (L5). The only neural unit in L5 is connected to all units in L4. The node calculates the final output, y, of the fuzzy system by adding all the incoming weighted consequents:

N

iiyy

1

(2.10)

2.4.1 Learning Procedure of Adaptive Components As mentioned above, both the premise (non-linear) parameters of the input membership functions in the nodes of L1 and the coefficients in the knowledge rule consequents (linear) parameters in the neural units of L4,of the FIS should be tuned, utilizing the so-called learning process, to optimally represent the factual mathematical relationship between the input space and output space. Normally, as a first step, an approximate fuzzy model is initiated by the system and then improved through an iterative adaptive learning process. The training algorithm, namely ANFIS, was developed by [49]. Basically, ANFIS takes the initial fuzzy model and tunes it by means of a hybrid technique combining gradient descent back-propagation and mean least-squares optimization algorithms in [48] and [84] see Figure (2.3). At each epoch, an error measure, usually defined as the sum of the squared difference between actual and desired output, is reduced. Training stops when either the predefined epoch number or error rate is obtained. The gradient descent algorithm is mainly implemented to tune the non-linear premise parameters while the basic function of the mean least-squares is to optimize or adjust the linear consequent parameters The consequent parameters are estimated using a least square estimation (LSE) procedure. From (2.9) and (2.10) each input-output training pattern can be written as:


٢٣

Consequent parameters

Premise parameters

Updat

Forward pass

Backward pass

Forward pass Backward pass

MF parameter (nonlinear)

fixed

steepest descent

Coefficient parameter (linear)

least-squares

fixed

nrn

rrrN

rr xcxcxccy

221101

where n is number of the system inputs, and N number of rules. Expanding and using vectors:

TNn

NNnnnnnn ccccccxxxxy 1011

11011111 (2.12)

Figure (2.3) ANFIS learning using hybrid technique

RMSE

LMS

Gradient descent

m nq

(2.11)


٢٤

Considering all M input-output training patterns together:

(2.13) Through appropriate definitions, (2.12) can be written as: Y=XC (2.14) where Y is M×1, X is M×(n+1)N, and C is (n+1)N×1. Usually the problem in (2.13) to calculate the parameters C is over-determined; there is more patterns than parameters to calculate, M > (n+1)N, and there is no exact solution. Instead, a least squares estimate of C that minimizes the squared error ||XC-Y||2 is obtained:

(2.15) where 1)( XX T is the pseudo-inverse of X if )( XX T is nonsingular. The solution in (2.14) is computationally expensive due to the matrix inversion, or impossible if )( XX T is singular. To avoid these problems, a more efficient recursive procedure is used. Let T

ix be the ith row vector of matrix X and yi the ith element of vector Y. Then LSE solution for C can be computed recursively using the widely adopted method [40]:

iTi

Tiiiii CxyxCC 11111 (2.16)

(2.17) for i=0,1,2,…,M-1, then Clse=CM, where Ψ is called the covariance matrix.

nM

n

n

N

N

N

MN

N

N

N

N

N

nM

n

n

MM x

xx

x

xx

x

xx

x

xx

y

yy

2

1

1

12

11

2

1

1

1

1

1

12

11

1

1

1

1

1

1

2

1

Nn

N

N

n

c

cc

c

cc

1

0

1

11

10

XYXXC Tlse

1

11

111 1

ii

Ti

iTiii

ii xxxx


٢٥

The initial conditions are C0 = 0 and Ψ0 = γI, where I is a size (n+1)N identity matrix and γ is a large positive number.

The changes to the antecedent parameters are determined by backpropagation [48]. Let z be any of the, b, or c parameters of any membership functions μ, and E be the usual error measure given by the sum of squared difference between the target output, y*, and actual output, y. Then the change in z, Δz, for a single rule after a pattern has been propagated is given by:

zEz

(2.18)

where is an arbitrary learning rate factor. Successive application of the chain rule in (2.17) yields:

(2.19)

where the last factor depends on the membership function parameter being considered:

(2.20)

(2.21)

(2.22)

The learning process is carried out iteratively, with two phases per iteration. First, the input patterns are propagated keeping the antecedent parameters constant, then the optimal consequent parameters are estimated using the least square estimation procedure in (2.16) and (2.17). Second, the input patterns are propagated again while keeping the consequent parameters constant, then the antecedent parameters are modified by backpropagation using (2.19) through (2.22).

z

yyy

zyyy

zy

yEz

rrr

r

r

rrr

r

r

r

1

1

*

*

b

ii

acx

ax

a

22

122

b

ii a

cxxbb

b

i

i

i

acx

cxxb

c

222


٢٦

2.5 Parameter Tuning 2.5.1 Tuning by Genetic Algorithm (GA) Two operators, crossover and mutation, give each individual the chance of optimization and ensure the evolutionary tendency with the selection mechanism of survival of the fittest. GA also proves to be convergent under the condition of maintaining the best individual found over time after selection [3] and [38]. Because the two genetic operators make individuals change randomly and indirectly during the whole process, they do not only give the individuals the evolutionary chance but also cause certain degeneracy. In some cases, these degenerative phenomena are very obvious. On the other hand, there are many basic and obvious characteristics or knowledge in a pending problem. However the crossover and mutation operators in GA lack the capability of meeting an actual situation 2.5.2 The Artificial Immune System

There are two inter-related systems by which the body identifies foreign materials: the innate immune system and the adaptive immune system, explained in Figure (2.4) [38]. The innate immune system: this name comes from the fact that the human body is born with the ability to recognize certain microbes and immediately destroys them. The innate immune system can destroy many pathogens on first encounter. The innate immunity is based on a set of receptors known as pattern recognition receptors (PRRs). The adaptive immune system: uses somatically generated antigen receptors which are clonally distributed on the two types of lymphocytes: B cells and T cells. These antigen receptors are generated by random processes and, as a consequence, the general design of the adaptive immune response is based upon the colonel selection of lymphocytes expressing receptors with particular specificities according to the antigens nature [24] and [25]. 2.5.3 Pattern recognition in the immune system

Recognition in the immune system occurs at the molecular level and is based on shape complementarily between the binding site of the receptor and a portion of the antigen called an epitome [69]. While antibodies posses a single kind of receptor, antigens may have multiple epitomes, meaning that a single antigen can be recognized by different antibody molecules as described in Figure (2.4).


٢٧

2.5.4 Antigen and Antibody

The antigen (Ag) and antibody (Ab) representations will partially determine which distance measure shall be used to calculate their degree of interaction or complementary [13] Figure (2.5). The affinity between an antigen and an antibody is related to their distance that can be estimated via any distance measure between two strings (or vectors). If the coordinates of an antibody are given by <ab1, ab2, ..., abn> and the coordinates of an antigen are given by <ag1, ag2, ..., agn>, if antigens and antibodies are represented as sequences of symbols then we can use Hamming shape-space, Eq(2.23). When the distance D between two sequences is maximal, the molecules constitute a perfect complement of each other and their affinity is maximal.

L

iii

i otherwiseagabif

whereD1 ,0

,1 (2.23)

The shape-spaces that use real-valued coordinates can measure distance in the form of Eq (2.23) called Euclidean distance. The standard selection algorithm [24] can be summarized as follows. i. Randomly generate initial population of Ab ii. Determining the fitness of each Ab. iii. Select the antibodies, n, with best affinity.

Antibody 101101000

Antigen 010010111

Figure (2.4).antigen epitope is recognized by an antibody

Figure (2.5) The complement relation between the antigen and antibody


٢٨

iv. Generate selected sets of clones v. Mutate clonal set affinity maturation vi. Calculate affinity clonal set vii. Select memory cell candidate(s) viii. Replace lowest affinity, d, antibodies. ix. Repeating steps iii-vi until a pre-defined stopping condition is reached.

2.6 MV-ANFIS Controller for SISO Plant

Generated ANFIS controller structure is given in Figure (2.6). In the controller, total number of adjusted parameters is 39. Since each input is graded with three MFs and one of them consists of two parameters, twelve of adjusted parameters come from the premise part of the controller network. Consequent part of the controller consists of 27 parameters due to the nine rules with constant output. Controller parameters are adapted at each sampling instant. A code for simple backpropagation algorithm is written to update the parameters of the ANFIS controller in closed-loop system simulation. The description of the mathematical equations of proposed plant is as follows: Y=M1*(X) (2.24) X=M2*(Π*K/3) (2.25) where Y, and X are the output, and input of plant,M1 and M2 are the constant variables, and K is an iteration number. As mentioned in section (2.4), we consider here two inputs for MV-ANFIS, the error between the desired and the actual output (e) and its changes (Δe) and one control output (u) as depicted in Figure (2.6). The problem consists in finding the values of the parameters of the membership functions in the rule antecedents and the coefficients in the rule consequents of the TSK-type fuzzy systems, the knowledge rules of the fuzzy system have the form:

rr eLiseandLeiseIF : ececcuTHEN r

ere

ro

r : (2.26) where r=1,2,...,R is the rule number, rLe and reL are the linguistic terms of the input signals e and e ,respectively, in the r-th rule , ru is the contribution of the r-th rule to the total output of the fuzzy system, and

roc , r

ec , and r

ec are the consequent coefficients, the output of the fuzzy system is given by:


٢٩

R

r

r

rR

r

r

w

uwu

1

1 (2.27)

where wr, for r = 1,2,...,R, are the rule fulfillment weights. For each rule, its weight is calculated as the product of the input membership values as:

)().( eew rr eLLer

(2.28)

where (.)(.) rr eLLe and

are are the membership functions corresponding to the linguistic terms rr eLandLe respectively, in the r-th rule. In addition, note that (2.3) can be written as in [49]:

R

r

rR

r

rrrR

rR

r

r

r

uuwuw

wu111

1

(2.29)

∏

∑

∩

∩

∩

∩

∩

∩

∏

∏

∏

* * * * * * * * *

N

N

N

N

N

* * * * * * * * *

e ce

e

ce

e ce

e ce

e ce

e ce

Premise Prameters Consequent Parameters

y

Figure (2.6) ANFIS Architecture with nine rules

L L L L L L


٣٠

Where rw for r=1,2,…, R can be equivalently called the normalized rule

consequents:

R

r

r

rr

w

ww

1

(2.30)

In our case the complete knowledge base will have 3×3=9 rules of the form given in (2.5), also, the network will have 2 distribution units in layer L0, 6 neurons in L1, 9 neurons in L2, L3, and L4, and 1 neuron in L5. So the tuned parameters using different fuzzy sets are illustrated as follow: In case of using 3 fuzzy sets: 9 rules * 3 consequent parameters per rule=27 consequent parameters. 2 inputs * 3 membership function per input* 3 parameters per membership function=18 membership function parameters. Then, the total number of parameters to be determined is 27 + 18 = 45 per fuzzy system. In case of using 5 fuzzy sets : 25 rules * 3 consequent parameters per rule=75 consequent parameters. 2 inputs * 5 membership function per input* 3 parameters per membership function=30 membership function parameters. Then, the total number of parameters to be determined is 75 + 30 = 105 per fuzzy system. In case of using 5 fuzzy sets: 49 rules * 3 consequent parameters per rule=147 consequent parameters. 2 inputs * 7 membership function per input* 3 parameters per membership function=42 membership function parameters. Then, the total number of parameters to be determined is 147 + 42 = 189 per fuzzy system. This numbers clearly illustrate the difficulty of tuning a fuzzy system following a trial and error approach, which simply gets worse as the number of input linguistic terms increases. Fortunately, this process can be fully automated using the neuro-fuzzy paradigm and a low-dimension fuzzy system will perfectly do the job, as will be shortly shown. L1 fuzzifies the incoming input signal using bell-shaped membership functions using the form described bellows:


٣١

xxfi )(1 (2.31)

bi

i

i

iii

acx

xgfgy 2111

1

1)()(

(2.32)

where i=1, 2, …, 6 is the neuron number, e and e is the input signal, 1yi is the i-th neuron output, and ai, bi, and ci are the parameters of the bell-shaped output function. L2 calculate the rule fulfillment weight for each rule using the following input and output processing functions:

iiiii eeeef 11112 ,, (2.33)

21

11222

iiiiir xxfgyw (2.34)

where i=1, 2, …, 9 is the neuron number, 21

11

ii xandx are the inputs to

the i-th neuron, iy2 is the output of the i-th neuron, and rw is the rule

fulfillment weight of the r-thrule with r=i. L3 calculate the relative rule fulfillment weight for each rule through:

9

1

9

1

39

32

31

39

32

31

33 ,,,r

rj

ijiiiiiii wxxxxxxxf (2.35)

9

1

3

3333

rr

r

i

iiiiir

w

wfxfgyw (2.36)

where i=1,2,…,9 is the neuron number, ijx3 for j=1,2,…,9 are the inputs to

the i-th neuron coming from all the neuron outputs in L2, ijy3 is the output

of the i-th neuron, and rw is the (normalized) relative rule fulfillment weight of the r-th rule with r=i. L4 Calculate the normalized rule consequent for each rule through:

riii wxxf 444 (2.37)

)..(

)..(

,,

210

221104

21444

ececcwxcxccf

xxfgyu

or

orrr

or

orri

ooiiir

(2.38)


٣٢

where i=1,2,…,٩ is the neuron number, ix4 is the input to the i-th neuron,

iy4 is the output of the i-th neuron, and ru is the normalized rule

consequent of the r-th rule with r=i. L5 calculates the total system output:

9

19

52

51

59

52

51

55 ,,,r

riiiiiii uxxxxxxf (2.39)

9

1

555

rriii ufgyu (2.40)

where u is the total output of the FIS for system used in this description. 2.6.1 Simulation Results

Using the square wave as a reference for plant, with different constant variables M1 and M2 as depicted in Eq(2.24) and Eq(2.25), the simulations presented here are to evaluate the control system performance for various values of M1and M2 as well as the set point value se depicted in Table 2.1,also the RMSE values associated for different fuzzy set in each case presented in Table 2.1. The FIS knowledge base for the proposed controller using 3 fuzzy sets is as follows: R1: IF e1 is S and ( Δe) is S THEN f1=c1o+c11 e1+c12 Δe1 R2: IF e1 is S and ( Δe) is M THEN f1=c2o+c21 e1+c22 Δe1 R3: IF e1 is S and ( Δe) is B THEN f1=c3o+c31 e1+c32 Δe1 R4: IF e1 is M and ( Δe) is S THEN f1=c4o+c41 e1+c42 Δe1 R5: IF e1 is M and ( Δe) is M THEN f1=c5o+c51 e1+c52 Δe1 R6: IF e1 is M and ( Δe) is B THEN f1=c6o+c61 e1+c62 Δe1 R7: IF e1 is B and ( Δe) is S THEN f1=c7o+c71 e1+c72 Δe1 R8: IF e1 is B and ( Δe) is M THEN f1=c8o+c81 e1+c82 Δe1 R9: IF e1 is B and ( Δe) is B THEN f1=c9o+c91 e1+c92 Δe1 The detailed of proposed cases is as follows: Case1: In this case the set point changes ±0.9, M1 and M2 are 0.1 and 0.9 respectively, and we also show the response follow the changes of set point over all range as seen in Figure (2.7). The RMS value=.00453, 0.00450 and 0.00451 using 3 fuzzy sets, 5 fuzzy sets and 7 fuzzy sets respectively see Table 2.1. The initial and final FIS shown in Table 2.2 and Table 2.3, the comparison between initial and final coefficient of consequent parameters is seen in Figure (2.8).


٣٣


Cases M1 M2 RMS 3MF RMSMF RMS 7MF Set point changes

Case1 .1 .9 0.00453 0.00450 0.00451 ±.9

Case2 .5 .8 0.0102 0.0101 0.0101 ±1.8

Case3 4 .75 0.0456 0.0456 0.0455 ±5.9

It is obvious that the rule number 2, 5 and 8 only have the changes of coefficient between initial and final update. The final updated of FIS can be described as: R1: IF e1 is S and (Δe1) is S THEN f1=0.219649+0.301238 e1+0.587055 Δe1 R2: IF e1 is S and (Δe1) is M THEN f1=1.280275+-0.02789e1+0.668751 Δe1 …………………………………………………………… ……………………………………………………………. R8: IF e1 is B and (Δe1) is S THEN f1= -0.0901-0.19452 e1+0.784686 Δe1 R9: IFe1 is B and (Δe1) is M THEN f1=0.268936+0.556756 e1+0.135706 Δe1

Table 2.2 Initial FIS in case1 using 3 fuzzy set Rules e Δe C0 C1 C2

R1 S S 0.219649 0.301238 0.587055 R2 S M 0.902049 0.523746 0.668751 R3 S B 0.676881 0.952923 0.623936 R4 M S 0.4579 0.647764 0.978867 R5 M M 0.421449 0.975787 0.518607 R6 M B 0.542896 0.379125 0.84917 R7 B S 0.54558 0.81515 0.485749 R8 B M 0.116194 0.143432 0.784686 R9 B B 0.268936 0.556756 0.135706

Table 2.3 Final FIS in case1 using 3 fuzzy set

Rules e Δe C0 C1 C2 R1 S S 0.219649 0.301238 0.587055 R2 S M 1.280275 -0.02789 0.668751 R3 S B 0.676881 0.952923 0.623936 R4 M S 0.4579 0.647764 0.978867 R5 M M 0 0.988583 0.518607 R6 M B 0.542896 0.379125 0.84917 R7 B S 0.54558 0.81515 0.485749 R8 B M -0.09011 -0.19452 0.784686 R9 B B 0.268936 0.556756 0.135706


٣٤

Case2: In this case the set point changes ±1.8, M1 and M2 are 0.5 and .75 respectively, the results show that the actual output of the introduced controller much close to set point over depicted in Figure.(2.9). The RMSE value=.0102, 0.0101 and 0.0101 using 3 fuzzy sets, 5 fuzzy sets and 7 fuzzy sets respectively, as we see these vales nearly close to each other. The comparison between initial and final coefficient of consequent parameters is seen in Figure (2.10), as in case1 the rule number 2,5 and 8 also have the changes of coefficient between initial and final update. Case3: In this case the set point changes ±5.9, M1 and M2 are 4 and 0.8 respectively, the results show that the actual output of the proposed controller follow the changes of set point over all range as depicted in Figure (2.11). The RMS value=.00456, 0.0456 and 0.0455 for use of 3 fuzzy sets, 5 fuzzy sets and 7 fuzzy sets respectively, as we see these vales nearly close to each others. The comparison between initial and final coefficient of consequent parameters is seen in Figure (2.12), also as in case1and case2 the rule number 2,5 and 8 also have the changes of coefficient between initial and final update.

Figure (2.7) Case1: The simulation result of the proposed controller with change of set point ±.9


Iteration

Coefficient Initial FIS

final FIS


٣٥

Figure (2.11) Case3 :The simulation result of the proposed controller with change of set point ±1.8

Figure (2.12) Case3:Initial and final coefficient of consequent parameters

Initial FIS final FIS

Figure (2.9) Case2: The simulation result of the proposed controller with change of set point ±1.8

Figure (2.10) Case2:Initial and final coefficient of consequent parameters

with 3 fuzzy sets



٣٦

2.7 Modeling linear and Nonlinear Plants

Number and type of membership functions, number of rules. These two structural parameters are mutually related (for more membership functions more rules must be defined) and determine the level of detail, called the granularity, of the model. The purpose of modeling and the amount of available information (knowledge and data) will determine this choice. Automated, methods can be used to add or remove membership functions and rules. A MATLAB code was used to train the ANFIS structure in the training step. The steps in ANFIS for modeling design in this study are as follows: 1. Generated training data is loaded. 2. Design parameters, number of input MF, type of input and output MF, are chosen. Thus, initial ANFIS structure is formed. 3. The code for the training is run with the initial structure. 4. ANFIS structure constituted after training is saved to use as modeling. ANFIS uses backpropagation learning to determine premise parameters and least mean squares estimation to determine the consequent parameters. This is referred to as hybrid learning. A step in the learning procedure has got two passes: in the first or forward pass, the input patterns are propagated, and the optimal consequent parameters are estimated by an iterative least mean square procedure, while the premise parameters are assumed to be fixed for the current cycle through the training set. The overall output can be expressed as a linear combination of the consequent parameters. The proposed MV-ANFIS network was conducted on two test plants, one linear and the other non-linear. Three modeling tasks were employed in [61] to evaluate the performance of the ANFIS and AMLP network. They are described below.

2.7.1 Modeling Task 1

One sequence of 500 points, constituting a sinusoidal signal was applied to the test plants and the corresponding outputs recorded. This provided a training data file of 500 points. The magnitudes of the input signals were normalised in the range 0-1. In this task, the pattern employed to generate the training input-output points for the ANFIS and AMLP network [61] is defined as follows:

500k0 ,250

k 2πsinu(k)

(2.41) Eq. (2.41) also used as the test pattern in this modeling task.


٣٧

2.7.2 Modeling Task 2

The training input-output pattern employed in the last modeling task was used for training the test processes. A superposition of two sinusoidal signals as defined in Eq. (2.41) was used as the test pattern in this modeling task. That is:

500k0 ,250

k 2πsin0.2250

k 2πsin0.8u(k)2

(2.42)

2.7.3 Modeling Task 3 In this task, two sequences of 500 and 300 points respectively, one forming a sinusoidal signal and the other a superposition of two sinusoidal signals, were applied to the test processes and the corresponding outputs recorded. This provided a training data file of 800 points. The input was normalised in the range 0-1.The input signal employed to generate the training points for the

ANFIS and AMLP network is defined as: , 500k0 ,250

k 2πsinu(k)

800k500 ,250

k 2πsin0.2250

k 2πsin0.8u 2

k

(2.43)

The first sequence defined in Eq.(2.42) was employed to test the two networks in this modeling task.

2.7.4 ANFIS Partitioning In simulations described below the input and the output universes of discourse of the ANFIS are partitioned in three ways, one with 3 fuzzy sets, second with 5 fuzzy sets and the third with 7 fuzzy sets, all set described with bell-shaped membership functions that are defined by

2

j

jc)(xj σ

cxexp,a

(2.44)

ly.respectivefunction theof (or width) varianceandmean)(or centre theareσ and c andinput theis x function, activationan is (.)a where jjj

The input and output vectors were

T2)y(k 1)y(k y(k) 1)u(k u(k)x and T1)y(ky respectively. Wang’s and Mendel’s method was employed to generate the fuzzy rule base [97].


٣٨

2.7.4.1 MV-ANFIS Network in Modeling

Although the ANFIS network is aimed at complex processes, it was first tested using a simple third-order linear system, to demonstrate its soundness. The discrete time difference equation of the system is, Narendra,.K and Parthasarathy,k. 1990[70]:

2)(k*1)(k*(k)**1)(k*(k)**1)(k y0.183y0.9y0.70.3u0.82u0.50.25y (2.45) The outputs of the ANFIS and the process are depicted in Figure (2.13). The RMS error as defined in Eq.(2.45) was computed for the trained network using the test data. Table 2.4 shows the RMS error obtained for above linear system with different fuzzy sets, and premise parameters.

T

1k

2Y[k])-(Yd[k]T1errorRMS (2.46)

period. test theduring samples ofnumber theis T and outputs actual theand desired theare ly,respective Y[k] and Yd[k] where

The proposed MV-ANFIS was tested using three modeling tasks by 3,5, and 7 membership function. In case of using 3 fuzzy sets, the network constructed by 16 node, 6 premise parameters, and 6 consequent parameters, so the total number of tuned parameter=12. Table 2.4 show details of constructed network for 3,5, and 7 fuzzy sets, the RMS values using 3 fuzzy sets are 108.35 * 10-6 ,8.41*10-7 and 8.00*10-5 associated for each task respectively. Comparing this values to that given by 5 and 7 fuzzy sets shown that they may be accepted as depicted in Table 2.4. The response of modeling linear dynamic system using 7 fuzzy sets depicted in Figure (2.13)(a) as we see the results near close to the actual output of plant task(1), where the out shown as sine wave from sample number 0 to 500, while it steady at constant value after 500 sample up to 800 sample. This can be explain the changing of MSE from 0 to .5*10-4 and finally steady at 0 after sample number 500. The MSE for modeling task1 fluctuated between 0 to 2*10-4 and also steady at 0 after sample number 500 as obvious in Figure (2.13) (b). The MSE for modeling task3 from sample 0 to 500 changed between 0 to .25*10-4, and fluctuated between 0 to 1* 10-4 after sample number 500 respect to the shape of output as shown in Figure (2.13)(a),(b).In general despite modeling structure using 3 fuzzy sets have minimum number of node it given good results, beside the MSES are too small. Second, the ANFIS network was tested using a non-linear plant, to confirm the initial confidence in it. The plant's discrete time difference equation is, Narendra,.K and Parthasarathy,k. 1990[70]:

2)(k

21)(k

2(k)1)(k*1)(k*2)(k*1)(k*(k)

1)(kyy1

u1yuyyyy

(2.47)


٣٩

The responses of the network for the non-linear plant using the three modeling tasks described above are shown in Figure (2.14), also as case of linear plant the proposed ANFIS was tested using three modeling tasks by 3,5, and 7 membership function. In case of using 3 fuzzy sets, the construction of network is the same as in previous we show from Table 2.5,for instance the MSES using 5 fuzzy set is 20 time less than that from using 3 fuzzy set ,and half time the MSES for 7 fuzzy set.

Table 2.4 RMS errors in modeling linear dynamic system using ANFIS with different fuzzy sets membership

No of nodes

training data pairs

premise

Total RMSE1 e-6

RMSE2 e-7

RMSE3 e-5

3 16 799 6 12 ٨.٠٠٥٥ ٨.٤١٤٥ ١٠٨.٣٥٠٠

5 ٢٤ 799 10 20 18.567 ٨.٠٠٩٨ ١.٨٨٣٨

7 ٣٢ 799 14 28 .00٧.٨٦٦٥ ١.٣٢٣٩ ٥٠٧٥

Mod

elin

g ta

sk 2

M

odel

ing

task

3

Mod

elin

g ta

sk 1

Figure (2.1٣) (a) Modeling of the linear dynamic system using the MV-ANFIS with 7 fuzzy sets (b) Mean squares errors corresponding to each model

(a) (b)


٤٠

The RMS error obtained for above non-linear system with different fuzzy sets and number of rules generated that approximate the non-linear system is depicted in Table.2.5. We can see from Table 2.5, the all RMSE values are in acceptable range , where it is multiplied by e-8 , e-9 , and e-4 for 3,5 and 7 fuzzy respectively, also as in linear plant the RMSE is nearly the same for various fuzzy specially in modeling task 3 as depicted in Table 2.5.

Mod

elin

g ta

sk 2

Mod

elin

g ta

sk 3

Mod

elin

g ta

sk 1

Figure (2.١٤) (a) modeling of the Non-linear dynamic system using the ANFIS with 7 fuzzy sets

(b) Mean squares errors corresponding to each model

(a) (b) K(samples) K(samples)

Table 2.5 RMS errors in modeling Non-linear dynamic system using ANFIS with different fuzzy sets members

hip No of nodes

training data pairs

Premise parameters

Total RMSE1 e-8

RMSE2 e-9

RMSE3 e-4

3 16 799 6 12 ٣.٨٨٩١ ٩٨.٨٨٤ ١٣٠.١٠ 5 ٢٤ 799 10 20 .٩.٧٦٥٧ ٤.٦٦٧٠ ٠٤١٣٥٦ 7 ٣٢ 799 14 28 .٥.٦٧٧٨ ٩.٨٤١٣ ١٧٤٢٦

MSE

MSE

MSE


٤١

The average RMSE computed for the trained ANFIS network with different fuzzy sets using the test data for linear and Non-linear dynamic system is shown in Table. 2.6. The initial and final membership functions of Non-linear dynamic system using the ANFIS with 3 fuzzy sets for all modeling takes are depicted in Figure (2.15). Table 2.6 Average RMS error for different fuzzy sets in modeling Non-

linear dynamic system using ANFIS.

Processes Modeling task 1 Modeling task 2 Modeling task 3

Linear 36.11667e-6

3.432767e-7

5.33843e-5

Non-linear 43.43854e-8

37.79743e-9 6.4442e-4

Mod

elin

g ta

sk 2

Mod

elin

g ta

sk 3

Mod

elin

g ta

sk 1

(a) (b)

Figure (2.١٥)Membership function of Non-linear dynamic system using the ANFIS with 3 fuzzy sets for all modeling takes (a) Initial membership function (b) final membership


٤٢

2.7.4.2 Discussion of ANFIS and AMLPs Networks

This section analyses and compares the ANFIS and AMLPs networks [61] from the point of view of, generality and stability based on the three modeling tasks described in subsection 2.7.4.1. This comparison was conducted using two test plants, one linear and the other non-linear. The networks were tested under the same conditions, such training epochs, number of tested data as described before. Table 2.7, Table 2.8, and Table 2.9, show the RMS errors obtained with the networks. The percentage reduction in RMS errors, also given in the tables, is calculated using Equation (2.48).

AMLP of RMS

ANFIS of RMS - AMLP of RMSReduction %

(2.48) Table.(2.7) shows that both the ANFIS and AMLPs networks are approximately the same from the identifiable point of view in linear process while the ANFIS give better performance than the AMLPs in case of non-linear process. Substantial differences can be noted in the stability of the two networks, with the ANFIS network showing a much better performance than the AMLPs network because the former can create new Prototypes for new input patterns while the latter cannot specially in case of nonlinear process as depicted in Table. 2.8. However, the generality of the networks is different as can be seen in Table.2.9. The modeling using AMLPs network is relatively poor. Nevertheless, for control purposes the accuracy achieved by the NN forward model is sufficient. Also from all previous results of the proposed ANFIS model, it is seen that the responses are correlated very well with the target model. This model very well capable for controller design and evaluation. Note that this modeling can be applied to any plant for which a mathematical model is not available.

Table 2.7 Comparison between ANFIS and AMLPs networks(Modeling task 1) RMS error

Process-type AMLPs ANFIS % Reduction

Linear 4.00E-05 3.61E-05 9.7342 Non-linear 9.2506e-7 43.43854e-8 53.042


٤٣


RMS error Process-type AMLPs ANFIS % Reduction

Linear 1.07e-5

3.43e-7

96.802

Non-linear 2.458e-6 37.79743e-9

98.462

Table 2.9 Comparison between ANFIS and AMLPs networks (Modeling task 3)

RMS error

Process-type AMLPs ANFIS % Reduction

Linear 8.0325e-5 5.33843e-5 33.539 Non-linear 0.0013 6.4442e-4 50.429

2.8 Case study: Multi-input Multi-output Modeling of Drum Boiler

The boiler model employed in this section is the Bell-Astrom boiler-turbine alternator model [18]. The process is third order non-linear dynamical model that has non-linear equations utilized in the predictions of three outputs, drum pressure (y1) Bar, output power (y2) MW (and drum water level (D/L)) (y3) mm. These outputs being functions of three inputs, fuel flow (u1), control valve position (u2) and feed water flow (u3). The simulation contains the major inputs and outputs which are needed for the overall plant control. The model parameters have been estimated from a 160 MW oil-fired unit on the Swedish grid system, and may represents the power station at west Delta Company for electricity production on Damnhour-Egypt. The complete model with all numerical values being adapted to the swedish unit on which the equations were developed is given in details in section 4.2 chapter 4.The direct static model direct and inverse static model for drum boiler unit is presented in appendix A.


٤٤

2.8.1 Modeling using Multivariable ANFIS (MV-ANFIS) MV-ANFIS is a generalized ANFIS. MV-ANFIS combines some single-output ANFIS models to produce a multiple-output model with nonlinear fuzzy rules which is an advantage of MV-ANFIS model. Constructing and simulating neuro-fuzzy models from the collected data patterns was customized and carried out in [28]. All developed MV-ANFIS models used the generalized bell membership function (MF) with three MFs per input and TSK fuzzy model proposed by Takagi, Sugeno and Kang for fuzzy part in these hybrid systems. There are many ways to form a MV-ANFIS from ANFIS [46] and [48] and one of them is illustrated in Figure (2.16). This diagram is used to maintain the same antecedents of fuzzy rules among multiple ANFIS models. It means that fuzzy rules are constructed with shared membership values to express possible correlations between outputs in this diagram. Simulation results of the developed model with 3 inputs and 3 outputs under different numbers of membership functions for fuzzy part are shown in Figure.(2.17).The 90 samples of data used to test the output response of the

O1

O2 W1C12

W2C21

W1C11

W1+ W 2

W1+ W 2

W1

x

y

A1

A2

B1

B2

∏

∏

∑

∑

∑

∑

/

/

x, y : inputs ; O1, O2 : outputs MFs: Membership functions for fuzzy variable

W2

MFs

Figure (2.16).Two-output MV-ANFIS architecture with two rules per output.

x y

W2C22

x y


٤٥

proposed model, these samples include all possible values of pressure changed between minimum value(108 Bar ) to maximum value(140 Bar) Figure (2.17) shows the response of pressure using 5 and 7 fuzzy set much close to each other and correlated, rather the response of 3 fuzzy set. Also as depicted in Figure (2.17) (b),(c) the response of the introduced MV-ANFIS model for power and density using 5 and 7 fuzzy set is more close to actual output , and give a better performance..

The initial and final membership function of three inputs, fuel flow (u1), control valve position (u2) and feed water flow (u3) for the introduced MV-ANFIS model are given in Figure (2.18).We show how the ANFIS able to updating there premise parameters by the backpropagation method.

Figure (2.17) Response between actual and desired output values in developed MV-ANFIS model with 3,5, and 7 member ship function (a) pressure (b)power (c)density

(d)d

ensi

ty(K

g/cm

3 )

(b) p

ower

y2(

Mw

)

(a) p

ress

ure(

Bar

)


٤٦

Figure.(2.18) membership function using ANFIS with 3 fuzzy sets . (a) Initial membership function (b) final membership

(a)f

uel f

low

ra

te (u

1)

(c

)fee

d w

ater

flo

w (u

3)

(b)c

ontro

l val

ve

posi

tion

(u2)

(a)f

uel f

low

ra

te (u

1)

(c

)fee

d w

ater

flo

w (u

3)

(b)c

ontro

l val

ve

posi

tion

(u2)

(a) Initial membership function

B2


٤٧

2.8.2 Comparison of NN and MV-ANFIS models.

The RMSE between the inputs and outputs is measured for the NN model and the proposed MV-ANFIS model. As shown in Figure (2.19), the RMSE in MV-ANFIS model is less than NN model for the Power, Pressure, Density, and Drum water level. This concludes that modeling MIMO process using MV-ANFIS is more accurate in describing the physical behavior of the studied system.

Figure (2.19) Root mean square error value in case of MV-ANFIS & NN

modeling


٤٨

2.9 Summary In this chapter we introduced a MV-ANFIS controller tuned by Immune genetic algorithm (IGA) to maintain the natural interactions between input and output process variables on the complicated industrial processes. The ANFIS methodology, Network representation of the proposed MV-ANFIS, and learning procedure of adaptive component also detailed. The proposed controller includes the designing of (FF) and (FB), where the (FF) controller deals with all inputs of system as MIMO using Takagi-Sugeno (TS) fuzzy system of first order. The (FB) controller deals with the control signals using the MISO Takagi-Sugeno (TS) fuzzy system tuned Immune genetic algorithm (IGA). The premise and consequent parameters was tuned by LSE and gradient descent respectively. The application of the introduced scheme for controlling simple examples is presented. The modeling of linear and non-linear plant are studied and discussed with MV-ANFIS and AMLP network. Finally a Case study for Multi-input Multi-output Modeling of drum boiler turbine unit also simulated using the proposed MV-ANFIS scheme.

Chapter 3 Cascaded Distributed Multivariable ANFIS (CD-MV-

ANFIS) with Immune Genetic Algorithm: Proposed Approach 2

As mentioned in chapter 2 the multi-variable ANFIS (MV-ANFIS) controller may suffer from a memory problem that results from huge fuzzy number of fuzzy rules generated. In that scheme, all inputs are involved in fuzzy rules of which comprising several AND-conditions. Much efforts have been conducted to generate a strong knowledge base by using training a process from examples as described in chapter 2 for large problems, however, this conventional multi-variable ANFIS system becomes impractical. This is because the number of fuzzy rules increases exponentially with the number of input variable. For example, if a process has 6 inputs and three outputs variables and each input was described by 3 membership functions, the knowledge base would potentially need to hold 36 or 729 rules. In this chapter we introduce the Distributed Multi-variable ANFIS Controller (CD-MV-ANFIS) scheme, which dividing the conventional controller into sub models. This controller maintains the strong coupling between each input variables, besides their parameters are tuned by an immune genetic algorithm. The structure of Feed forward (CD-MV-ANFIS) controller is depicted in Section 3.1.The Immune Genetic Algorithm (IGA) is depicted in Section 3.2. The learning methods for designing ANFIS is explained in section 3.3.The application of the proposed scheme on simple examples is studied in section 3.4. 3.1 Design of (CD-MV-ANFIS) controller This chapter extends a process modeling idea [35] to a process control. The former replaces the process be modeled by a set of sub-models, while, the latter replaces the MIMO conventional MV-ANFIS scheme described in chapter 2 by a set of sub MISO ANFIS scheme. The introduced neural network of feedforward fuzzy controllers is depicted in Figure (3.1). The cascaded distributed process described in Figure (3.2),that consists sub controllers each of which is a MISO controller connected in distributed form, Dividing conventional controller into sub models reduces the fuzzy rules drastically. The following equation is resulted from using the proposed (CD-MV-ANFIS) scheme.

Chapter 3: Cscaded Distibeted Multivariable ANFIS with Immune Genetic lgorithm (IGA)

٥٠

Figure.(3.1) ANFIS Architecture for n inputs

X11

X12

∏

∑

∩

∩

∩

∩

∩

∩

∏

∏

∏

* * * * * *

N

N

N

N

N

* * * * * *

X1 X2

X1

X2

X1 X2

X1 X2

X1 X2

X1 X2

∏

∑

∩

∩

∩

∩

∩

∩

∏

∏

∏

* * * * * *

N

N

N

N

N

* * * * * *

X11 X2

X11

X3

X11 X2

X11 X2

X11 X2

X11 X2

Premis Consequent Parameters

X1n

∏

∑

∩

∩

∩

∩

∩

∩

∏

∏

∏

* * * * * *

N

N

N

N

N

* * * * * *

X1(n-1) Xn

X1n-1

Xn

X1(n-1) Xn

X1(n-1) Xn

X1(n-1) Xn

X1(n-1) Xn


٥١

The number of fuzzy rules =

mod

1model

i , model= mn (3.1)

Where mod is the number of models used, m is the number of fuzzy sets, and n is the number of system inputs. For example mod=5, m=3, n=2. The number of fuzzy rules =32+32+32+32+32 = 45 rules instead of 729. The cascaded distributed process described in Figure (3.2), is employed in this work to implement the following conventional controller. R: IF X1 is ….. AND X2 is ….. AND e2 is ….. AND Δe2 is ….. AND e3 is ….. AND Δe3 is ….. THEN Δu1 is…. AND Δu2 is….. The proposed control scheme remodels this conventional fuzzy rule as describe in Figure (3.2) as follows:

Figure (3.2). A(CD-MVANFIS) controller

FLM1

FLM3

FLM2

x12

x13

x14

FLM4

FLM5

X1

X2

FLM n ANFIS-Mn

X3

X4

X5

X6

Xn-1

Xn

ANFIS-M1

ANFIS-M2

ANFIS-M3

u1(k)

u2(k)

u2(k)

un(k)


٥٢

IF X1 is Ai AND X2 is Bj THEN X12 is C1k

R2: IF X11 is Ai AND X3 is Bj THEN X13 is C2k

R3: IF X13 is Ai AND x4 is Bj THEN X14 is C3k



Rn: IF X1n-1 is Ai AND Xn is Bj THEN X1n is Cnk

where, Ai , Bj ,and Ck are fuzzy sets and i, j, k=1, 2,3,….n

The rule base is generated by expertise, and is revised based on the

performance of the process be controlled [14] and [59]. The scaling factors of

each sub-model developed are also adapted using immune genetic algorithm

as described later in section 3.2 to improve the final outcomes of the process.

The developed scheme has a set of sub-models, through which the

information is distributed. Each sub-model deals with a unique portion of the

input space, and addresses a specific aspect of the model. The developed

scheme consists of n fuzzy controller distributed as follows:

FLM1, FLM2 , FLM3, FLM4, and FLM5 and ….. FLMn are connected in

series to contribute the output of fuzzy system as depicted in Figure (3.2).

The X11, X12, X14,…….and X1n-1 are internal states., and X1,X2,X3,X4,……. and

Xn are the input states.

The FLMn is feedforward the other n ANFIS module (ANFIS-M1, ANFIS-

M2, ANFIS-M3,…….ANFIS-Mn) each of which represents the MISO

ANFIS with two inputs in each module as depicted in Figure(3.3) [88].


٥٣

3.1.1 Feedback fuzzy controller

The three fuzzy sets used for all n fuzzy variables are defined by the membership functions shown in Figure (3.4). The feedback controller merged to the overall controller as depicted in Figure (3.5). Consider a Mamdani PI-type discrete-time fuzzy controller [63], the inputs of the feed back fuzzy controller defined as:

)()()( kykyke d (٣.2) )()1()( kekekce (٣.3)

where yd and y denote the applied set point and the plant output of the discrete-time system, respectively. The fuzzy variables for the inputs are e and ce and output variable is u, so in this case we have two variables for each three inputs to the controller as follows:

A2 B1 B2

x

y

A1

∏

∏ N

N

Σ

Layer 1 Layer 2 Layer 3

Layer 4

Layer 5 W1

w2

f1

f2 x, y : inputs

f: output

x y

X (b)

f = w1+w2 w1*f1+w2*f2

A1 B1

A2 B2

w1

w2

f1 =p1 x+q1 y+r1

x y (a) f2 =p2 x+q2 y+r2

Figure (3.3).(a) A two-input first-order sugeno fuzzy model with two rules; ( b) equivalent ANFIS architecture


٥٤

The error X1( k) = yd1( k) - y1( k) and ΔX1( k)== X1( k) – X1( k-1), and X12(k) is inner control signal (1). The error X3( k) = yd2( k) – y2( k) and ΔX3( k)== X3( k) – X3( k-1), and X13(k) is inner control signal (2). The error Xn-1( k) = ydn-1( k) – yn-1( k) and ΔX-1n( k)== Xn-1( k) – Xn-1( k-1), and X1n-

1(k) is inner control signal (n-1). The error Xn( k) = ydn( k) – yn( k) and ΔXn( k)== Xn( k) – Xn( k-1), and X1n(k) is outer control signal (n). The membership functions in Figure (3.4) are constructed intuitively. Furthermore, the tuning of the scaling factors is usually done without using a formula [62] and [76]. 3.1.2 Fuzzy Control Rules

What follows is a Mamdani PI-type fuzzy control rule. Example a PI-controller is described by: Δu(t) = kP[ce(t) + 1/Ti e(t) ] (3.4) where e(t), ce(t), u(t), and Δu(t) are the error between the desired and actual outputs, its changes, the control signal, and its changes. The kp, and Ti are constants. The fuzzy sets for e(t), ce(t), and Δu(t) are commonly used as described in Figure (3.4).For simplicity, The rules can be described as follows: IF e1 is N and ce1 is Z THEN Δu is P (3.5)

-0.20

0.20.40.60.8

11.2

-3 -2 -1 0 1 2 3

Z N P

Figure (3.4) Applied membership function


٥٥

+ ufb

FB

Feedforwrd controller

Referenc governer

Fossil-fuel Power unit

Immune Genetic

algorithm tuning

Fuzzy PI controller

u uff +

Unit load demand

yd

+ -

y

Knowledge base Output

Membership Function

Rules

Input Membership

Function

ufb Rate of error

Defuzzification Interface

Decision making logic

Fuzzification Interface

Error

e

e.

Fuzzy controller

d/d

t IGA

y

yd ufb

Figure (3.5) Feedback fuzzy controller tuned by Immune Genetic algorithm


٥٦

Although this type of fuzzy rule is friendly to human beings, the controller parameters need to be tuning, unlike trial and error. The main operations of a fuzzy controller include fuzzification, inference and defuzzification. During the control process, the controller inputs are scaled for fuzzification before the rule inference, we define a function of the input scaling factors, S1e1 and S1ce1 and as follows: if is e1 is * and ce1 is * then u is (,S1e1, S1ce1). (3.6) Ψg PZN ,, Where Ψg (,S1e1, S1ce1).can then be used to map the appropriate output fuzzy sets. A defuzzification function basically maps the fuzzy consequent obtained from the fuzzy domain into crisp outputs in a crisp domain. These outputs should best represent the distributed fuzzy control action. In order to systematically design an optimal fuzzy controller, the IGAs were integrated in the design procedure as described in Figure (3.5) which will be described in the next section. 3.2 Immune Genetic Algorithm (IGA) The purpose of the immune operation is to avoid locally optimal solutions, or to avoid finding an optimal solution with a low convergence speed. Individuals are considered to be antibodies (analogous with the biological immune system) and the immune operation consists of two steps: calculating antibody density and activating and suppressing antibodies. Antibody density is the density of similar individuals in the population [13]. Similarity between individuals is the affinity, which is based on Hamming distance. Activating and suppressing antibodies involves adjusting the selection probability of an antibody (individual) for reproduction and is based on both its fitness (fitness is based on how many faults the individual detects and the antibody's density. The effect of either higher fitness or higher density, increases the probability of selection and the effect or either lower fitness or lower density, decreases the probability. Findings show both a reduction in test sizes and an improvement in execution times compared with other results for combinational benchmark circuits. This immune concept tries to keep the population immune from local optima by increasing the chances of higher density individuals for selection and suppressing chances of lower density individual. The pseudo code of proposed IGA algorithm is shown in Figure (3.6). Immune operators are shown in the dotted frame. The description of each step of the proposed algorithm is as follows:


٥٧

3.2.1 Generation the initial antibodies: In this step, the antibodies (test vectors) are created randomly on feasible space. Population size should be large enough in order to ensure adequate diversity; however, it is a trade off between getting higher convergence rate with larger search space and less genetic operation time. Population size in proposed algorithm is constant value for all circuits. 3.2.2 Calculating the fitness: The fitness function provides a quantification of the quality of the chromosome. It is the fitness of a chromosome that determines whether the

Figure (3.6) Immune Genetic Algorithm

Create Initial Random Population

Evaluation Fitness Functions of Each Individual

Calculate the Densities of Antibodies

Activating and suppressing of Antibodies

Create a New population (Selection, Crossover )

Terminate criterion

satisfied

Over No

Yes


٥٨

chromosome will be selected to produce offspring and quantifies its chance for survival among the other chromosomes in the population to the next generation. 3.2.3 Calculation of affinities Affinity refers to the degree of binding of the cell receptor (Lymphocytes) with the antigen. Lymphocytes are able to recognize non-self (i.e. antigens) by binding to them with chemical [23]. To ensure that immune system can recognize as many antigens as possible, exact match is not required. A match occurs if a given number of contiguous features complement each others. The number of features required to bind, before a match can be made, is known as affinity threshold. The higher the affinity, the stronger the binding and as a result, better the immune recognition and response. The degree of similarity between two vectors is considered as the affinity [24]. As the antibody (Ab) and antigen (Ag) affinity is related to their distance, it can be estimated via any distance measure between two strings (or vectors), such as the Euclidean, the Manhattan, or the hamming distance. Hence, if the coordinates of an antibody are given by Ab=(Ab , Ab1 , …, Abn ) and those of an antigen are given by Ag=(Ag1 , Ag2 , …, Agn ), then the distance λ between these two vectors could be defined as Eq. (2.23) in section 2.4.4 in chapter 2. 3.2.4 Crossover and Mutation: Crossover is the key to genetic algorithms power that is to exchange corresponding genetic properties from two parents, to allow useful genes on different parents to combine in their offspring [38]. Most common crossover types are one-point, two-point and uniform crossover, as shown in Figure (3.7), two-point crossover is used as a crossover operator [39]. The next genetic operator to be applied to the population is mutation, which employed to introduce diversity into the population. As shown in Figure (3.8) in the random mutation, random genes in the chromosome are selected and each gene's value is replaced with its complement or a new random value (with probability pm). The role of mutation in GA is to prevent the premature convergence of GA to suboptimal solution by restoring lost or unexplored genetic material into the population. The mutation probability (pm) is proportional to the affinity between the antibody and antigen. Small value of pm is essential for the successful working of GA, because the moderately large value of promotes the expensive recombination of schemata, while high value of pm is necessary to prevent the disruption of schemata. Especially,


٥٩

pm must decrease to survive the individuals with high fitness; therefore pm needs to be zero for the solution with the maximum fitness. The expression for pm is given in [13] and [109].

1011 101010 0101 1110 111001 0111

1110 111001 0111 1011 111001 0101

Figure (3.7): Two-point crossover

1 1 0 1 0 1 1

1 1 0 1 1 1 1

Figure (3.8) Mutation in binary

Parent A Parent B

K

Offspring 2 Offspring 1

J


٦٠

3.3 ANFIS as a Controller Before the Neuro-Fuzzy approaches, most controller design methods used only the linguistic information to build a fuzzy controller. Manual trial and error processes were involved to fine tune the MFs. To deal with the problems mentioned above in control applications, ANFIS can be used. An adaptive Neuro-Fuzzy controller with a small number of weights can be designed by using the ANFIS architecture. The ANFIS structure, with very few weights, can overcome the problem of excessive tuning parameters and the need for modeling of the process by a separate network model such as NN, fuzzy or ANFIS. Inverse learning is one of the methods of designing Neuro-Fuzzy controllers. It involves two phases: learning and application phases. In the learning phase training set is obtained by generating inputs randomly, and observing the corresponding outputs produced by the plant. In the application phase, the ANFIS identifier is copied to the ANFIS controller for generating the desired output. Learning phase and application phase of inverse learning are shown in Figures (3.9) and (3.10), respectively. This method seems straightforward and only one learning task is needed to find the inverse of the plant. It assumes the existence of the inverse plant, which is not valid in general. Minimization of the network error does not guarantee minimization of the overall system error. However, inverse learning is an indirect approach that tries to minimize the network output error instead of overall system error (defined as the difference between desired and actual trajectories). Instead of this method, “specialized learning” (illustrated in Figure (3.11) can be used as an alternative that tries to minimize the system error directly by backpropagating error signals through the plant block. In order to backpropagate the error signals through the plant, a model representing the behavior of the plant is needed. In other words, Jacobian

matrix of the plant, uy

, is required. It can be estimated online from the

changes of plant’s inputs and outputs. The desired behavior of the overall system can also be implicitly specified by a (usually linear) model that is able to achieve the control goal satisfactorily. In literature [101] used an iterative approach to evaluate the plant Jacobian information [103] also used a similar approach, called one-step ahead indirect adaptive control, with a single linear neuron in the output layer and many nonlinear neurons in the hidden layer of the network.


٦١

plant

ANFISidentifier

+

-

u(k)

x(k)x(k+1)

x(k)x (k)

ANFIScontroller plant x(k+1)d

u(k)

Saerens and Soquet [86] used the sign of the process gain to approximate the process Jacobian. Jutan and Krisnapura [52] proposed the use of sigmoidal function that has the property of having continuous derivatives to approximate the plant Jacobin. Their approach of using the sigmoidal function to represent the unmodifiable process layer in controller process network gives an approximation to both the process gain as well as its sign. In the control part of this study, specialized learning algorithm shown in Figure (3.11) is used in power plant system to see the performance of the ANFIS as a controller. Therefore, a simple ANFIS controller designed.

Figure (3.10) application phase of the Inverse Learning

Figure (3.9) Learning phase of the Inverse Learning


٦٢

plant

u(k)

x(k+1)

+

-ANFIScontrollerx(k)

ex

x (k+1)d

When designing the ANFIS controller, first, inputs to the controllers are decided. Two inputs are chosen. They are the error between actual and desired value and its change at the previous sampling instant. Since Gaussian MF has two parameters, it is chosen as an input MF. Three MFs labeled with the Small (S), Medium (M) and Big (B) as linguistic variables are used for input MFs. Thus, ANFIS controller, with two inputs and three MFs on each input, has nine control rules in the controller rule base due to the grid partition method mentioned in previous chapters. For simplicity we start designing our ANFIS controller for SISO plant before appliing it to the practical real plant see Figure (3.12). 3.4 ANFIS Controller for SISO Plant

Generated ANFIS controller structure is given in Figure (3.12). In the controller, total number of adjusted parameters is 39. Since each input is graded with three MFs and one of them consists of two parameters, twelve of adjusted parameters come from the premise part of the controller network. Consequent part of the controller consists of 27 parameters due to the nine rules with constant output. Controller parameters are adapted at each sampling instant. A code for simple backpropagation algorithm is written to update the parameters of the ANFIS controller in closed-loop system simulation. The description of the mathematical equations of proposed plant is as follows: y=cons1*(x) (3.7) x=cons2*(Π*K/3) (3.8) where y, and x are the output, and input of plant,cons1 and cons2 are the constant variables, and K is iteration number.

Figure (3.11) Specialized Learning


٦٣

∏

∑

∩

∩

∩

∩

∩

∩

∏

∏

∏

* * * * * * * * *

N

N

N

N

N

* * * * * * * * *

e ce

e

ce

e ce

e ce

e ce

e ce

Premise Parameters Consequent Parameters

ƒ

Figure (3.12) ANFIS Architecture with nine rules

L1 L2 L3 L4 L5 L0

As mentioned in section (2.4) in chapter 2 for designing ANFIS controller, we consider here two inputs for ANFIS, the error between the desired and the actual output (e) and its changes (Δe) and one control output (u) as depicted in Figure.(3.12). The problem consists in finding the values of the parameters of the membership functions in the rule antecedents and the coefficients in the rule consequents of the TSK-type fuzzy systems, the knowledge rules of the fuzzy system have the form:

rr eLiseandLeiseIF :ececcuTHEN r

ere

ro

r : (3.9)

where r=1,2,...,R is the rule number, rLe and reL are the linguistic terms of the input signals e and e ,respectively, in the r-th rule , ru is the contribution of the r-th rule to the total output of the fuzzy system, and

roc ,

rec , and

rec are the consequent coefficients, the output of the fuzzy

system is given by:


٦٤

R

r

r

rR

r

r

w

uwu

1

1 (3.10)


)().( eew rr eLLer

(3.11) where (.)(.) rr eLLe and

are are the membership functions corresponding

to the linguistic terms rr eLandLe respectively, in the r-th rule. In addition, note that (٤.4) can be written as:

R

r

rR

r

rrrR

rR

r

r

r

uuwuw

wu111

1

(3.12)

Where rw for r=1,2,…, R can be equivalently called the normalized rule

consequents:

R

r

r

rr

w

ww

1

(3.13)

In our case the complete knowledge base will have 3×3=9 rules of the form

given in (3.9), also, the network will have 2 distribution units in layer L0, 6

neurons in L1, 9 neurons in L2, L3, and L4, and 1 neuron in L5.

So the determined parameters using 3 fuzzy sets as follow:

9 rules * 3 consequent parameters per rule=27 consequent parameters.


٦٥

2 inputs * 3 membership function per input* 3 parameters per membership function=18 membership function parameters. Then, the total number of parameters to be determined is 27 + 18 = 45 per fuzzy system. In case of using 5 fuzzy sets the determined parameters is as follows: Table 3.1 shows the number of tuned parameters based on number of fuzzy sets for each input. As shown from Table 3.1, this numbers of tuned parameters clearly illustrate the difficulty of tuning a fuzzy system following a trial & error approach, which simply gets worse as the number of input linguistic terms increases. Fortunately, this process can be fully automated using the neuro-fuzzy paradigm and a low-dimension fuzzy system will perfectly do the job, as will be shortly shown [49]. L1 fuzzifies the incoming input signal using bell-shaped membership functions using the form described bellow:

xxfi )(1 (3.14)

bi

i

i

iii

acx

xgfgy 2111

1

1)()(

(3.15)

where i=1, 2, …, 6 is the neuron number, e and e is the input signal, 1yi is the i-th neuron output, and ai, bi, and ci are the parameters of the bell-shaped output function. L2 calculate the rule fulfillment weight for each rule using the following input and output processing functions:

iiiii eeeef 11112 ,, (3.16)

21

11222

iiiiir xxfgyw (3.17)


11

ii xandx are the inputs to

the i-th neuron, iy2 is the output of the i-th neuron, and rw is the rule

fulfillment weight of the r-thrule with r=i. L3 calculate the relative rule fulfillment weight for each rule through:


٦٦

9

1

9

1

39

32

31

39

32

31

33 ,,,r

rj


9

1

3

3333

rr

r

i

iiiiir

w

wfxfgyw (3.19)

where i=1,2,…,9 is the neuron number, ijx3 for j=1,2,…,9 are the inputs to

the i-th neuron coming from all the neuron outputs in L2, ijy3 is the output

of the i-th neuron, and rw is the (normalized) relative rule fulfillment weight of the r-th rule with r=i. L4 Calculate the normalized rule consequent for each rule through:


)..(

)..(

,,

210

221104

21444

ececcw

xcxccf

xxfgyu

or

orrr

or

orri

ooiiir

(3.21)

Table 3.1 Total number of parameters to be tuned for different fuzzy sets Total no

of parameters to be tuned

Total no of consequence parameters

No of consequence for

each rule

No of rules

Total no of premise

parameters

parameters per input

Total no of fuzzy sets

fuzzy sets

No of inputs

45 27 9 18 6 3

105 75 25 30 10 5

189 147

3

49 42

3

14 7

2


٦٧

where i=1,2,…,٩ is the neuron number, ix4 is the input to the i-th neuron,

iy4 is the output of the i-th neuron, and ru is the normalized rule

consequent of the r-th rule with r=i. L5 calculates the total system output:

9

19

52

51

59

52

51

55 ,,,r

riiiiiii uxxxxxxf (3.22)

9

1

555

rriii ufgyu (3.23)

where u f is the total output of the FISU system used in this description. 3.4.1 Simulation results

Using the same square wave as a reference for plant, with different constant variables M1 and M2 as depicted in Eq(3.7) and Eq(3.8), the simulations presented here are to evaluate the control system performance for various values of M1 and M2 as well as the set point value . Case1: In this case despite the set point change between ±3.5, and ±3.5, the results show that the actual output of the proposed controller track the changes of two set point as obvious in Figure (3.13). The RMS value=.001904, 0.01893 and 0.01982 for use of 3 fuzzy sets, 5 fuzzy sets and 7 fuzzy sets respectively, as we see these vales nearly close to each others. The comparison between initial and final coefficient of consequent parameters using 3 and 5 fuzzy set are depicted in Figure (3.14) and (3.15) , we show from Figure (3.14), the rule number 2,5 and 8 have the changes of coefficient between initial and final update. Case 2: In this case we have two sets one change between ±5, and other change between ±8, in to sets we see the output of the proposed controller follow two set point as depicted in Figure (3.16). The RMS value=0.04896, 0.048980 and 0.04897 for use of 3 fuzzy sets, 5 fuzzy sets and 7 fuzzy sets respectively, also as in previous cases the values of RMS values seems to be identical . The initial and final coefficient of consequent parameters with 5 fuzzy sets are depicted in Figure (3.17)


٦٨

Figure (3.13) Case1 :The simulation result of the proposed controller with changes of set point ±3.5 and ±1.5

Figure (3.14)Case 1:Initial and final coefficient of consequent parameters with 3 fuzzy sets


Figure (3.15)Case 1:Initial and final coefficient of consequent parameters with 5 fuzzy sets



٦٩

Case 3: In this case there were changes between ±1.9; we see the output of the proposed controller follow the set point as depicted in Figure (3.18). The RMS value=c for use of 3 fuzzy sets, 5 fuzzy sets and 7 fuzzy sets respectively, also as in previous cases the values of RMS values seems to be identical . The comparison between initial and final coefficient of consequent parameters using 7 fuzzy set are depicted in Figure (3.19). From all cases demonstrated, we can see that the proposed controller able to controlling the plant in different set points very well using 3 fuzzy set only with less RMS value as shown in Table (3.2).

Figure (3.16) Case2: The simulation result of the proposed controller with changes of set point ±5 and ±8 using 3fuzzy sets




٧٠


Cases cons1 cons2 RMSE

3MF

RMSE5

MF

RMSE

7MF

Set point

changes

Case 1 .4 .5 0.01904 0.01893 0.01892 ±3.5, ±1.5

Case 2 2 1 0.04896 0.04898 0.04897 ±5, ±8

Case 3 2 2 0.03215 0.31013 0.034897 ±0.8



٧١

3.4 Summary In this chapter we introduced a CD-MV-ANFIS controller tuned by Immune genetic algorithm (IGA) to maintain the natural interactions between input and output process variables on the nonlinear industrial processes. The proposed controller includes the designing of (FF) and (FB), where the (FF)controller deals with all inputs of system in the frame of cascaded form, each of which representing MISO using Takagi-Sugeno (TS) fuzzy system of first order. The premise and consequent parameters was tuned by LSE and gradient descent respectively. The (FB) controller deals with the control signals using the MISO Takagi-Sugeno (TS) fuzzy system tuned Immune genetic algorithm (IGA). The introduced controller was tested by two simple examples.


Chapter 4 Application of Proposed Approaches 1 and 2 to Drum

Boiler turbine units Control of nonlinear systems is difficult in the absence of a systematic procedure as available for linear systems. Many techniques are limited in their application to special class of systems. Here again, more commonly available methods are heuristic in nature and the fuzzy logic and neuro-fuzzy technique can reduce the arbitrariness in the design of a controller to a great This chapter studies the application of two approaches 1and 2 (MV-ANFIS) and (CD-M-ANFIS) for third and seven orders of drum boiler turbine units. A comparison between ANFIS controller and different kinds of controllers are present here to show the effectiveness and soundness of proposed controller. Non-linear models (third and seven orders) of the drum boiler-turbine unit are explained in section 4.2. The design of MV-ANFIS controller for drum boiler turbine unit is detailed in section 4.3. Section 4.4 includes effectiveness of membership function number and tuning epochs.The Control loop Interaction and tuning is described in section 4.5. The Performance of the drum boiler- turbine unit based on MV-ANFIS controller is detailed in section 4.6. Effect of Immune genetic algorithm for tuning is explained in section 4.7. The application of Cascaded Distributed Multivariable ANFIS (CD-MV-ANFIS) for drum boiler turbine units as well as comparison with other controllers is described in details in section 8 and section 9 respectively. 4.1 Introduction The Multi-variable ANFIS controller (MV-ANFIS) is shown in Figure (4.1) presented for fusel fuel power unit (FFPU) and tested by the third and seven order of drum boiler-turbine unit. The purpose of the proposed controller is to facilitate wide-range set-point driven operation for the FFPU, and to provide off-line operator-requested system adaptability to achieve optimal operation. The (MV-ANFIS) module consists of a feedforward controller and a supervisory designer. The feedforward controller is an open non-linear MIMO fuzzy compensator that implements the inverse static model of the FFPU; having the set-points, yd, as inputs, it provides the feedforward control signals, uff, as outputs. The supervisory designer, activated by the operator, uses a neuro-fuzzy paradigm to tune the feedforward controller off-line to fit a given set of optimal steady-state input-output training data patterns. In general, the MIMO fuzzy structure will

Chapter 4: Application of Proposed Approach 1 and 2 to Drum Boiler turbine units

٧٣

consist of several independent MISO fuzzy sub-modules, one per each feedforward control signal to be generated. Each sub-module is feed with the set-points signals of all the control loops considered by the coordinated control, and implements a nonlinear multivariable function that provides a feedforward control signal in terms of the set-point values throughout the whole operating range of the FFPU [8]. This approach guarantees wide-range applicability. For the introduced controller, the feedforward controller consists of three MISO fuzzy systems, which provide the feedforward control signals for the fuel, u1ff, steam, u2ff, and feedwater, u3ff, control valves, in terms of the power, Ed, pressure, Pd, and level, Ld, set-points Figure (4.2).

Figure (4.1) Multivariable ANFIS controller

uff +

ufb +

yd

Power unit

Fuzzy Feedback Controller Tuned by Immune Genetic

algorithm

Neural Network Learning

Fuzzy Feedforward

Control

y

- +

Figure (4.2) Feedforward ANFIS controller


٧٤

Effective participation of (FFPU) in wide-range load-following duties requires the ability to undertake large power variations in the form of daily, weekly, and seasonal cycles, as well as random fluctuations about those in.[8]&[29].Currently, most control systems at FFPUs are multi-loop configurations of PID controllers. Such approach has proved its value during normal operation at base load; where plant characteristics are almost constant, nearly linear and weakly coupled (there is no interaction between inputs). Conversely, wide-range operation imposes strong physical demands on unit equipment, and leads inherently to conflicting operational and control situations, since FFPUs were designed to operate at constant load conditions. Under these circumstances, traditional control schemes, designed and tuned for regulation and disturbance rejection, but for set-point tracking, may decrease the global performance of the unit; making them less acceptable for wide-range cyclic operation. In what follow the two models (third and seven order orders models) of drum boiler turbine units studied

4.2 Non-linear Models of Drum Boiler-Turbine Unit

The essential overall dynamics of a fusel fuel power unit (FFPU) have been remarkably captured for a 160 MW oil fired drum-type boiler-turbine-generator unit in a third order multi-input multi- output nonlinear model by [17]. The model represents the boiler unit P16 and the turbine unit G16 at Oresundsverket in Malmo, Sweden, and has been an active research topic for the last 3 decades. It can be considered the best simple model currently available for simulation of the overall dynamics of (FFPU). The first version of this model appeared in [9], Åström and Eklund [11], which modeled the electric power output and drum pressure by a second order nonlinear model. Later, in Bell and Åström 1979 additions were made to predict the drum water level, increasing the model to seven orders. Also, actuator dynamics for the fuel, feedwater and throttle control valves were included. In Bell and Åström 1987a,[17] two versions of the model were proposed, the main issue being the integration of evaporation rate concept by [68] which simplified the drum level prediction and the model reduced back to the third order. In Bell and Åström 1987b[18] the results of a comparative study among several low order model were presented, where the third order model performed satisfactorily. More recently, in [10] the modeling of the drum water level was supported in physical first principles without increasing the model order. Finally, in [16] the drum boiler part of the model was revisited and increased to fourth order to account more precisely for the shrink and swell effect in the drum water level. A schematic diagram of the boiler turbine unit is depicted in Figure (4.3).


٧٥

The main outputs of the boiler and its input shown in Figure (4.4) [17] and [18] we present in the next sections the mathematical equations, the operation conditions also presented.

DRUM

BOILER

TURBINE

Pressure (Bar) Fuel flow u1

Water level D/L Feed water u3

Output power Control valve u2

Inputs Output

Figure (4.4) The main outputs of boiler and its input

Figure (4.3) Schematic diagram of the Drum- boiler-turbine unit


٧٦

4.2.1 Mathematical Model of third Order Drum Boiler-Turbine Unit The complete model with all numerical values being adapted to the Swedish unit [18] for which the non-linear model equations of the third order were developed:

),(. uxfx (4.1) where;

),,(3

),,(2

),,,(

323

221

32111

3

2

1

uuxf

uxxf

uuuxf

x

x

x

(4.2)

where

.1x =-0.0018 u2 x1

(9/8)+0.9u2-0.15u3 (4.3)

.2x ==(0.73u2+0.016)x1(9/8)-0.1x2 (4.4)

.3x =(141u3 –(1.1u2-0.19) x1)/85 (4.5)

ld / =0.05(0.13073x1+ 100αcs+ qe/(9-67.975) (4.6)

11 xy (4.7)

22 xy (4.8)

ldy /3 (4.9)

where; αcs =(1-0.001538ρf)(0.8p-25.6/ρf(1.0349-.001234p) (4.10)

qe =(0.84u2-0.147)p+45.59u1-2.51u3-2.096) (4.11)

The three state variables 321 ,, xandxx are drum steam pressure (in Bar), electric power (in MW), and steam-water fluid density in the drum (in kg/m3), respectively. The three outputs y1,y2, and y3 are drum steam pressure (x1), electric power (x2), and drum water level deviation (D/L in cm), respectively. The y3, drum water level, is calculated using two algebraic calculations αcs and qe which are the steam quality (mass ratio) and the evaporation rate (kg/s), respectively. The three inputs,u1 ,u2 and u3 are normalized positions of valve actuators that control the mass flow rates of


٧٧

fuel, steam to the turbine, and feedwater to the drum, respectively. The operating conditions are given in Table 4.1 [18]. The outputs responses of the drum boiler-turbine model to step changes in the input fuel flow, throttle valve position and feedwater respectively described in case of low load an for full load illustrated in Appendix A

4.2.2 Mathematical model of seven Order Drum Boiler-Turbine Unit The non-linear dynamical model of the seven order Drum boiler-turbine-unit is also used in this work. The outputs responses of seven orders drum boiler-turbine model load illustrated in Appendix B. The complete model with all numerical values being adapted again to the Swedish unit on which the equations were developed [18]. That is:

),(. uxfx (4.17) where;

)(),(),(

)()(

),,(),,,,(

77

376

545

44

33

2212

321311

.7

.6

.5

.4

.3

.2

.1

xfuxfxxf

xfuf

uxxfuuuxxf

xx

xxx

xx

(4.13)

15.09.15.09.00018. 1318/9

12.1 uuuxux (4.14)

Table 4.1 Rated operating conditions of third order model Units Value Specification MW 160 Electric power Bar 140 Drum steam pressure o C 535 Superheated steam temperature

o C 300 Feedwater temperature m3 40 Volume of drum m3 11 Volume of downcomers m3 38 Volume of risers Kg 40000 Mass of water in system Kg 20000 Mass of steam in system


٧٨

10/))16.073(. 28/9

12.2 xxux (4.15)

ts vwux /)141( 3.3 (4.16)

14.4 /)( Ccs Txx (4.17)

2/))(1000( 54

.5 ccs Txxx (4.18)

20/)( 73.6 xux (4.19)

20/)55.3( 7.7 xwx s (4.20)

21 SS ccs (4.21)

12 )19.01.1( xuw s (4.22) .76

.5

.4 03.05.02086029 xxxxvwV csW (4.23) )5.65(50 Ww VX (4.24)

)/1/()/1( wswCS vv (4.25)

Where: 1x : drum steam pressure

2x : electrical output power u1 : normalized fuel mass flow rate u2 : normalized throttle valve position u3 : normalized feedwater mass flow rate Ws : steam mass flow rate

tv : total volume of drum and risers : density of fluid in complete system

s : density of fluid in drum vw : specific volume of water

cs : average quality of steam in complete system TC1 : time constant associated with state 4x TC2 : time constant associated with state 5x

4x : state to limit high frequency response to 22 / tcs

5x : state to limit high frequency response to 22 / tcs

6x : state to account for shrink and swell phenomena effect

7x : state to account for shrink and swell phenomena effect VW : volume below the drum water level Xw : drum Water Level and Vt=85 m3 : VW =0.0001538 m3/Kg CS1= 0.8 sec : CS2= -25.6 sec


٧٩

TC1 =TC2 =10 sec The model contains 7 states 7654321 ,,,,,, xandxxxxxx . However the essential non-linearities to enable control strategies for start-up, shut-down and normal regulation have been included. The equations for drum pressure and electrical output are basically those in the Astrom-Eklund model with several small modifications made accounting for the inertia effects of the turbine-alternator and the energy passing to the condenser and feedwater heaters. An extra term was also included in equation (4.14) to account for the transient increase in pressure when the circulation rate increases due to feedwater changes. The development of the drum water level equations was separated into the effects of two mechanisms. The first mechanism was the displacement of the water from the drum to the risers, or the reverse, due to the quantity of steam being produced in the risers. Equations (4.16), (4.21), and (4.22) are accounted for this response and the states 43 , xx are included to limit the high frequency components in the 22 / tcs term. The second drum water level mechanism was the changing circulation mass flow rate experienced with fluctuations in the density of the drum fluid. The two first order states

65 , xx were sufficient to describe for this phenomena. Physically it can be seen that an increasing in the feedwater will initially cool the water in the drum and risers, thereby its density and its mass flow rate in the downcomer riser loop are increased. This increase is more pronounced during the initial phase of the change and tends to decrease as steam bubbles in the riser loop collapse, and the average density in the risers increases. This accounts for both the 6

.6 , xandx and

terms in equation (4.19). Similarly if steam flow increases, the resultant drop in pressure will cause more boiling to take place in the risers. This decreases the average density and increases the circulation mass flow rate. It is sufficient to have 7x in equation (4.19) since the increase in circulation mass flow rate will be maintained if the steam flow rate stays at its new value. The simulation contains the major inputs and outputs, which are needed for describing the overall plant control and its essential non-linearities. Regulation at normal operating conditions may investigate the shrink/swell phenomena which is unusual for such a low-order model. The initial conditions for the state variables are given in Table.4.2 [18]. The model described above was also simulated. All inputs are scaled to range 0-1 as in case of 3rd order model.


٨٠

4.3 Multivariable ANFIS (MV-ANFIS) Controller for drum boiler turbine unit 4.3.1 Neuro-Fuzzy Feedforwad Controllers As mentioned earlier, the feedforward controller consists of three MISO fuzzy systems that provide the feedforward control signals for the fuel, u1ff, steam, u2ff, and feedwater, u3ff, control valves, in terms of the power, Ed, pressure, Pd, and level, Ld, set-points, as was shown in Figure (4.5). The feedforward controller design problem may be stated as: Given a set of steady-state input-output patterns, [u1 u2 u3 E P L], determine the MISO fuzzy systems FISU1, FISU2, and FISU3. More specifically, the problem consists in finding out the values of the parameters of the membership functions in the rule antecedents and the coefficients in the rule consequents of the three Takagi-Sugeno fuzzy (TSF) systems, so that the set of inverse steady-state input-output patterns, [E P L u1 u2 u3], are matched. Note that FISU1, FISU2, and FISU3 should reproduce the sets of patterns: [E P L u1], [E P L u2], and [E P L u3] as [Ed Pd Ld u1ff], [Ed Pd Ld u2ff], and [Ed Pd Ld u3ff], respectively, once embedded in the (FF./FB) control system. The feedforward controller design problem is solved independently for each fuzzy system using the necessary data from the same set of steady-state input-output patterns, [u1 u2 u3 E P L]. All three fuzzy systems are of the Takagi-Sugeno (TS) type [88] and have similar structures, so without loss of generality and to simplify the

Table 4.2 Rated operating conditions of seven order model

Variable Full load Low load

Steam pressure= P(0) (Bar) 127 108

Power =PO(0) (Mw) 140 65

(0) (Kg/m3) 389 425

x1(0) 0.06 0.06

x2(0) 0.0 0.0

x3(0) 0.4 0.4

x4(0) 250 250


٨١

presentation, and unless otherwise specified, hereafter all explanations refer to FISU1, the system that generates u1ff. The knowledge rules of the fuzzy system have the form [49]:

andisIF LEE rdd: andis LPP r

dd LLL r

dd is

LcPcEccu dr

Ldr

Pdr

E

rr

ffTHEN 01: (4.26)

where r=1,2,⋅⋅⋅,R is the rule number, LLLPLE r

d

r

d

r

d andand are the linguistic terms of the input signals LPE ddd and,, respectively, in the r-th

rule, u rff1

is the contribution of the r-th rule to the total output of the fuzzy

system, and cccc r

L

r

P

r

E

r and,,, ,0are the consequent coefficients. For a

given input pattern T

ddd LPE ,the output of the fuzzy system is given by:

R

r

r

rff

R

r

r

ff

w

uwu

1

11

1 (4.27)

where rw , for r = 1,2,…,R, are the rule fulfillment weights. For each rule, its weight is calculated as the product of the input membership values as:

)().().( dLLdLPdLEr LPEw rd

rd

rd

(4.28)

where (.)(.)(.) rd

rd

rd LLLPLE andand are the membership functions

corresponding to the linguistic rd

rd

rd andLlLPLE ,, terms respectively, in

the r-th rule. In addition, note that Eq.(5.2) can be written as:

R

r

rff

R

r

rff

rrff

R

rR

r

r

r

ff uuwuw

wu1

11

111

1

1 (4.29)

Where rw for r=1,2,…, R are the so called (normalized) relative rule

fulfillment weights:


٨٢

R

r

r

rr

w

ww

1

(4.30)

, for r=1,2,…, can be equivalently called the normalized rule consequents: ff

rrff uwu 11 (4.31)

Each fuzzy system is to be designed with the previously explained ANFIS technique. To this aim, the fuzzy system is represented as a 3-input and one output, 5-layer feedforward neural network, as shown in Figure (4.5).Each input signal spans its whole operating range with three overlapping fuzzy regions, that is using three fuzzy sets with bell-shaped membership functions and linguistic terms: low, medium, and high. Therefore, for this case a complete knowledge base will have 3×3×3=27 rules of the form given in Eg.(4.26). Also, the network will have 3 distribution units in layer L0, 9 neurons in L1, 27 neurons in L2, L3, and L4, and 1 neuron in L5. With these dimensions, the number of parameters to determine is calculated as follows: 27 rules × 4 consequent parameters per rule = 108 consequent parameters,and 3 inputs × 3 membership functions per input × 3 parameters per membership function = 27 membership function parameters. Then, the total number of parameters to be determined is 108 + 27 = 135 per fuzzy system. The numbers clearly illustrate the difficulty of tuning a fuzzy system following a trial and error approach, which simply gets worse as the number of input linguistic terms increases. Fortunately, this process can be fully automated using the neuro-fuzzy paradigm and a low-dimension fuzzy system will perfectly do the job, as will be shortly shown. Each neuron in layer L1 fuzzifies the incoming input signal using bell-shaped membership functions. In this layer, the neuron’s input and output processing functions are of the form as in [ [48] and [47]:

xxfi 1

(4.32)

bi

i

iiii

acx

xgfgy 2111

1

1

(4.33) Neurons in layer L2 calculate the rule fulfillment weight for each rule

using the following input and output processing functions:

3

12

11

13

12

11

12 ,,,, iiiiiii xxxxxxf (4.34)


٨٣

31

21

11222 ,,)( iiiiiir xxxfxgyw (4.35)


21

11 ,, iii xandxx are the

inputs to the i-th neuron, iy2 is the output of the i-th neuron, and rw is the

rule fulfillment weight of the r-th rule with r=i. Neurons in layer L3 calculate the relative rule fulfillment weight for each rule through:

27

1

27

1

327

32

31

327

32

31

33 ,,,r

rj


27

1

3

3333

rr

r

i

iiiiir

w

wfxfgyw (4.37)

where i=1,2,…,27 is the neuron number, ijx3for j=1,2,…,27 are the inputs

to the i-th neuron coming from all the neuron outputs in L2, iy3 is the

output of the i-th neuron, and rw is the (normalized) relative rule fulfillment weight of the r-th rule with r=i. Neurons in layer L4 calculate the normalized rule consequent for each rule through:


drdrdrror

rrrroi

iiir

LcPcEccwxcxcxccf

xxxfgyu

.....

,,,

321

30

320

210

14

30

20

10444

(4.39)

where i=1,2,…,27 is the neuron number, ix4 is the input to the i-th neuron,

iy4 is the output of the i-th neuron, and ru is the normalized rule consequent of the r-th rule with r=i. The unique neuron in layer L5 calculates the total system output via:

27

127

52

51

527

52

51

55 ,,,r

riiii uxxxxxxf (4.40)

27

11

51

51

51

rrff ufgyu (4.41)

where ffu1 is the total output of the FISU1 system used in this description.


٨٤


∏

∑

Premise parameters

∩

∩

∩

∩

∩

∩

∩

∩

∩

∏

∏

∏

∏

∏

∏

∏

∏

* * *

* *

* * *

N

N

N

N

N

N

N

N

N

* * *

* *

* * *

E P L

E P L

E P L

E P L

E P L

E P L

E P L

E P L

E P L

E

P

L

U1ff

Figure (4.5) Neural network structure of feedforward fuzzy controller.

L0 L1 L2 L3 L4 L5


٨٥

4.3.2 Neural-Network Supervisory Designer As for the neuro-fuzzy feedforward controller, the description of the supervisory design process is given for the FISU1 system for the case with three linguistic terms per input that is with 27 knowledge rules. An analogous description applies to the other fuzzy systems. Given a set of M steady-state input-output patterns {[u11 u21 u31 E1 P1 L1], … , [u1M u2M u3M EM PM LM]}, and an initial MISO TS fuzzy system defined as in Eq.(4.36)-(4.31) and specified by arbitrary sets of parameters {[a1 b1 c1] , … , [ a9 b9 c9]} and {[cO1 cE1 cP1 cL1] , … , [cO27 cE27 cP27 cL27]} corresponding to the membership functions and the consequent coefficients, respectively; the supervisory designer adjust the parameters of FISU1 so that it reproduces the set of patterns {[E1 P1 L1 u11], … , [EM PM LM u1M]} corresponding to the inverse static model to generate u1ff. The consequent parameters are to be estimated using LSE procedure. From Eq.(4.48) and (4.38), each input-output pattern is related by:

iLriiErrr

rr LcPcEccwu ..Pr10

27

1

(4.42)

where u was used instead of ffu 1 to simplify the notation. Using vectors and considering all M input-output training patterns:

(4.43) Through appropriate definitions, Eq. (4.42) can be written as:

U=XC (4.44)

where U is M×1, X is M×(4)(27)=M×108, and C is 108×1. In general the

problem is overdetermined, that is M>108. An LSE solution for C can be

computed recursively [40] using Eq.(4.45) and (4.46) as follow:

(4.45)

27

27

27

027

1

1

1

01

E

L

P

L

P

E

c

cc

c

cc

cc

MMMMMM

M

LwPwEwwLwPwEww

LwPwEwwLwPwEww

27272727111

27112727111111

Mu

u

1

iTi

Tiiiii CxuxCC 11111


٨٦

(4.46) where T

ix is the ith row vector of matrix X and iu is the ith element of vector U, for i=0, 1,2,…, M-1, and Ψ is the covariance matrix. The initial conditions are C0 = 0 and Ψ0 = γI, where I is a size 108 identity matrix and γ is a large positive number. At the end of iterations: C=CM. Complementarily, the changes to the membership function parameters are determined by backpropagation [48]. The parameter changes for a single rule after a pattern has been propagated as calculated using the relationships Eq.(2.19) through Eq. (2.22) in chapter 2 yielding:

b

rrr acE

awwuuua

22

1 (4.47)

)1(22

1

b

rrr acE

abwwuuub

(4.48)

b

rrr acE

cEbwwuuuc

22

21 (4.49)

As previously mentioned the learning process is carried out iteratively. The procedure consists of the following steps: 1) Propagate all patterns from the training set and determine the consequent

parameters by the iterative LSE in Eq.(4.45) and (4.46). During this step the antecedent parameters remain fixed.

2) Propagate all patterns again and update the antecedent parameters by backpropagation using Eq.(4.48)-(4.49).During this step the consequent parameters remain fixed.

3) If the error is reduced in four consecutive steps then increase the learning rate by 10%. If the error is subject to consecutive combinations of increase and reduction, then decrease the learning rate by 10%.

4) Stop if the error is small enough, otherwise continue with step 1. For practical application, the learning process is incorporated in a three stage design process. First, a set of input-output data, to be used as training data, needs to be generated or obtained from the process. Another optional data set can be used as checking data after training to evaluate the performance of the learning process. Second, initial structures for the FIS need to be created. For each input, the range of operation, number of membership functions, as well as their shape, must be defined. Finally, the previously defined learning process is carried out using the training data set to adjust the membership functions, and to determine the consequent parameters. The resultant FIS is verified using the checking data set.

11

111 1

ii

Ti

iTiii

ii xxxx


٨٧

4.4 Design of Neuro-Fuzzy Controllers

In this section the supervisory designer is used to implement the proposed neuro-fuzzy controllers. Some results are provided to demonstrate the feasibility of the proposed approach to design the feedforward controller and to show its main characteristics. First, the data of four cases of interest to design the controllers is presented. Second, the effect of number of membership functions and number of training epochs on the approximation accuracy of the neuro-fuzzy controller to the inverse static model of the FFPU is illustrated for the sliding pressure case. Finally, the design of the neuro-fuzzy controllers is presented for all four cases. 4.4.1 Case studies The four cases (Constant, Sliding, upper, and lower) pressure illustrating the design of the neuro-fuzzy feedforward controller include the constant-pressure operating policy in [15] are defined in Table 4.3, the sliding-pressure operating policy defined in Table 4.4, Table 4.5 and Table 4.6 provide some numerical values of the operating points, ie, the upper and lower limits of the power-pressure operating region. These cases constitute a reasonable good sample of power-pressure policies covering the whole operating window of the FFPU. All necessary steady-state input-output data to design the controllers is obtained from these sources as explained in Appendix A. Recall that since the controllers are to approximate the inverse static behavior of the FFPU, the control signals will be considered as outputs and the power, pressure and drum water level deviation will be the inputs. Figure (4.6) shows the data for the pressure, P, and the control signals u1, u2, and u3, for the upper-limit pressure case with power E as independent variable. Note that the drum water level deviation L is not shown since in steady-state it is always zero for all loads. Figure (4.7) provides the steady-state input-output data for the constant-pressure case. Figure (4.8) provides the steady-state input-output data for the sliding-pressure case. Finally, Figure (4.9) comprehends the lower-limit pressure case.

Table 4.3 CONSTANT PRESSURE EQUILIBRIUM POINTS

E P ρf u1 u2 u3 L (MW) Bar ( kg/m3) m

10 140 457.0796 0.1999 0.2302 0.0949 0 20 140 448.4947 0.2464 0.2748 0.1453 0 40 140 431.0214 0.3393 0.3641 0.2462 0 60 140 413.0712 0.4322 0.4534 0.3472 0 80 140 394.5281 0.5251 0.5428 0.4481 0

100 140 375.2257 0.618 0.6321 0.549 0 120 140 354.9094 0.7109 0.7214 0.6499 0 140 140 333.1566 0.8038 0.8107 0.7508 0 160 140 309.1649 0.8967 0.9 0.8517 0 180 140 280.9982 0.9896 0.9893 0.9526 0


٨٨

Table 4.6 LOWER PRESSURE LIMIT EQUILIBRIUM POINTS


10 32 493 0.0785 0.4205 0.0708 0 20 32 485.2 0.1274 0.6554 0.1315 0 40 36.3 468.8 0.2287 1 0.2504 0 60 52.1 449.9 0.3392 1 0.3591 0 80 67.29 430.2 0.4486 1 0.4637 0 100 82.1 409.2 0.5574 1 1.5654 0 120 96.5 386.2 0.6656 1 0.6649 0 140 110.7 360.2 0.7734 1 0.7626 0 160 124.6 328.8 0.8808 1 0.8587 0 180 138.4 284.6 0.9879 1 0.9534 0

Table 4.5 UPPER PRESSURE LIMIT EQUILIBRIUM POINTS


10 237.4 318.1 0.3225 0.2102 0.1226 0 20 231.8 312 0.361 0.2362 0.1683 0 40 220.9 300.8 0.4385 0.2965 0.2607 0 60 210.2 290.1 0.5167 0.3551 0.3544 0 80 199.7 278.9 0.5956 0.4251 0.4495 0

100 189.5 268.1 0.6752 0.5032 0.5459 0 120 179.5 257.8 0.7555 0.5907 0.6439 0 140 169.7 247.1 0.8366 0.689 0.7434 0 160 160.2 236.8 0.9183 0.7996 0.7996 0 180 150.9 226.3 1 0.9245 0.9245 0

Table 4.4 SLIDING PRESSURE EQUILIBRIUM POINTS


10 65 484.7999 0.1129 0.2914 0.0762 0 20 70 475.7112 0.1659 0.3803 0.1323 0 40 80 457.1753 0.2715 0.5208 0.2418 0 60 90 437.932 0.3765 0.626 0.3485 0 80 100 417.647 0.4812 0.7071 0.4527 0 100 110 395.8517 0.5854 0.7712 0.5549 0 120 120 371.7977 0.6894 0.8229 0.6553 0 140 130 344.0761 0.7932 0.865 0.7542 0 160 140 309.1649 0.8967 0.9 0.8517 0 180 150 242.5809 1 0.9293 0.948 0


٨٩

Figure (4.6) Input-output steady-state data for upper-pressure limit case.

Power (MW)

Pres

sure

(Bar

) C

ontro

l sig

nal(M

w)

Figure (4.7) Input-output steady-state data for constant-pressure case.

Power (MW)

Pres

sure

(Bar

) C

ontro

l sig

nal


٩٠

Figure (4.8) Input-output steady-state data for sliding-pressure case.

Power (MW)

Pres

sure

(Bar

) C

ontro

l sig

nal

Figure (4.9) Input-output steady-state data for lower-pressure limit case.

Power (MW)

Pres

sure

(Bar

) C

ontro

l sig

nal


٩١

4.4.2 Effect of Membership Function Number and Training Epochs

Assuming that the data required designing the neuro-fuzzy controllers is already available, two major decisions have to be made in order to obtain controllers with satisfactory performance. First, the number of linguistic terms (equivalently the number of membership functions) to be used to fuzzify the input signals has to be decided. The number of linguistic terms per input not only determines the size of the knowledge base, that is, the number of knowledge rules, but also will determine the number of parameters to be calculated, and the number of input-output data patterns required for the learning process. Second, it must be decided how to stop the learning process. The stopping condition may be set in terms of reaching a predefined approximation accuracy, or in terms of the execution of a predefined number of training iterations (epochs). Whatever is decided, the effect of major interest is the impact on the accuracy of the resulting fuzzy system to approximate the set of data patterns provided for learning the fuzzy system components, that is, the main concern is with the accuracy of the inverse steady-state model of the power unit [. In any case the performance is evaluated as a measure of the output approximation error. Ideally, it will always be preferred a low dimensional system requiring a small number of training iterations if the obtained approximation accuracy is reasonably close to that of a high dimensional system requiring a large number of training iterations. In what follows the effect of both the number of linguistic terms and the number of learning iterations on the approximation accuracy is shown. Note that since all three neuro-fuzzy controllers exhibited similar characteristics, only the results for FISU1 are provided. The membership functions for the power and pressure inputs are provided since, for all cases, the membership functions of the drum water-level deviation are singletons at L=0. The effect of the number of training epochs is illustrated for the sliding-pressure case with 3 input membership functions; the root squared mean error and the resulting membership functions are plotted for training during 20 epochs in Figures (4.10) and Figure (4.11). By inspection of these results, it can be seen that very good approximations of the inverse steady-state model of the plant can be obtained with low-dimension systems and small number of training epochs. This is due to the fact that the nonlinear steady-state behavior of the plant is kind that is the non-linearities are smooth and continuous.


٩٢

Figure (4.11) FISU1 membership functions for sliding-pressure case, 3 mf, 20 epochs.

Figure.(4.10) RSME for sliding-pressure case, 3, 5 and 7 mf, 20 epochs.

RSME


٩٣

4.4.3 Feedforward fuzzy systems

With the observations made in the last section, what rests to demonstrate is that the three FIS in the proposed controller can be satisfactorily constructed anywhere in the power- pressure operating window of the unit. To this aim, the design of FISU2 and FISU3 is presented along with the already shown FISU1 for the four cases being considered: high- pressure limit (HP), constant pressure (CP), sliding pressure (SP), and low-pressure limit (LP) [18]. In all cases, 3 membership functions and 10 training epochs were considered. First, Table 4.7 summarizes the approximation performance of each FIS in generating the corresponding steady-state feedforward control signals. Second, Figure (4.12) and Figure (4.13) show the resultant membership functions for the power and pressure inputs for FISU1. Then, Figures (4.14) through (4.16) show the fuzzy surfaces over the power-pressure plane for each FIS for the four power-pressure relationships being considered. Note that each FIS is graphically represented by a fuzzy inference surface, which is a more intuitive and the mean square errors for different membership functions are depicted on Table (4.7).

LP(m

f)

SP

(mf)

C

P(m

f)

H

P(m

f)

Power (MW) Figure (4.12) FISU1 power membership functions.


٩٤

It is obvious that when number of fuzzy sets associated for every crisp inputs increased, the MSES are decreased and vice versa. On the other hand, the tuned parameters increased as fuzzy sets increase, and this effect to the performance of controller, where its need the extra time for tuning its parameters. In our cases, we used the 3 fuzzy sets, because it gives the small MSES and also the number of parameters without effect on performance. The corresponding knowledge base is an alternative for the hereunder mentioned figures. This can be appreciated comparing Figure (4.14c) , Figure (4.15c), and Figure (4.16c) to Table 4.8, Table 4.9, and Table 4.10 respectively all representing FISU1, FISU2, FISU3 for the sliding pressure cases. Also, the graphical representation has the advantage that it changes relatively little with increasing number of membership functions, but the table will exhibit the curse of dimensionality problem (i.e., the number of rules increases geometrically with the number of membership functions).

Pressure (Bar) Figure (4.13) FISU1 pressure membership functions.

LP(m

f)

SP(

mf)

CP(

mf)

H

P(m

f)


٩٥

Table 4.7 MSES based on the number of fuzzy sets order model based on number of 3 for MSES

membership function Fuzzy sets

Pressure power Drum/level No of tuned parameters

2 1.8997 0.1411 0.0023 18 3 0.0387 0.0026 0 108 5 0.00046 0 0 600 7 0 0 0 1372

Figure (4.14) FISU1 fuzzy inference surfaces.


٩٦




٩٧

TABLE 4.8 FISU1 KNOWLEDGE BASE FOR SLIDING-PRESSURE: CASE

WITH 3 MF no Pd Ed Ld CI CP CE CL 1 mf1 mf1 mf1 0.7261 -0.5385 -0.77 -0.0018 2 mf1 mf1 mf2 9.9862 -7.4055 -10.5893 -0.0249

3 mf1 mf1 mf3 0.715 -0.5302 -0.7581 -0.0018 4 mf1 mf2 mf1 2.8681 -1.3331 0.6746 -0.0071 5 mf1 mf2 mf2 39.4475 -18.3351 9.2785 -0.0981 6 mf1 mf2 mf3 2.8243 -1.3127 0.6643 -0.007 7 mf1 mf3 mf1 0.8506 -0.5185 0.4771 -0.0021 8 mf1 mf3 mf2 11.6993 -7.1309 6.5623 -0.0291 9 mf1 mf3 mf3 0.8376 -0.5105 0.4698 -0.0021 10 mf2 mf1 mf1 1.2621 -0.2629 -1.2228 -0.0031 11 mf2 mf1 mf2 17.3591 -3.6164 -16.8184 -0.0432 12 mf2 mf1 mf3 1.2429 -0.2589 -1.2041 -0.0031 13 mf2 mf2 mf1 5.7845 -1.2329 2.0595 -0.0144 14 mf2 mf2 mf2 79.5588 -16.9566 28.3266 -0.1979 15 mf2 mf2 mf3 5.6962 -1.214 2.0281 -0.0142 16 mf2 mf3 mf1 2.9137 0.8541 1.6905 -0.0072 17 mf2 mf3 mf2 40.0749 11.7471 23.251 -0.0997 18 mf2 mf3 mf3 2.8692 0.8411 1.6647 -0.0071 19 mf3 mf1 mf1 0.4976 0.4815 -0.297 -0.0012 20 mf3 mf1 mf2 6.8433 6.6224 -4.0853 -0.017 21 mf3 mf1 mf3 0.49 0.4741 -0.2925 -0.0012 22 mf3 mf2 mf1 2.2511 2.378 0.4556 -0.0056 23 mf3 mf2 mf2 30.9616 32.7063 6.2659 -0.077 24 mf3 mf2 mf3 2.2168 2.3417 0.4486 -0.0055 25 mf3 mf3 mf1 1.4472 0.7626 1.1243 -0.0036 26 mf3 mf3 mf2 19.9046 10.4883 15.4633 -0.0495 27 mf3 mf3 mf3 1.4251 0.7509 1.1071 -0.0035


٩٨

Table 4.9 FISU2 KNOWLEDGE BASE FOR SLIDING-PRESSURE: CASE

WITH 3 MF no Pd Ed Ld CI CP CE CL 1 Mf1 mf1 mf1 1.3912 -1.2255 -1.553 -0.0035 2 Mf1 mf1 mf2 19.1339 -16.856 -21.3591 -0.0476 3 Mf1 mf1 mf3 1.3699 -1.2068 -1.5292 -0.0034 4 Mf1 mf2 mf1 4.1964 -1.7254 0.8025 -0.0104 5 Mf1 mf2 mf2 57.7165 -23.7311 11.038 -0.1435 6 Mf1 mf2 mf3 4.1323 -1.6991 0.7903 -0.0103 7 Mf1 mf3 mf1 0.8869 -0.4338 0.1808 -0.0022 8 Mf1 mf3 mf2 12.1985 -5.9668 2.487 -0.0303 9 Mf1 mf3 mf3 0.8734 -0.4272 0.1781 -0.0022

10 Mf2 mf1 mf1 2.8565 -0.4014 -2.8422 -0.0071 11 Mf2 mf1 mf2 39.2879 -5.5203 -39.0906 -0.0977 12 Mf2 mf1 mf3 2.8129 -0.3952 -2.7988 -0.007 13 Mf2 mf2 mf1 8.8974 -1.3961 2.4804 -0.0221 14 Mf2 mf2 mf2 122.3735 -19.2022 34.1149 -0.3044 15 Mf2 mf2 mf3 8.7616 -1.3748 2.4425 -0.0218 16 Mf2 mf3 mf1 3.6925 1.4368 1.431 -0.0092 17 Mf2 mf3 mf2 50.7856 19.7621 19.6821 -0.1263 18 Mf2 mf3 mf3 3.6361 1.4149 1.4092 -0.009 19 Mf3 mf1 mf1 1.4551 1.4169 -0.8938 -0.0036 20 Mf3 mf1 mf2 20.0131 19.4874 -12.2932 -0.0498 21 Mf3 mf1 mf3 1.4329 1.3952 -0.8802 -0.0036 22 Mf3 mf2 mf1 4.0297 4.1262 -0.5243 -0.01 23 Mf3 mf2 mf2 55.4242 56.7508 -7.2105 -0.1378 24 Mf3 mf2 mf3 3.9682 4.0632 -0.5163 -0.0099 25 Mf3 mf3 mf1 1.5967 0.6395 1.0102 -0.004 26 Mf3 mf3 mf2 21.9608 8.7957 13.8942 -0.0546 27 Mf3 mf3 mf3 1.5723 0.6297 0.9948 -0.0039


٩٩

4.5 Control loop Interaction and Tuning

The main difficulty for the proposed controller of multivariable processes is that of tuning the controllers because of control loop interaction due to the coupling dynamics among the process inputs and outputs. Interaction among the main inputs and outputs of a FFPU [10] and [11] was shown in appendix A, through the open-loop response to steps in the control valve demands. Now, the effects of control loop interaction for the same FFPU are shown through the closed-loop response to unit and ramp steps in the set-points as explained hereafter. The process operating window is partitioned to take into


no Pd Ed Ld CI CP CE CL 1 mf1 mf1 mf1 -0.7829 -1.39 0.4877 0.002 2 mf1 mf1 mf2 10.765 -19.1132 -6.7025 -0.0278 3 mf1 mf1 mf3 0.7705 -1.3681 -0.4796 -0.002 4 mf1 mf2 mf1 3.3318 -1.4276 0.1399 -0.0083 5 mf1 mf2 mf2 45.8253 -19.6343 1.9246 -0.114 6 mf1 mf2 mf3 3.2809 -1.4057 0.1378 -0.0082 7 mf1 mf3 mf1 0.6537 -0.3326 0.3968 -0.0016 8 mf1 mf3 mf2 8.9902 -4.5751 5.4577 -0.0224 9 mf1 mf3 mf3 0.6437 -0.3276 0.3908 -0.0016 10 mf2 mf1 mf1 1.2411 0.4231 -1.0925 -0.0031 11 mf2 mf1 mf2 17.069 5.8197 -15.0253 -0.0425 12 mf2 mf1 mf3 1.2221 0.4167 -1.0757 -0.003 13 mf2 mf2 mf1 6.4792 -0.8002 2.5651 -0.0161 14 mf2 mf2 mf2 89.1138 -11.006 35.2799 -0.2216 15 mf2 mf2 mf3 6.3803 -0.788 2.5259 -0.0159 16 mf2 mf3 mf1 3.2291 1.3005 1.4261 -0.008 17 mf2 mf3 mf2 44.4131 17.8875 19.6143 -0.1105 18 mf2 mf3 mf3 3.1798 1.2807 1.4043 -0.0079 19 mf3 mf1 mf1 0.9388 0.8565 -0.6007 -0.0023 20 mf3 mf1 mf2 12.9115 11.7808 -8.262 -0.0321 21 mf3 mf1 mf3 0.9244 0.8435 -0.5915 -0.0023 22 mf3 mf2 mf1 2.7353 2.6271 -0.0045 -0.0068 23 mf3 mf2 mf2 37.6202 36.1324 -0.0626 -0.0936 24 mf3 mf2 mf3 2.6935 2.587 -0.0045 -0.0067 25 mf3 mf3 mf1 1.4683 0.6575 1.0474 -0.0037 26 mf3 mf3 mf2 20.1942 9.0429 14.4062 -0.0502 27 mf3 mf3 mf3 1.4458 0.6474 1.0314 -0.0036


١٠٠

account the process nonlinear characteristics, and tuning is carried out by an Immune Genetic Algorithm (IGA) at the points of interest in the partitions [13]. In the previous section we discussed the process of tuning parameters in each of the premise and consequent parameters using gradient descent and LSE estimator respectively in the (FF) path, here we introduced another tuning tool to adapt the parameters of (FB) feed back fuzzy controller as depicted in chapter 3 Figure (4.1). The application of the IGA to the optimization of the scaling factors of inputs to control signal controller parameters was done by converting the scaling factor parameters associated for difference errors between set-points and actual values for pressure, power, and drum level, which are Scalf-P, Scalf-E Scalf-L to unsigned binary code with a length of 12 bits, where the binary string (chromosome) can be take the form

Lscalfscalfscalfs

011001101010100100101001010101:

The fitness of each possible solution S is obtained by evaluating a fitness function, which can be defined in terms of a performance index. In this case the fitness function is a simple function of the form [3]:

JJf

11)(

where J is any adequate performance index of the system response, for instance the integral absolute error (IAE) index of the error response, e(t), of the controlled system output to a set-point step, from the initial time ti to the final time tf:

dtteJf

i

t

t )(

With these definitions, the implementation of the IGA start with Produce an initial population of randomly generated sets of parameters (Scalf-P, Scalf-E Scalf-L .The complete algorithm can be done as explained in details in chapter 3 section 3.2. 4.6 Performance of Drum Boiler- Turbine Unit Based on MV-ANFIS

Controller

4.6.1 Step Load Response of Third Order Drum Boiler Model Process optimization under changing operating scenarios will certainly demand operation at different operating points. This situation leads to another


١٠١

drawback of the tuning configuration. The unit performance will not be the same at different operating points. Figure (4.17) to Figure (4.19) shows the FFPU responses at different changes of operation under introduced MV-ANFIS controller. Figure (4.17) shows the step responses at the operating point defined by E=66.65 MW, P= 108Bar, and L=0 m, to E= 120 MW, P= 120 Bar, and L=.75 m Figure (4.18) shows the step responses at the operating point defined by E=66.65 MW, P= 108 Bar, and L=0 m, to E= 129 MW, P= 140 Bar, and L=1 m Figure (4.19) shows the step responses at the operating point starting from full load defined by E=129 MW, P= 140 Bar, and L=1 m to low load defined by E=66.65 MW, P= 108Bar, and L=0 m. In each figure, the graphs in the left column present the FFPU response to the steps, and the graphs in the right column show the behavior of the associated control signals. Each row corresponds to the variables is paired through the control loop. As seen from Figure (4.19), the results with 5 fuzzy sets give best performance rather than given by using 2 fuzzy sets and 3 fuzzy sets. The results show that the output responses track the set points in all cases, even in case of changing from low to full load and vice versa, and all control signal changes within specific limits. The MSES and percentage errors for three outputs at different changing in the set point is depicted in Table.4.11. Results also show that the strongest and most disturbing interaction is from the pressure control loop to the power output, which normally require the tightest control for either tracking or regulation. Second in importance is the interaction from the power loop to the pressure output, which may adversely affect the physical condition of the plant equipment. In the remaining parts of this chapter, there will be symbols for pressure (P), Power (E), drum level (L), which are the same as y1, y2, and y3 respectively.


١٠٢

Table. 4.11 MSES and percentage of errors 3 order model with tuned parameters

Change of set point Multivariable ANFIS controller 3 order model with tuned parameters

Pressure (P)

Power (E)

Drum (L)

MSES (P)

MSES (E)

MSES (L)

% (P) errors

% (E) errors

% (L) errors

± 32 Bar ± 18 Mw ± .25 m 4.21E-01 9.26E-02 3.47E-05 -2.66E-01 9.33E-03 2.46E-03

± 12 Bar ± 55 Mw ±.75 m 4.12E-01 4.94E-02 3.47E-05 -2.85E-01 1.46E-02 9.04E-04

± 32 Bar ± 62 Mw ± .75 m 1.22E-04 4.75E-01 8.42E-01 5.81E-01 -2.64E-01 2.60E-01

± 32 Bar ± 62 Mw ± 1 m 4.55E-01 8.35E-01 3.49E-04 -2.44E-01 2.44E-01 2.66E-02

Figure (4,17) System response to changes in the pressure, power &drum level (± 12 Bar, (± 55 Mw, ±0 .75m)

y1

y2

y3

u1

u2

u3

Time(min)

P(Bar)

E (Mw)

L (m)

Fuel

flow

rate

C

ontro

l va

lve

posi

tion

Feed

wat

er fl

ow ra

te


١٠٣

P(Bar)

E (Mw)

L (mm)

Figure (4.19) System response to changes in the pressure, power &drum level (From full -to low load) at different fuzzy sets

y1

y2

y3

u1

u2

u3

Time(min)

y1

y2

y3

u1

u2

u3

Figure.(4.18) System response to changes in the pressure, power &drum level ( From low-to full load)

Time(min)

P(Bar)

E (Mw)

L (m) Fu

el fl

ow ra

te

Con

trol

valv

e po

sitio

n Fe

edw

ater

flow

rate

Fu

el fl

ow ra

te

Con

trol

valv

e po

sitio

n Fe

edw

ater

flow

rate


١٠٤

4.6.2 Ramp Response for Third Order Drum Boiler Model

Certainly, nice step responses are an indicator of good control performance. Most control systems of all kinds are usually demonstrated using this approach. Unfortunately, for the case of nonlinear MIMO systems subject to wide-range reference-tracking operation requirements it is not sufficient to guarantee good performance. In the case of FFPUs there are several practical considerations that prevent the utilization of step responses; ramp responses are preferred. Strictly speaking, ramp responses provide the same amount of information over the system as step responses do. Step responses will be used in the remaining of this work to exhibit the behavior of the system solely in simulation experiments. Now, the ramp response of the FFPU [17] is investigated for a not very demanding ramp-up loading maneuver using the same controller parameters as in Section 4.6.1, which provided excellent step responses. Power is required to increase from 66.65 MW (half load) to 85 MW in 150 seconds that is a 6.25% power set-point change with a rate of 2.5 % min, which would be normally considered an easy test. Accordingly, the pressure set-point is obtained from the unit load demand through the mapping:

651018065150

d

That implements a typical sliding-pressure operating policy, which is a fairly

common practice schemes. As can be seen from the graphs in Figure (4.20),

the power set-point tracking is just good, with an excellent control activity.

Pressure set-point tracking is also good, and control activity is excellent. The

oscillations in the water level are fine and the control activity is also

excellent. Figure (4.21) shows another set point changes , we see that despite

the ramp demand changes from low to full level, all responses track the set

points also good ,it is interest to know that all control signals is kept within

safe limits.


١٠٥

y1

y2

y3

u1

u2

u3

Figure (4.20) Ramp load tracking with tuned controller parameters. Time(sec)

Time(sec) Figure (4.21) Ramp load tracking with tuned controller parameters from low to full load.

y1

y2

y3

u1

u2

u3

P(Bar)

E (Mw)

L (m)

P(Bar)

E (Mw)

L (m)

Fuel

flow

rate

C

ontro

l va

lve

posi

tion

Feed

wat

er fl

ow ra

te

Fuel

flow

rate

C

ontro

l va

lve

posi

tion

Feed

wat

er fl

ow ra

te


١٠٦

4.6.3 Step Load Response of Seven Order Drum Boiler Model

In these tests, the proposed control scheme is tested using the 7th order Bell and Astrom boiler [15]. As mentioned above, the power(y2), pressure(y1), and drum water level (y3)configured are controlled using a set of controlled inputs; the steam throttle valve (u2), fuel flow (u1), and feed water flow (u3). The boiler model in this case has a severe scaling problem, where the input variables are normalized but the outputs are not as described in chapter-4. To test the accuracy of the proposed Multi-variable ANFIS controller (MV-ANFIS) scheme, set of tests were performed at low load and full load using the boiler system. These tests are described as follows: Figure (4.22) describes the system responses with changes in the boiler operating points (± 15 Mw, ± 4 bar, ±60 cm), with scaling factor for pressure, power and drum level are 0.7449, 0.7128 and 0.00992 respectively and the MSES

T

1k

2Y[k])-(Yd[k]T1errorMS

for pressure, power and drum level respectively are 0.0062, 0.008131, and .11436. Figure(4.23) describes the system responses with changes in the boiler operating points (± 35 Mw, ± 7 bar, ±85 cm), with scaling factor for pressure, power and drum level are 0.7449, 0.7128 and 0.00992 respectively and the MSES for pressure, power and drum level respectively are 1.43E-02, 2.22e-01, and 2.72e+00. Figure (4.24) describes the system responses with changes in the boiler operating points (± 15 Mw, ± 12 bar, ±85 cm), with scaling factor for pressure, power and drum level are 0.7449, 0.7128 and 0.0992 respectively and the MSES for pressure, power and drum level respectively are 1.00e-04, 0 .09444, and 1.44e-01. Figure (4.25) shows the system responses to changes in pressure, power, and drum level from low to full load. The scaling factor for pressure, power and drum level are 0.7189, 0.7189, and 0.0058 respectively and the MSES values for pressure, power and drum level receptively are 1.15e-01, 1.32e+00, and 1.33E+01. The MSES and percentage errors for three outputs at different changing in set point is depicted in Table.4.12 The MSES for different fuzzy sets are showed in Table 4.13, where the values of MSES are nearly close to each other. The initial scaling factors of (FF/FB) of proposed controller are depicted in Table. 4.14


١٠٧

y2

y3

y2

y3 Time(min) Figure (4.22) System response to changes in the pressure, power &drum level (± 4 Bar, ± 15 MW, ±65 cm)

y1

y2

y3

u1

u2

u3

u1

u2

u3

Figure (4.23) System response to changes in the pressure, power &drum level (± 7 Bar, (± 35 Mw, ±.85 cm)

y1

y2

y3

Time(min)

P(Bar)

E (Mw)

L (cm)

P(Bar)

E (Mw)

L (cm)

Fuel

flow

rate

C

ontro

l va

lve

posi

tion

Feed

wat

er fl

ow ra

te

Fuel

flow

rate

C

ontro

l va

lve

posi

tion

Feed

wat

er fl

ow ra

te


١٠٨

Time(min) Figure (4.24) System response to changes in the pressure, power &drum level (± 12 Bar, (± 15 Mw, ±85 cm)

y1

y2

y3

u1

u2

u3

P(Bar)

E (Mw)

L (cm)

Fuel

flow

rate

C

ontro

l va

lve

posi

tion

Feed

wat

er fl

ow ra

te

P(Bar)

E (Mw)

L (cm)

Time(min) Figure (4.25) System response to changes in the pressure, power &drum level (From low-to full load)

y1

y2

y3

u1

u2

u3

Fuel

flow

rate

C

ontro

l va

lve

posi

tion

Feed

wat

er fl

ow ra

te


١٠٩

Table 4.13 MSES for seven order model based on number of membership function

Fuzzy sets

Pressure power Drum/level No of tuned parameters

2 0.003262 0.045722 1.719958 32 3 0.003252 0.045721 1.504465 108 5 0.003251 0.045721 1.504465 600

Table. 4.14 Scaling factors of (FF/FB) of proposed controller Scale

factor for drum leve

Scale factor for

power

Scale factor for pressure

Change of set point

Multivariable controller

0.0373 0.7189 0.7956 Low-high 0.8726 0.7189 0.7956 Low-medium 0.8734 0.7189 0.7956 High- medium 0.8782 0.7189 0.7956 High- Low

three order MV-ANFIS

0.0709 0.8734 0.7413 Low-high 0.2935 0.8734 0.7413 Low-medium 0.0944 0.8734 0.7414 High- medium 0.087 0.8734 0.7413 High- Low

seven order MV-ANFIS

Table 4.12 MSES& percentage of errors for seven order model

Change of set point Multivariable ANFIS controller 3 order model with tuned parameters

Pressure (P)

Power (E) Drum

(L)

MSES (P)

MSES (E)

MSES (L)

% (P) errors

% (E) errors

% (L) errors

± 4 Bar ± 35 Mw ± 65cm 4.59E-03 3.05E-02 2.45E+00 -6.11E-

04 9.06E-03 5.37E-01

± 7 Bar ± 35 Mw ± 85 cm 1.43E-02 2.22E-01 2.72E+00 -8.01E-

03 1.24E-01 1.64E+00

± 12 Bar ± 35 Mw ± 85 cm 4.37E-02 2.21E-01 4.24E+00 1.07E-02 1.45E-01 2.58E+0

0

± 19 Bar ± 75 Mw ± 135 cm 1.15E-01 1.32E+0

0 1.33E+01 -6.27E-02 3.04E-01 7.23E+0

0


١١٠

4.7 Effect of Immune genetic algorithm for tuning The adjusted parameters of the fuzzy-PI controllers (FB) using an Immune Genetic Algorithm (IGA) tuning for the power-pressure operating policy of the unit changes and upon request by the operator allows optimization of one or more scaling factor parameters, as required, and it is used off-line to speed up the parameter tuning by applying it sequentially through the steps of the previously described tuning procedure. By comparing the responses of the proposed (MV-ANFIS) controller with and without tuning based on (IGA) for the third and seven order drum boiler model, we show that in all cases starting form low to full load, and starting from full to low load, the responses under genetic tuning is the best as can be seen from the following sample examples, note all dash line represents the results with (IGA).

Figure (4.26) shows the system responses under low level conditions where pressure set-point =108 Bar, and power = 65 Mw, and drum level at zero m. We show that all system outputs track the set-points in case of proposed controller with and without tuning of the FB controller, but we can see the smoothing of responses especially in control signals in case of tuning with genetic as depicted in dashed line.

Figure (4.27) shows the system responses under high level conditions where pressure set-point =140 Bar, and power = 129 Mw, and drum level at .98 m, we show also that all system outputs track the set-points in case of proposed controller with and without tuning of the FB controller, the smoothing of responses is obviously in throttle valve (u2) with genetic tuning as depicted in dash line.


١١١

y1

y2

y3

u1

u2

u3

Figure (4.26) System response at low load with and without (IGA) Time(min)

Time (min)

y1

y2

y3

u1

u2

u3

P(Bar)

E (Mw)

L (m)

P(Bar)

E (Mw)

L cm)

Fuel

flow

rate

C

ontro

l va

lve

posi

tion

Feed

wat

er fl

ow ra

te

Fuel

flow

rate

C

ontro

l va

lve

posi

tion

Feed

wat

er fl

ow ra

te

Figure (4.27) System response at high load with and without (IGA)


١١٢

4.8 Application of Cascaded Distributed Multivariable ANFIS (CD-MV-ANFIS)for drum boiler turbine units The (CD-MV-ANFIS) controller scheme for drum boiler turbine units consists of three main controllers, drum water level, power, and pressure. This scheme included a set of sub controllers put in the cascaded form each has two inputs and on outputs in the form of Multi-input Single-output (MISO) structure with (FB) PI fuzzy controller as in case of the proposed (MV-ANFIS) in chapter 3. The proposed control scheme remodels the conventional MV-ANFIS controller that depicted in section 2 to the cascaded distributed form as describe in Figure (4.28) as follows: A comparison between ANFIS controller and different kinds of controllers are present here to show the effectiveness and accuracy of proposed controller. 4.8.1 Controller third and seven order Drum Boiler processes

A controller structure that has few parameters is constructed. Since the controller has two inputs and three MFs on each input, its rule base consists of nine rules. A code for parameter update is written according to the backpropagation algorithm explained in chapter2. For instant the fuzzy inference system for control signal u1 (FISU1),ie , the knowledge base for loop1 is as follows: For instant the FISU1 knowledge base loop1 as follows: R1: IF x14(k) is S and ( Δx3(k)) is S THEN f1=c1o+c11 x14(k)+c12 Δx3(k)

R2: IF x14(k) is S and ( Δx3(k)) is M THEN f1=c2o+c21 x14(k)+c22 Δx3(k)

R3: IF x14(k) is S and ( Δx3(k)) is B THEN f1=c3o+c31 x14(k)+c32 Δx3(k)

R4: IF x14(k) is M and ( Δx3(k)) is S THEN f1=c4o+c41 x14(k)+c42 Δx3(k)

R5: IF x14(k) is M and ( Δx3(k)) is M THEN f1=c5o+c51 x14(k)+c52 Δx3(k)


١١٣

Figu

re (4

.28)

The

pro

pose

d (C

D-M

VA

NFI

S) c

ontro

l sch

eme

for b

oile

r sys

tem

s


١١٤

R6: IF x14(k) is M and (ΔX3 (k)) is B THEN f1=c6o+c61 x14(k) +c62 ΔX3(k)

R7: IF x14(k) is B and (ΔX3 (k)) is S THEN f1=c7o+c71 x14(k) +c72 ΔX3 (k) R8: IF x14(k) is B and (ΔX3 (k)) is M THEN f1=c8o+c81 x14(k) +c82 ΔX3(k) R9: IF x14(k) is B and (ΔX3(k)) is B THEN f1=c9o+c91 x14(k)+c92 ΔX3(k)

The FISU1 after training is as follows R1: IF X14(k) is S and (ΔX3 (k)) is S THEN f1=0.8426+0.20658 X14(k) + 0.5400ΔX3 (k) R2: IF X14(k) is S and (ΔX3 (k)) is M THEN f1=0.3810+0.8076 x14(k) +0.6773Δx3 (k) ………………………………… ………………………………… R9: IF X14(k) is B and (ΔX3 (k)) is B THEN f1= 0.1223+0.1806X14(k) + 0.1767ΔX3 (k) The changes of consequent parameters through application phase for three loops are given in Figure (4.29)

Figure (4.29) Initial and final values of consequent parameters within 5 fuzzy sets (a) for pressure loop (b) for power loop (c) for drum level loop

(a)

(b)

(c)


١١٥

4.8.2 Effectiveness of Membership Function Number and Tuning Type In what follows the effect of the number of linguistic terms on the approximation accuracy for two models is depicted in Table.4.15,the (MSES) in case of using 3, 5, and 7 membership functions is included. Despite the (MSES) associated with 7 fuzzy sets is very small, the one given by 3 fuzzy sets is also small and accepted. The comparison between performance of proposed controller based on, without tuning, using genetic, and immune genetic is shown in Table.4.16. We see that the MSES and percentage of errors is very small in case of tuning based on immunity system for 3rd model and 7th order model. Also Figures.(4.30) and (4.31) show the performance at starting points using 3, 5, and 7 fuzzy sets for both 3rd model and 7th order model. From these Figures we can see that all actual output responses (pressure, power, and drum water level) reach its desired values at 10 minute. The performance of the proposed controller tuned by an immune genetic algorithm (IGA) has small overshoot and steady sate error is for pressure, power, and drum water level as seen in Figure (4.32).

Figure(4.30)Performance of proposed controller based on Immune Genetic Algorithm using different fuzzy sets at low load for third order model

u1

u2

u3

7 fuzzy set 5 fuzzy set 3 fuzzy set

Time(min)

y1(Bar)

y2(Mw)

y3(Mm)

P(Bar)

E (Mw)

L (m)

Fuel

flow

rate

C

ontro

l va

lve

posi

tion

Feed

wat

er fl

ow ra

te


١١٦

Table. 4.15 Effectiveness of fuzzy set on performance accuracy for two models

MSEs and % of errors with different fuzzy sets based on immune genetic

algorithm Pressure(p) Power(E) Level(L)

Model type

MSES %error MSES %error MSES %error Fuzzy set

0.978 1.7140 0.0020 0.0840 1 *e-3 0.0440 3 0.102 0.4310 0.0001 0.0140 .00002 0.0070 5

3 order model 0.007 0.0190 0.00008 0.0190 .00001 0.0040 7

0.016 0.2330 1.44*e-6 0.4100 0.9819 0.0813 3 .0000 0.0320 1.45*e-6 .0070 0.4306 0.0262 5

7order model

.0000 0.0470 1.45*e-6 0.0040 .4401 0.0287 7

Table. 4.16 MSES and % of errors with different cases based on tuning tools

MSES and % of errors with different cases based on tuning tools Pressure(p) Power(E) Level(L)

Adapting parameters

MSES %error MSES %error MSES %error Without tuning

1.119 1.562 0.104 0.509 0.104 0.052

Using genetic

0.48 1.325 .123 .204 .005 0.0045

3 order model Immune

genetic 0.23 1.002 0.011 0.233 .0001 0.0004

Without tuning

0.105 0.473 1.4501 0.41 0.9819 0.0813

Using genetic

0.066 0.486 1.223 0.202 0.8845 0.0728

Immune genetic

0.016 0.233 1.101 0.057 0.5388 0.0475

7order model


١١٧

u1

u2

u3

7.5 Simulation results for boiler systems

Figure (4.31)Performance of proposed controller based on immune genetic algorithm using different fuzzy sets at low load 7order model

y1

y3

u2

u3

y2

u1

u2

u3

u1

Figure (4.32) Performance of proposed controller based on genetic and an immune genetic algorithm using for 3rd order model

Time(min)

Time(min)

y1(Bar)

y2(Mw)

y3(cm)

y1(Bar)

y2(Mw)

y3(mm)

P(Bar)

E (Mw)

L (cm)

Fuel

flow

rate

C

ontro

l va

lve

posi

tion

Feed

wat

er fl

ow ra

te

Fuel

flow

rate

C

ontro

l va

lve

posi

tion

Feed

wat

er fl

ow ra

te

P(Bar)

E (Mw)

L (cm)


١١٨

In these tests, the proposed CD-MV-ANFIS scheme is tested using the boiler system, a set of tests at low and full load for 3 and 7 order model are performed to test the reliability of the proposed scheme at different circumstances. The percentage of errors and MSES for two models is depicted in Table.4.17 and Table. 4.18 at different changes of set points. Some of the above changes are depicted as follow: Figure.(4.33) shows the system responses under low level conditions for 3 order model where pressure set-point =108 Bar, and power = 65 MW , and drum level at zero m , we show that all system outputs track the set-points in case of proposed controller with without tuning of the FB controller by immune genetic algorithm.. Figure.(4.34) shows the system responses under low level conditions for 7 order model where pressure set-point =108 Bar, and power = 65 MW , and drum level at 85 cm , we show also that all system outputs track the set-points in case of proposed controller with immunity tuning of the FB controller

.

Table. 4.17 MSES& percentage of errors for third order using CD-MVANFIS controller

Change of set point Multivariable ANFIS controller third order model with tuned parameters

Pressure (P)

Power (E)

Drum (L)

MSES (P)

MSES (E)

MSES (L)

% (P) errors

% (E) errors

% (L) errors

± 32 Bar

± 18 Mw ± .25m 4.1E-01 4.9E-02 3.4E-05 -2.8E-01 1.47E-02 9.0E-04

± 12 Bar

± 55 Mw ±.75m 4.8E-02 6.2E-01 9.7E-05 -5.9E-02 1.65E-01 1.3E-02

± 32 Bar

± 62 Mw .75 m 4.8E-01 8.4E-01 6.4E-05 -2.6E-01 2.60E-01 1.2E-02

± 32 Bar

± 62 Mw 1 m 4.7E-01 8.3E-01 2.9E-04 -2.7E-01 2.72E-01 2.6E-02


١١٩

Table. 4.18 MSES& percentage of errors for 7th order using CD-MVANFIS controller

Change of set point Multivariable ANFIS Controller 7 order model

Pressure (P)

Power (E)

Drum (L)

MSES (P)

MSES (E)

MSES (L)

% (P) errors

% (E) errors

% (L) errors

± 4 Bar

± 35 Mw ± 65cm 4.4E-03 2.5E-02 2.6E+0 -5.4E-03 3.4E-02 9.3E-01

± 7 Bar

± 35 Mw ± 85 cm 1.4E-02 2.3E-01 2.24E+0 8.1E-03 1.37E-01 8.3E-01

± 12 Bar

± 35 Mw ± 85 cm 4.3E-02 2.2E-01 1.9E+0 1.0E-02 1.55E-01 2.6E+00

± 19 Bar

± 75 Mw ± 135cm 1.1E-01 1.1E-01 1.3+0 8.5E+00 3.1E-01 4.2E+0

Figure.(4.33) System response to changes in the pressure, power &drum level (± 32 Bar, (± 65 Mw, ±1 m) for third order model

y1

y2

y3

u1

u2

u3

Time(min)

P(Bar)

E (Mw)

L (m)

Fuel

flow

rate

C

ontro

l va

lve

posi

tion

Feed

wat

er fl

ow ra

te


١٢٠

The MSE of (pressure, power, and drum/level) for third, and seven order drum model are depicted in Figure (4.35). The left hand side of figure represents the MSE of three outputs of 3 order model, where, Column (1) represents drum Column (2) represents power Column (3) represents pressure From this figure we can see that the MSE based on immune genetic tuning are very small compared to genetic tuning. Also the MSE for all outputs of seven order model based on immune tuning

are smallest one as depicted in right hand side Figure (4.35).

.

Figure (4.34 System response to changes in the pressure, power &drum level (± 7 Bar, (± 15 Mw, ±85 cm) for seven order model

y1

y2

y3

u1

u2

u3

Time(min)

P(Bar)

E (Mw)

L (cm)

Fuel

flow

rate

C

ontro

l va

lve

posi

tion

Feed

wat

er fl

ow ra

te


١٢١

4.8.3 Comparison between two approaches 1 and 2. The approach 1(CD-MV-ANFIS) for third order model solved the problems of huge number of fuzzy rules, premise parameters, and consequence parameters, where these parameters are very large by using the MV-ANFIS controller. The detailed comparison between two controllers is depicted in Table.4.19, despite of the total par to be tuned in case of using CD-MV-ANFIS controller is very small compared to that in case of MV-ANFIS controller, the average mean squared errors were nearly equals in two controllers as showed in Table.4.19. Here also for controlling the seven order model the rules number and total parameters given by CD-MV-ANFIS is very small compared to that for MV-ANFIS controller, besides the average of MSES errors in all outputs at different set-point are close for both approaches 1and 2( CD-MV-ANFIS and MV-ANFIS) controllers as seen in Table.4.20.

Figure.(4.35) MSE for drum boiler using proposed controller based on tuning type left column for three order model, right column seven order model


١٢٢

Table.4.19 Comparison of performance accuracy between MV-ANFIS and

CD-MV-ANFIS controller for third order model CD-MV-ANFIS MV-ANFIS

Fuzzy sets 3 3 Premise parameters 18 27

Consequence parameters 27 108 Total parameters 45 135

MSES error% MSES error% pressure 3.22E-01 -5.35E-02 3.52E-01 -2.20E-01

power 3.63E-01 9.82E-04

5.89E-01 1.78E-01

Average of

mean square errors& error%

Drum/l 2.11E-01 7.25E-02 1.23E-04 1.31E-02

Table.4.20 Comparison of performance accuracy between MV-ANFIS and CD-MV-ANFIS controller for seven order model

CD-MV-ANFIS MV-ANFIS Fuzzy sets 3 3

Premise parameters 18 27 Consequence parameters 27 108

Total parameters 45 135 MSES error% MSES error%

pressure 4.45E-02 -1.52E-02 4.41E-02 2.14E-02

power 4.50E-01 1.45E-01 4.46E-01 1.53E-01

Average of

mean square errors& error%

Drum/l 5.11E-01 2.99E-01 1.96E-01 2.15E-01


١٢٣

4.9 Comparing results with other controllers To show the effectiveness of the proposed MV-ANFIS controller, it is interested to study distinguishes between the introduced MV-ANFIS with other controllers (linear quadratic regulators (LQR) [27] and fuzzy controller [37]. To evaluate the performance of power plant under the proposed controller a different cases (different working conditions) are studied and compared to linear quadratic regulators (LQR) and fuzzy controller based on inverse model of boiler-turbine system. The initial condition is considered to be as the vectors as in Eq (4.50 to (4.52) in all cases. X0= [90 45 460.24] (4.50)

Y0= [90 45 0] (4.51)

U0= [0.2436 0.6094 0.3066] (4.52)

The steady-state initial condition is determined to be different from the controller design points. Since there is a mapping between desired power and the drum pressure, the set points for both must be determined with regard to each other. Three different cases used to evaluate the performance of proposed controller are as follows:

Set-point changes Pressure(kg/cm) Power(MW) Drum/level(m) Case(1) 90 to 110 45 to 70 Zero Case(2) 90 to 125 45 to 100 zero Case(3) ±90 to ±110 ±45 to ±70 zero

Figure.(4.36) shows the system response under different controllers. It is clear that system response under MV-ANFIS controller inverse model controller is much faster than the LQR controller, and fuzzy controller. Besides, in both cases drum pressure dos not have oscillations which are acceptable. Furthermore, drum water level deviation reaches zero much faster in case of proposed controller as depicted in Figure.(4.37). Controlling inputs variations for MV-ANFIS, LQR, and fuzzy controllers are showed in Figures.(4.38 ) to (4.39). In all cases the controlling inputs reaches its set points smoothly and faster using MV-ANFIS controller as showed. The mean squared errors for the three cases are depicted in Table. 4.21. From this table we can see that the all mean square errors associated for MV-ANFIS controller are very small compared to that given by other controllers.


١٢٤

Figure.(4.36) Compare system response under LQR , fuzzy, and ANFIS controller, where drum pressure and power changes from 90 to 125, and from 45 to 100 respectively .

Wat

er le

vel (

m)

Figure.(4.37) Compare system response under LQR , fuzzy, and ANFIS controller, in case of equal drum water level deviation equal zero .

Time (min)

Time (min)


١٢٥

Figure.(4.39) Controlling inputs for u2 (throttle valve position ) using ANFIS, LQR, and fuzzy controllers.

Figure (4.38) Controlling inputs for u1(fuel flow rate) using ANFIS, LQR, and fuzzy controllers.

Time (min)

Time (min)

Fuel

flow

rate

C

ontro

l va

lve

posi

tion


١٢٦

Figure (4.40) Controlling inputs for u3 (feedwater flow) using ANFIS, LQR, and fuzzy controllers.

Table 4.21 Compared MSES of the proposed controller with different controllers at different ranges of operation

LQR FUZY MV-ANFIS 3.407E-01 2.550E-01 1.158E-03 Pressure 1.382E-01 6.250E-02 8.772E-02 Power 1.554E-05 1.749E-05 9.328E-06 Drum

Case(1)

9.212E-01 1.475E+00 3.032E-01 Pressure 8.800E-02 2.080E-01 4.992E-03 Power 6.056E-05 2.586E-04 6.051E-05 Drum

Case(2)

8.475E-01 8.887E-01 9.801E-02 Pressure 2.725E-01 2.788E-01 5.610E-02 Power 5.827E-05 8.022E-05 2.414E-05 Drum

Case(3)

Time (min)

Feed

wat

er fl

ow ra

te


١٢٧

Another comparison was made using three different kinds of controllers for third order drum boiler unit, the first is the fuzzy controller[43], the second is the adaptable nonlinear controller (ANC) [58]and the third is the exact feedback linearization (EFL) controller [36], all with same input variables. From Figure (4.40), we show that the output pressure(y1) given by CD-MV-ANFIS able to track the changes of set points with small over shoot than other controllers, also the changing on control signal (fuel flow rate (u1)) is very smooth. The performance of the proposed controller reveals that the output demand power (y2) correlated very well with set point, and changes of control valve position (u2) is very good compared to that of other controller as depicted in Figure (4.40). Due to the changes of pressure and power outputs, the drum level (y3) changed only in points of change without any fluctuations, rather than other controllers as seen in Figure (4.40). The MSES associated for different previous controllers emphasize that the proposed CD-MV-ANFIS controllers is best controllers from all others in case of all outputs as we see in Figure (4.41). The comparison between the proposed controller and fuzzy using MSES for the seven order model is also depicted in Figure (4.42), the values shown that the proposed controller is better than fuzzy controller for all set points


١٢٨

Figure (4.41) Comparison between the proposed CD-MV-ANFIS controller with adaptable nonlinear, effective feedback, and fuzzy controllers for third order model

y1

y2

y3

u1

u2

u3

Time (sec)

Figure (4.42) Comparing MSE for using (ANFIS, adaptable nonlinear, effective feedback, and fuzzy) controllers for third order model

00.0004

0.00080.00120.00160.002

MSE

ANC EFL FUZZY ANFIS

Time (sec)

P(Bar)

E (Mw)

L (m)


١٢٩

power

power

1.04E-02 1.04E-02 1.04E-02 1.04E-02 1.04E-02 1.04E-02 1.04E-02

fuzzy

anfisfuzzyanfis

pressure

pressure

0.00E+00 1.00E-03 2.00E-03 3.00E-03 4.00E-03

fuzzy

anfisfuzzyanfis

drum/level

drum/level

0 0.02 0.04 0.06 0.08 0.1

fuzzy

anfis fuzzy

anfis

Figure (4.43) Comparing MSES for all outputs using the proposed MV-ANFIS,

and fuzzy) controllers for seven order model

MSE

MSE

MSE


١٣٠

4.10 Summary This chapter presented an application of the proposed two approaches 1 and 2 for the third and seven orders of a 160 Mw nonlinear boiler-turbine unit. Simulation results revealed that the two proposed controllers were capable of closely reproducing the optimal performance. All different demands of power grid, such unit step and ramp was studied. These results also revealed the robustness of the introduced controllers for variations in plant set points. In addition to the desired performance and robustness, these proposed controllers have added implementation quality. The comparison of the performances of two proposed controllers (MV-ANFIS and CD-MV-ANFIS) on two types of drum boiler turbine units was made. The results showed that the performance of two controller are much close to each other, besides the reduction of tuning parameters as well as the consuming time for CD-MV-ANFIS controller was achieved. Also, the comparison studies for different controllers emphasize that the proposed controllers have capability to handle any variation on grid demand over a wide range operations .without any effect on safety of valves.

Chapter 5 Application of Proposed Approaches 1 and 2 to

a Greenhouse Climate System

In this chapter, the greenhouse climate model introduced and explained as a one of industrial process. The greenhouse system (GH) is physical non-linear dynamical system, multi-input multi-output (MIMO), and includes the internal interaction between input output parameters. The two approaches (MV-ANFIS and CD-MV-ANFIS) introduced also for a greenhouse system (GH) to emphasis the accuracy of two approaches for controlling non-linear process. An immune genetic algorithm (IGA) for tuning the MV-ANFIS and CD-MV-ANFIS controller parameters is also proposed . The CD-MV-ANFIS controller used to enhance the performance of a greenhouse climate control system, where controller parameter tuned by Blend Immune Genetic Algorithm (BIGA).In the proposed algorithm, some of the main characteristics of the immune system were used to enhance the GA algorithm .The introduce (CD-MV-ANFIS) and (MV-ANFIS) scheme was compared where the results show that the best performance achieved by our two proposed schemes as described later. Also the comparison between the CD-MV-ANFIS and (MV-ANFIS) controllers and different kinds of controllers are present here to show the effectiveness and soundness of proposed controllers. 5.1 Introduction Going back 2000 years in the literature, it can be discovered that the Romans already recognized the benefits of protecting crops from unfavorable outdoor climatic conditions by means of light transmitting shelters to facilitate the cultivation of exotic crops. Moreover, people seemed to be aware of the fact that crop productivity could be improved by actively modifying the climate in these shelters. Also, the people seemed to be aware of the fact that crop productivity and quality could be improved by actively modifying the climate in these shelters [54]. However, the limited qualitative knowledge of the processes involved in the crop growth and production, as well as the poor technical status of the equipment available for climate conditioning, did not allow for any advanced climate control strategies. The climate in a protected crop cultivation has a great influence on the plant growth, and hence on fertility, production yield, quality, and maintenance processes of the plants. Environmental control is a central

CHAPTER 5 APPLICATION OF PROPOSED APPROACH 1 AND 2 TO A Greenhouse Climate System

١٣٣

feature of modern production systems, whether within plant growth chambers, greenhouses, or totally closed environments such as those envisioned for food production and waste treatment in space. Greenhouses provide a protected environment in which crops can be grown under a tightly controlled climate. Since the control of the greenhouse is costly, its optimization has been studied by several authors [94] and [93]. Optimization requires models of the greenhouse and of the crop, but because of the complex interaction between the crop and the greenhouse and for simplicity, the crop model is disregarded. The greenhouse models described in the literature can be classified into two categories: physical models, and black-box models. Physical models are based on energy balance equations between the indoor air, the outdoor air, and the greenhouse soil (in which heat storage takes place). In order to be accurate, such models require the calibration of a relatively large number of parameters such as cover transmissivity, and heat transfer coefficient, air-soil heat transfer coefficient, soil heat capacity, etc. The calibration of such parameters requires time-consuming dedicated experiments. In order to avoid calibration of these physical parameters, accurate modeling of a greenhouse is essential for the evolution of greenhouse control towards high quality intelligent systems. Modeling such a complex system cannot be done by simply dismissing the problem structure, the use of black-box neural network models was suggested by [77]. In this chapter, the fault detection and isolation systems are described in section 5.3. In section 5.4, hierarchical decomposition of greenhouse climate management is presented. The control of the greenhouse ventilation model is detailed in section 5.5. A summary of the chapter is given in section 5.6 5.2. Fault detection and isolation systems Automatic controlled systems are vulnerable to faults. Due to the complexity of modern control systems, and the growing demand for safety, quality and cost efficiency, the last 20 years have witnessed a growing interest for automatic failure diagnosis. Once the basis of failure detection and isolation in linear time invariant systems was firmly established, subsequent research focused on (1) robustness of the residuals in the presence of modeling errors, and (2) generalization to non-linear (or time varying) systems. The applications for Wireless Sensor Networks are many and varied. They are used in commercial and industrial applications to monitor data that would be difficult or expensive to monitor using wired sensors.


١٣٤

They could be deployed in wilderness areas, where they would remain for many years (monitoring some environmental variable) without the need to recharge/replace their power supplies [45]. Over the years, greenhouse climate control has become computerized, and currently involves many sensors and actuators, inside as well as outside of the greenhouse. In the absence of automatic failure diagnosis, sensor and actuator biases or drifts affect the greenhouse operation until changes large enough to be noticed by the grower occur. Similarly, the grower is solely responsible for noticing abnormal behavior of the crop [41]. Providing automatic detection of failures occurring in a greenhouse would free the grower from these time consuming activities. Moreover, if failures could be detected at any early stage, the resulting damage could be minimized. Identification of the faulty element (failure isolation) would enable early repair and reconfigureuration of the control policy, in order to operate the greenhouse efficiently despite the failure (failure accommodation). 5.3. Hierarchical decomposition of greenhouse climate management Industrial process control is often characterized by hierarchical control because of the many inherent complexities of the controlled systems. Plant culture can exhibit the same degree of complexity due to the many time scales of response and the intimate involvement of a biological system [60]. The environment, naturally, has many effects on the biological system, and the biological system has numerous effects on the closing environment. The response time of a greenhouse exposed to the sun's sudden emergence from be measured in days or perhaps weeks. In general, the physical systems of the plant production respond quickly, whereas the biological systems respond relatively slowly.

Process variables may be classified as “fast” or “slow”, but no reason exists to limit decomposition of the control system to only these categories. A four level decomposition is shown in Table 5.1 for greenhouses. Level 3 control can be assumed as a function of market considerations and is generally left to the discretion of the facility manager. Level 2 controls is composed of biological consideration but should be the ultimate consideration for the system, as driven by level 1 control. The interactions of control levels 1 and 2 lead to considerations of optimal control for energy and production cost management. The efficiency of level 1 control depends


١٣٥

strongly on level 0, which can become a serious concern because of the large sizes of commercial greenhouse air spaces. Large commercial greenhouse operations are sized by hectare (i.e.,10000 m2), and the actions of level 0 control may not propagate throughout the system under control influence for many minutes[6]. Table 5.1. A hierarchical decomposition of greenhouse climate management from [93],[54].

Table 5.1. A hierarchical decomposition of greenhouse climate management

Level Control of Time scale 3 Production space and time Growing season

/year 2 Crop growth and production Hours/days/weeks 1 Greenhouse climate Minute 0 Actuators(eg..,fans and

valves) Seconds/Minutes

5.3.1.Greenhouse crop production process A schematic diagram of the greenhouse crop production process is depicted in Figure (5.1) [41]. Generally, two sub-systems of the greenhouse crop production are considered in modeling research namely the greenhouse climate and the crop [93]. Greenhouse climate management was established by defining a hierarchical set of subsystems, where each sub-system is operated along guidelines defined at the higher levels. The main reason for this hierarchical decomposition of greenhouse climate management is the inherent complexity of the process considered. The large number of process variables related to crop production and greenhouse climate as well as the complex interaction between the crop and the greenhouse climate, inevitably demand decomposition in sub-problems that are more tractable in control system design. The main premise for the decomposition was the fact that in the crop production process considerable differences in response times exist. Compared with the fast dynamic response of the greenhouse climate, crop growth responds rather slowly to changes in the inputs. Also, the response


١٣٦

time of the valves and servo motors is relatively short compared with the dynamic response of the greenhouse climate. When a complex high dimensional system contains mutually interacting subsystems with large differences in response times, it is standard engineering practice to make simplifications by neglecting time constants whose presence cause the system to be more complex than acceptable for practical design of optimally controlled systems.

Figure (5.1). A schematic diagram of the greenhouse crop production process. Then, based on engineering experience, the process variables are classified as “slow” and “fast”. The only dynamics used in short term studies are determined by the “fast” variables, disregarding the dynamics of the “slow” process variables. While, in long term studies, only the dynamics determined by the “slow” state variables are considered and the dynamics of the “fast” process variables are neglected. The four-level hierarchical process control scheme presented in Table5.1 [54] illustrates the basic ideas about a hierarchical decomposition of greenhouse climate management. In greenhouse climate management, level 0 is concerned with the efficient operation of the valves of the heating system and carbon dioxide supply system as well as the servo motors of the ventilation windows. The settings for the valves and servo motors are determined at level 1 which is concerned with control of greenhouse climate

Air temp. Co2 conc. Humidity Crop dray

weight

Solar radiation Co2 concentration

Humidity Air temp.

Wind speed

Heating Co2 supply Fog supply Ventilation Crop Greenhouse

Climate


١٣٧

variables such as air temperature, carbon dioxide concentration and humidity. The required values, or set-points, of these climate variables are determined at level 2. The process considered at level 0 and 1 have relatively short dynamic response times, i.e. of the order of minutes. Therefore, they are controlled on a minute by minute basis. In practice, level 0 and level 1 are commonly treated simultaneously in a cascade or master-slave control system concept in which the level 1 controller acts as the master on the slave controller at level 0. At levels 0 and 1, the present research has been mainly focused on the potentials of multi-variable control of the temperature and absolute humidity of the air. Level 2 is concerned with the control of crop growth and production. Therefore, the dynamic response of the crop is explicitly accounted for in the control system design. At this level, climate variables such as the temperature, carbon dioxide concentration and the humidity in the greenhouse are inputs which can be used to manipulate the crop production process. Consequently, control system design is aimed at the calculation of trajectories for these climate variables such that a specified crop production goal is achieved. These climate trajectories are to be used as set-point trajectories for greenhouse climate control at level 1. 5.3.2. Greenhouse dynamical model Greenhouse's interior is considered to be a perfectly stirred tank consisting essentially of one homogenous component, the greenhouse air. The main purpose of the greenhouse climate model is to predict the inside climate for a given state of the system, outside weather and control purposes. The dynamic model of the energy and mass balance of greenhouse air is shown to be highly nonlinear. A simple greenhouse heating-cooling ventilating model can be obtained by considering the differential equations, which govern sensible and latent heat, as well as water balances on the interior volume. These differential equations are as follows [54]:

)],()([

)]()([)()]()()([1)(

tTtTVC

UAtTtTV

tVtqtStqVCdt

tdT

outin

Poutin

Rfogiheater

P

in

(5.1a)

)],()([)())(),((1)(1)( twtwVtVtwtSE

Vtq

Vdttdw

outinR

inifogin

(5.1b)


١٣٨

where Tin is the indoor air temperature (oC), Tout the outdoor temperature (oC), A the heat transfer coefficient (W K-1), ρ the air density (1.2 kg m-3 ), Cp the specific heat of air (1006 J kg-1 K-1 ), qheater the heat provided by the greenhouse heater (W), Si the intercepted solar radiant energy (W), qfog the water capacity of the fog system (g H2O s-1), λ the latent heat of vaporization (2257 J g-1), VR the ventilation rate (m3 [air] s-1), win and wout the interior and exterior humidity ratios (water vapor mass ratio, g H2O kg-1 of dry air), respectively, and E(Si,win) the evapotranspiration rate of the plants (g H2O s-1). It should be noted that the air volume (V) to be used in the balances is the effective mixing volume. So by setting V=VT in equation (5.1a) and ρV=VH

in equation (5.1b), we note that the air volumes VT and VH to be used in the balances are the temperature and humidity active mixing volumes, respectively. Short circuiting and stagnant zones exist in ventilated spaces and the active mixing volume is typically significantly less than the calculated total volume. The active mixing volume of a ventilated space may easily be as small as 60 to 70% of the geometric volume. This, of course, means that indoor air temperature and humidity are unlikely to be uniform throughout the air space. Moreover, in a model with only one state for the temperature, the effective heat capacity usually must be taken larger than that determined by just the air volume, to encompass some of the heat capacity of construction materials and the plants. Similarly, the effective volume for humidity may be smaller or larger than the geometric one, depending on the degree of mixing and other effects such as air and humidity losses [54] and [78]. In this climate model, two variables have to be controlled namely indoor air temperature and humidity ratio through processes of heating, cooling, humidifying, and/or dehumidifying. Since dehumidification is some times expensive, dehumidifiers will not be used. But we will use heating and ventilation in combination for dehumidification in a greenhouse, ventilation brings in air, which is heated, allowing it to absorb some of the moist air from the building before exhausting it to the outside. Also, in warm climates and when the relative humidity of the outside air is very low, only ventilation can be used to dehumidify the greenhouse air by exchange moist air with drier outside air. Raising humidity levels requires some sort of evaporative device such as misters, fog units, or roof sprinklers, all of which cool and add water vapor to the air. Evaporative cooling devices require good ventilation rates. Fresh air must be continually got through and warm humidified air exhausted. When humidifying is occurred under sunny conditions, ventilation is necessary since the greenhouse would soon become a steam bath without


١٣٩

offering fresh dry air to evaporate more water, and to cool, humidify and displace hot greenhouse air. In warm climates, ventilation is required most of the day to lower the temperature, and a conflict exists between the need to ventilate and the desire to moisturizing. While common practice usually views ventilation and moisturizing as mutually exclusive [60]. Since the indoor climate is poorly isolated from the outdoor climate, outdoor climate conditions such as solar radiations, air temperature, and humidity, etc., have a strong impact on the energy and mass balances of the greenhouse interior. Moreover, solar irradiation is a necessary condition for crop growth. The variables and operating condition of a greenhouse (GH) system is illustrated in Appendix C 5.4 Control of the greenhouse ventilation model 5.4.1. Control model The control process is divided into two distinct control loops, the first maintaining the temperature by adjusting the ventilation rate, and the second maintaining the humidity ratio by adjusting the moisturizing rate. To this end, a control model is first derived. For summer operation, qheater in equation (5.1a) is set to zero. It is also worth noticing that to a first approximation the evapotranspiration rate E(Si(t),win(t)) is in most part related to the intercepted solar radiant energy, through the following relation [41] and [45]:

)()())(),(( twtStwtSE inTi

ini

(5.2)

where α is an overall coefficient to account for shading and leaf area index, and βT the overall coefficient to account for thermodynamic constants and other factors affecting evapotranspiration (i.e. holes, air motion, etc.). In other words, the two term[s account for the single term VPD (Vapor Pressure Deficit) [93],[54],and [78] used in literature. Figure (5.2.) shows the schematic diagram of the greenhouse climate control process. On the basis of these observations, equations (5.1a) and (5.1a) take the forms

)],()([

)]()([)()]()([1)(

tTtTVC

UAtTtTV

tVtqtSVCdt

tdT

outin

Poutin

Rfogi

P

in

(5.3a)

)],()([)()()(1)()( twtwVtVtS

Vtq

Vtw

Vdttdw

outinR

ifoginTin

(5.3b)


١٤٠

Figure. 5.2. A Schematic diagram of the greenhouse climate control process.

Equations (5.3a) and (5.3b) are obviously coupled nonlinear equations, which cannot be put into the rather familiar form of an affine analytic nonlinear system, due to their complexity appearing as the cross-product terms between control and disturbance variables. Other data-based approaches have been successfully applied to reduce the complexity of the model and design a control system with good disturbance-response characteristics [104]. Defining the inside temperature and the inside humidity ratio as the dynamic state variables, x1(t) and x2(t), respectively, the ventilation rate and water capacity of the fog system as the control (actuator) variables, u1(t) and u2(t), respectively, and the intercepted solar radiant energy, the outside temperature, and the outside humidity ratioas the disturbances, vi(t), i =1,2,3. The model, (5.3a) and (5.3b) can be put in the following state space form:

)()(1

)()(1)()()(1)()(

21

2121111

tvtuV

tvVC

UAtvVC

tuVC

tutxV

txVC

UAtxPPPP

(5.4a)

)()(1)()(1)()(1)()( 31121222 tvtuV

tutxV

tvV

tuV

txV

tx T

(5.4b)

5.4.2. Feedback-Feedforward linearization and decoupling There are two methods that can be applied in the present case of greenhouse climate control, the first method was described in [54] and the second method was described in details in the reference [78]. It is well known that affine nonlinear systems may be globally linearized and decoupled by nonlinear feedback. This is just the scheme of inverse dynamic control. The extension of this scheme to more complex cases, such

Control signals Controller

Sensory measurements IGA

Controller parameters

Outdoor climate

Set-points for environmenal

conditions


١٤١

as the one represented by equation (5.4), is sometimes feasible, since the disturbance variables of the greenhouse heating-cooling ventilating model can be readily measured. Furthermore, the complexity of such systems may be eased by the fact that the system states changes slowly and some state-dependent parameters (i.e., βT) can be considered constant (i.e., quasi-static system operation). Therefore, in the present case, a combined scheme of feedback with simultaneous feedforward linearization is plausible. Consider the system (5.4) to be linearized and decoupled, having the form [41] and [47]: )(~~)()( 11 tuKtx

VCUAtx TT

P

(5.5a)

)(~~)()( 22 tuKtxV

tx wwT

(5.5b)

)]()([)]()([)()()1()(~~)(~~

)(2312

211 txtvtxtvC

tvUAtvtuKVtuKVCtuP

wwTTP

(5.6a)

))()(())()(())()(())()()(~~()(

2312

32212 txtvtxtvC

ztvtxtvUAtvtuKVCtuP

TTP

(5.6b)

where

)())()(()(~~))()(( 12112 tvtvtxCtuKtxtvVCz PwwP

.

The above control law is feasible if the denominator:

)]()([)]()([)( 2312 txtvtxtvCt p (5.7)

is different from zero. Note that in the case, ∆(t) = 0, the input u1(t) affects the system states x1(t) and x2(t) the same way as u2(t); in this case, decoupling and feedback-feedforward linearization is impossible. The greenhouse interior temperature and relative humidity are measured by a thermometer and a hygrometer, respectively, usually located a certain distance from the greenhouse ventilators and the fog or wet-pad system. Hygrometers can present significant lag time. Hence, the changes in the temperature and absolute humidity are determined after a certain dead time dT and dw,


١٤٢

respectively (dT < dw). With this observation, it is easy to check that the response to input changes can be described by the following transfer function models:

)(~)()(~1

)(1 sUsGsUseK

sX TTTT

sdT

T

(5.8a)

)(~)()(~1

)(2 sUsGsUseK

sX wwww

sdw

w

(5.8b)

where X1(s), X2(s), )(~ sUT and )(~ sUw are the Laplace transforms of x1(t), x2(t),

)(~ tuT , and )(~ tuw , respectively, and

wT

wT

wTP

TP

T KVKVKUA

VCK

UAVC ~,,~,

At summer evaporative cooling conditions and for certain crops, the term βT

win(t) of equation (5.2) is relatively weak. To meet the real difficulty of the water addition process, if this term is omitted. Therefore, the second state equation (5.4b) becomes a perfect integrator. Indeed, in this case, relations (5.7b) and (5.8b) take the following respective forms:

)(~~)(2 tuKtx ww (5.9a)

)(~)(~)(~~)(2 sUsGsU

seKsX www

sdw

w

(5.9b)

On the bases of equations (5.8a) and (5.9b), temperature changes are modeled by a self-regulated first order plus dead-time (FOPDT) model while humidity ratio changes are modeled by an unstable integrator plus dead-time (IPDT) model. The overall control strategy of the proposed technique is depicted in Figure (5.3).


١٤٣

Figure (5.3). Overall control strategy in case of small delays and/or a slow desired time response where RT and RW are the temperature and humidity ratio set value respectively.

One must keep in mind that the nonlinear feedback-feedforward control law, which renders the overall system linear and decoupled, relies on current state and disturbance measurements. Therefore, time delays may affect the feedback-feedforward linearization procedure and could degrade its performance [47]. In order to avoid this problem, one must select τ1 and τ2, which are related to the speed of the closed-loop system response, to be large nough, resulting to a relatively slow closed-loop system. For example, a choice of τT > 4 dT and τw > 4 dw appears to be quite satisfactory compromise between the speed of the closed-loop system response and the performance of the feedback-feedforward linearizing control law. 5.5 Simulation Results The effectiveness of the proposed control schemes is demonstrated by a case study. In this example consider a greenhouse of surface area 1000 m2 and a height of 4 m. The greenhouse has a shading screen that reduces the incident solar radiation energy by 60%. The maximum water capacity of the fog system is 26 g[H2O]/s. Maximum ventilation rate corresponds to 20 air changes per hour (22.2 m3[air]/s). Parameter α (Shading and leaf area factor, dimensionless) takes the value 0.129524267 and βT = 0.015 kg.min/m2. The heat transfer coefficient is UA=25 W/k. Finally, we assume that unknown system and sensor dynamics contribute an overall dead time of 0.5 min in both temperature and humidity measurements (i.e., dT = dw = 0.5 min). Also, we assume that no crop was present in the greenhouse at the time of experiment, but the concrete floor was continuously wetted to simulate a greenhouse with a wet soil surface. Therefore, the results presented here are

Tu~

wu~

Measurable Disturbanc

Linearization and Decoupling

Block

Controller 1 Greenhouse (System with

delay) Controller 2 wuTu

2x1x

wRTR


١٤٤

supposed to apply to a greenhouse with small seedlings, which do not influence the greenhouse climate [60].The greenhouse climate control variables consisted of humidification and forced ventilation. A simulation experiment has been conducted to demonstrate the ability of the proposed control schemes to provide interacting control and smooth closed-loop response to set point step changes. 5.5.1 Performance of a greenhouse system based on M-ANFIS. The problem consists in finding the values of the parameters of the membership functions in the rule antecedents and the coefficients in the rule consequents of the TSK-type fuzzy systems [88]. The knowledge rules of the fuzzy system have the form:

rr LHisHandLTisTIF : HcTccuTHEN rH

rT

ro

r : (5.10)

where r=1,2,...,R is the rule number, rLT and rLH are the linguistic terms of the input signals temperature (T )and humidity ( H ),respectively, in the r-th rule , ru is the contribution of the r-th rule to the total output of the fuzzy

system, and roc ,

rTc , and

rHc are the consequent coefficients, the output

of the fuzzy system is given by:

R

r

r

rR

r

r

w

uwu

1

1 (5.11)


)().( HTw rr LHLtr (5.12) where (.)(.) rr LHLT and are the membership functions corresponding to the linguistic terms rr LHandLT respectively, in the r-th rule. In addition, note that Eq (5.11) can be written as [48] :

R

r

rR

r

rrrR

rR

r

r

r

uuwuw

wu111

1

(5.13)

Where rw for r=1,2,…, R can be equivalently called the normalized rule consequents:


١٤٥

9

9

09

1

1

01

9999911111

9999911111

99999111111

)(

2)(

1)(

H

T

H

T

M

cc

c

ccc

MHwTwwHT

HwTwwHT

HwTwwHT

V

V

R

r

r

rr

w

ww

1

(5.14)

In this case the complete knowledge base will have 3×3=9 rules of the form given in (7), also, the network will have 2 distribution units in layer L0, 6 neurons in L1, 9 neurons in L2, L3, and L4, and 1 neuron in L5. So the determined parameters using 3 fuzzy sets as described bellow: inputs Fuzzy sets Total no

of rules Premise parameters


total number of parameters

2 3 9 18 27 45

The consequent parameters are estimated using a least square estimation

(LSE) procedure . Using 3 fuzzy set , and 9 rules, each input-output training

pattern can be written as:

)T( 110

9

1HcccV rrr

rr

(5.15)

TTccccccccc

HTHTHTV

919

919

909

212

212

202

112

111

101

199199912212221111111 *

(5.16)

Considering all M input-output training patterns together: (5.17)

V=XC (5.18)


١٤٦

Through appropriate definitions, (14) can be written as where V is M×1, X is M×(2+1)N, and C is (2+1)9×1, that can be detailed as : V is M×1, X is M×(3)(9)=M×27, and C is 27×1. In general the problem is overdetermined, that is M>27. An LSE solution for C can be computed recursively [40].

(5.19)

where Tix is the ith row vector of matrix X and Vi the ith element of vector

V, for i=0, 1,2,…, M-1, and Ψ is the covariance matrix, then Clse=CM, where Ψ is called the covariance matrix. The initial conditions are C0 = 0 and Ψ0 = γI, where I is a size (2+1)N identity matrix and γ is a large positive number. At the end of iterations: C=CM. The changes to the antecedent parameters are determined by backpropagation [48] The proposed MV-ANFIS controller was described in detail in chapter 4, the dual parameters for each controller are obtained here using (IGA) through 100 generations by minimizing the mean square errors, The humidity ratio set point was start with 18(g/kg). The changing of temperature and humidity is as described bellow

Changing for Temperature Changing for Humidity t>199 T=20.0 t>299 H=25.0 t>399 T=28.0 t>499 H=22.0 t>599 T=32.0 t>699 H=25.0 t>799 T=25.0 t>899 H=25.0 t>999 T=30.0 t>1099 T=25.0

t>1199 T=33.0 t>1299 H=22.0

The system response under different fuzzy sets is depicted on Figure (5.4). As shown the results based on using 2 fuzzy sets for each input are relatively bad, while that with 3 fuzzy sets is clear and accurate. As shown in Figure (5.5.), the results describe how can the proposed IGA-ANFIS controller able to track its set points in two outputs, temperature, and humidity in all day operation. The ventilation rate and water capacity of fog system as internal control signals are shown in Figure (5.6).

(5.20)

iTi

Tiiiii CxVxCC 11111

11

111 1

ii

Ti

iTiii

ii xxxx


١٤٧

(b)

Figure (5.4) Greenhouse: (a) indoor air temperature (upper) and indoor air humidity ratio (bottom) ,(b) internal control signals: Ventilation (upper) and water capacity ratio (bottom). Using different fuzzy sets

(a)


١٤٨

Figure (5.5) Greenhouse outputs: indoor air temperature (upper) and indoor air humidity ratio (bottom) for all day operation, example1.

Figure (5.6). Greenhouse internal control signals: Ventilation (upper) and water capacity ratio (bottom).


١٤٩

The actual control signals, results from linearized and decoupling block ventilation are ( ventilation, water capacity of fog system, and heat transfer ) are described in Figure (5.7).

Figure (5.7) Greenhouse control signals: ventilation rate (upper),water capacity of fog system (middle), heat transfer (bottom). Step changes in disturbances were applied as a worst case of day operation. The step changes were: Si from 250 to 300 W/m2, Tout from 35 to 32 oC, and wout from 4 to 8 g[h2o]/kg[dray air], see Figure (5.8),With no uncertainty in the model parameters, weather conditions do not affect of Tin and win. In the second simulation experiment, the desired set points are Tin = 30oC and decreased to 20 oC at t = 200 min , and the humidity ratio set point was raised from 18 to 24 g/kg t = 300 min g. The responses for set point step changes in temperature and humidity ratio are show in Figure (5.9)a, and Figure (5.9)b respectively. As shown in these Figures the temperature and humidity ratio reaches desired values with less overshoot and rise time using (IGA).


١٥٠

Figure (5.8).Greenhouse disturbances: output temperature (upper),absolute humidity (middle), and solar radiation energy (bottom). The ventilation rate and water capacity of fog system as a control signals is shown in Figure (5.10). The simulation results clearly demonstrate the interacting control was attained and the closed-loop system response is very acceptable. Moreover, the response of the MV-ANFIS controller tuned by IGA is much faster than MV-ANFIS without tuning. The root mean square (RMS) error as defined in the following equation was computed for the outputs of the process for each individual controller [41]&[ 54] in the two experiments, as shown in Table 5.2.

T

1k

2Y[k])-(Yd[k]T1errorRMS

where Yd[k] and Y[k] are the desired and actual outputs respectively, and T is the number of samples used. From this Table we can see that the MSES based on introduced controller tuned by (IGA) is the smallest one for both experiments.


١٥١

Figure (5.9) Greenhouse outputs: indoor air temperature (upper) and indoor air humidity ratio (bottom) example2.

In the third simulation experiment, the different changes for all input output of greenhouse system were made to be recognized from effectiveness of the proposed controller. In all cases we can see that the proposed MV-ANFIS controller tuned by (IGA) track its set points with less errors than given by ANFIS without tuning of its parameters as following . Case (1), represents the change of the set point for temperature with changing in humidity also. We can see that the proposed controller able to track set point with less time and overshoot as shown in Figure (5.11). Case (2), represents the change of the set point for humidity with no changing in temperature. In addition, the response is accurate as described in Figure (5.12). Case (3) 1, 2, represents the change of the set point for temperature and humidity. Also, the response is close to the set point in a wide range of operation as described in Figure (5.13), (5.14).

IGA-ANFIS

a

b


١٥٢

Figure (5.10) Greenhouse control signals: Ventilation (upper) and water

capacity ratio (bottom)

5.5.2 Comparing the Performance the M-ANFIS controller to the other controllers The MSE of the proposed controller is the smallest comparing to Fuzzy controller [41] and PDF controller [54] for the first 300 minutes of operation as listed in Table 5.2. Table 5.3 show the changing of the scaling factors based on (IGA) at different ranges of operation and same number of generation. The MSES for temperature and humidity for introduced controller based on immune genetic algorithm (IGA) ate different fuzzy sets is depicted in Table 5.4. It is show that the minimum number of fuzzy sets that give accurate result is three fuzzy sets. The response using three fuzzy sets is used, where the response is accurate and tuning parameters is small. The RMSE for both temperature and humidity ratio introduced by MV-ANFIS controller compared to Fuzzy controller [41] and PDF controller [54] is shown in Figure (5.15) and Figure (5.16).

IGA-ANFIS Time(hours)


١٥٣

From these Figures, we can see that the the immune genetic algorithm tuning MV-ANFIS controller is much better for both outputs temperature and humidity.

Figure (5.11) Case 1 Greenhouse outputs: indoor air temperature, red line (IGA-ANFIS) and dash blue (ANFIS)

Table 5.2 RMS values for different controllers Controller

MSE1 10-3

MSE2 10-3

Duration of operation

PDF 8.2781 9.8175 FUZZY 7.3241 8.0239 ANFIS ٥6.046 ٥5.562

MV-ANFIS Tuned by Immune Genetic

1.0478 3.3053

At f

irst 3

00

min

ute

IGA-ANFIS Time (min)


١٥٤

Table 5.4 MSES for Green house system based on number of membership function

Fuzzy sets Temperature Humidity No of tuned parameters

2 1.9718 2.6089 12 3 0.0017 0.0005 27

5 0.0016 0.0004 75 7 0.0016 0.0005 147

Figure (5.12) Case2 Greenhouse outputs: indoor air temperature, red line (IGA-ANFIS) and dash blue(ANFIS)

Table 5.3. Normalized values tuned by immune genetic algorithm Time of

operation

Scalf1 Scalf2 No of generation

300 min ٥.٦٨٢٢ ٨.٠٣٣٨

١٠٠

12 hour ١٠٠ ٣.٤٦١٦ ١٨.٥٦٥٧ Day ١١.٠١٩٥ ٥.٩٤٤٥ 100

300 min ٥.٨٥٩٥ ٥.٥٦٥٤ 10 Day ١٠٠ ٥.٧٩٣٠ ١٠.٤٧٤

IGA-ANFIS Time(hours)


١٥٥

Figure (5.13). Case3 (1) Greenhouse outputs: indoor air temperature, red line (IGA-ANFIS) and dash blue(ANFIS)

Figure (5.14). Case3 (2) Greenhouse outputs: indoor air temperature, red line (IGA-ANFIS) and dash blue(ANFIS)

IGA-ANFIS

IGA-ANFIS


١٥٦

Figure (5.15). RMSE of temperature using MV-ANFIS controller tuned by genetic compared to other controller

Figure (5.16). RMSE of Humidity using MV-ANFIS controller tuned by genetic compared to other controller

IGA-ANFIS

IGA-ANFIS

IGA-ANFIS

IGA-ANFIS

IGA-ANFIS


١٥٧

5.6 (CD-MV-ANFIS) controller The introduced neural network of feedforward fuzzy controllers for a greenhouse system in the frame of cascaded distributed form is depicted in Figure (5.17). The cascaded distributed process described in Figure (5.18),that consists sub controllers each of which is a Multi-Input Single-Output MISO controller connected in distributed form,

The proposed control scheme remodels this conventional fuzzy rule as described in Figure.(5.18) as follows: IF e1 is Ai AND ce1 is Bj THEN X12 is C1k

R2: IF ce1 is Ai AND x12 is Bj THEN X13 is C2k

R3: IF e2 is Ai AND x13 is Bj THEN X14 is C3k

R4: IF ce2 is Ai AND X14 is Bj THEN X15 is C4k

where, Ai , Bj ,and Ck are fuzzy sets and i, j, k=1, 2,3,….n The rule base is generated also as described in chapter 4, and revised based on the performance of the process be controlled [14] and [59]. The scaling factors of each sub-model developed are also adapted using (IGA) to improve the final outcomes of the process. The developed scheme has a set of sub-models, through which the information is distributed. The developed scheme consists of n fuzzy controller distributed as follows: FLM1, FLM2 , FLM3, and FLM4 are connected in series to contribute the output of fuzzy system as depicted in Figure (5.18) The X11 and are internal states., and X1,X2,X3,X4,……. and X14 are the input states. The output of FLM3 is feedforward the other 2 ANFIS module (ANFIS-M1, ANFIS-M2) each of which represents the MISO ANFIS with two inputs in each module as depicted in Figure(5.19).


١٥٨

X12

X13

Figure (5.17) ANFIS Architecture for 2 inputs

∏

∑

∩

∩

∩

∩

∩

∩

∏

∏

∏

* * * * * *

N

N

N

N

N

* * * * * *

e1 e2

e1

e2

e1 e2

e1 e2

e1 e2

e1 e2

∏

∑

∩

∩

∩

∩

∩

∩

∏

∏

∏

* * * * * *

N

N

N

N

N

* * * * * *

X12 ce2

X12

Ce11

X12 ce2

X12 ce2

X12 ce2

X12 ce2

Premise Consequent Parameters

U1

∏

∑

∩

∩

∩

∩

∩

∩

∏

∏

∏

* * * * * *

N

N

N

N

N

* * * * * *

X12 ce2

ce2

X12 ce2

X12 ce2

X12 ce2

X12 ce2

X13


١٥٩

5.6.1 Controller of a greenhouse(GH) climate system

A controller structure that has few parameters is constructed. Since the controller has two inputs and three MFs on each input such as small (S), medium (M), and Big (B), its rule base consists of nine rules. A code for parameter update is written according to the backpropagation algorithm explained in chapter2, and chapter 4. The fuzzy inference system for control signal u1 (FISU1),ie , the knowledge base for loop1 is as follows: For instant the FISU1 knowledge base loop1 as follows: R1: IF x13(k) is S and ( ce2(k)) is S THEN f1=c1o+c11 x13(k)+c12 ce2 (k)

R2: IF x13(k) is S and (ce2 (k)) is M THEN f1=c2o+c21 x13(k)+c22 ce2 (k)

R3: IF x13(k) is S and (ce2 (k)) is B THEN f1=c3o+c31 x13(k)+c32 ce2 (k)

R4: IF x13(k) is M and (ce2 (k)) is S THEN f1=c4o+c41 x13(k)+c42 ce2 (k)

R5: IF x13(k) is M and (ce2 (k)) is M THEN f1=c5o+c51 x13(k)+c52 ce2 (k)

R6: IF x13(k) is M and (ce2 (k)) is B THEN f1=c6o+c61 x13(k)+c62 ce2 (k)

R7: IF x13(k) is B and (ce2 (k)) is S THEN f1=c7o+c71 x13(k)+c72 ce2 (k)

R8: IF x13(k) is B and (ce2 (k)) is M THEN f1=c8o+c81 x13(k)+c82 ce2 (k)

R9: IF x13(k) is B and (ce2 (k)) is B THEN f1=c9o+c91 x13(k)+c92 ce2 (k)

Figure (5.18) A(CD-MVANFIS) controller

FLM1

FLM3

FLM2

x12

x13

x14

e1

ce1

e2

ce2

ANFIS-M1

ANFIS-M2

u1(k)

u2(k)


١٦٠

Figu

re (5

.19)

The

pro

pose

d (C

D-M

VA

NFI

S) c

ontro

l sch

eme

for g

reen

hous

e (G

H)

syst

em


١٦١

5.6.2 Blend Immune Genetic Algorithm (BIGA) Genetic algorithms (GAs) are global search methods that emulate the process of biological evolution [64] see Figure (5.20). However, the simple GA has some problems, which can prevent it to reaches the global optima. The first one is the deception problem, when very bad strings can be generated from good building blocks. So simple GA can be misleading for some problems depending on the nature of the objective function. Such objective function is referred to as GA-deceptive problem. This phenomenon causes GA to converge to sub optimal points. The second one is the premature problem, it happens if the convergence occurs too rapidly due to sampling error and bias in the selection method. This problem is manifested as a premature loss of diversity in the population. Some other approaches used to solve these problems have been proposed by [39]. Such as inversion operator, messy genetic algorithm, hybridization of GA with another optimized techniques like simulating annealing All previous methods lead to find optimal solution but it required a higher computation time, so they are used off-line [13]. Online approach for learning only the neuro-fuzzy controller parameters with fixed rule base [30] and [33].. In this section an on-line approach for adjusting parameters of fuzzy controller using blend immune genetic algorithm (BIGA). The effect of decreasing or increasing the number of rules is also presented. In addition, the effect of adapting parameters and / or the rule based on achieving good performance is also introduced. 5.6.2.1 Algorithm of Blend Immune Genetic Algorithm (BIGA) There are two major processes contained within the proposed algorithm, the AIS and GA, in terms the AIS processes is initiated with the following procedures: i. Randomly generate initial population of Ab ii. Determining the fitness of each Ab. iii. Select the antibodies, n, with best affinity. iv. Generate selected sets of clones v. Mutate clonal set affinity maturation vi. Calculate affinity clonal set vii. Select memory cell candidate(s) viii. Replace lowest affinity, d, antibodies. ix. Repeating steps iii-vi until a pre-defined stopping condition is reached.


١٦٢

In the second process, GA usually starts with a random population. As explained previously in chapter 2, GA uses an input from the best population obtained in AIS in its procedures in this new method. The usual AIS are used for particular generation. For example, within 50 generation, the best population will be moved on to the next process replacing the usual random population used in the GA. The pseudo code of AIS-GA is depicted in Figure (5.21). AIS-GA starts with procedure as following: i. From the best population in AIS, generate initial population of individuals ii. Compute the fitness values of each of the individuals in the current population. iii. Individual selection for reproduction. iv Application of the crossover and mutation operator. v. Compute the fitness value of each individuals vi. Select the best individuals to create the new population. Repeat steps 3 to 6 until a pre-defined stopping criterion is attained. The flowchart Figure 7 shows the hybrid of AIS-GA.

Initial Population

Evaluation of Objective Function

Function Fitness Assignment

Function

Selection, Crossover Mutation

Generating of Fit Individuals

Termination Criteria

Figure (5.20) Genetic Algorithm (GA)


١٦٣

Start

Generate Ab randomly

Calculate affinity for Ab

Select n antibodies with best affinity

Generate clones of selected set

Mutate clonal set affinity maturation

Calculate affinity clonal set

Select candidate(s) memory cells

Replace lowest d affinity antibodies

Loop for G generation

NO

YES

Take memory pool as algorithm

End

Generate Initial population from best population in AIS

Measure /evaluate fitness

Select fittest

Crossover

Mutation

Reach Generation

NO

YES

Figure (5.21) Blend Immune Genetic Algorithm (BIGA)


١٦٤

5.7 Simulation results for greenhouse (GH) system The introduced CD-MV-ANFIS controller also tested by greenhouse (GH) system to show the capability of the controller to control a different type of non-linear process. Figure (5.22) shows the results of greenhouse outputs using CD-MV-ANFIS based on genetic algorithm, as we see the response have small overshoot in case of changing for both temperature and humidity based on genetic tuning. Figure (5.23) compare a temperature outputs for a greenhouse (GH) system based on a proposed controller with other controllers at first 30 minute, where the response under proposed controller based on genetic very clear and reach the set-point at 15 minute without overshoot. Figure (5.24) Compare a humidity outputs for a greenhouse (GH) system based on a proposed controller with other controllers at first 30 minute, where the response under proposed controller based on genetic very fast and reach the set-point at 5 minute without overshoot.

Figure (5.22) Compare a greenhouse outputs using CD-MV-ANFIS, based on genetic algorithm: indoor air temperature (upper) and indoor air humidity ratio (bottom) for all day operation.


١٦٥

The MSES of temperature and humidity for both (CD-MV-ANFIS) ,and (MV-ANFIS) based on tuning type are depicted in Figure (5.25) and Figure (5.26) .

5.7.1 Comparing the performance of greenhouse system by using the two approaches The mean square errors (MSE) of temperature and humidity for green house system (GH.) using CD-MV-ANFIS, and MV-ANFIS controller is depicted in Table.5.5. The MSES based on immune genetic type are smaller than that given by genetic, and without tuning for temperature, and humidity using CD-MV-ANFIS.

Figure (5.23) Response of temperature at first 30 minute for cascade (CD-MV-ANFISs) ,and (MV-ANFIS) tuned by genetic


١٦٦

Figure.(5.24) Response of humidity at first 10 minute for cascade (CD-MV-ANFISs) ,and (MV-ANFIS) tuned by Immune genetic algorithm

Figure (5.25) MSES of temperature for both (CD-MV-ANFIS), and (MV-ANFIS) based on tuning type.

C


١٦٧

Figure (5.26) MSE of humidity for both (CD-MV-ANFISs),and (MV-ANFIS) based on tuning type.

Table 5.5 Comparison of performance accuracy between MV-ANFIS and CD-MV-ANFIS controller for Greenhouse system based on tuning type

MSES Controller Tuning type

Temperature Humidity Genetic algorithm .0319 .002

Immune genetic algorithm

.0276 .0013

CD-MV-ANFIS

Without tuning .0619 .0017

Genetic algorithm .1369 .007 Immune genetic

algorithm .0275 .002

MV-ANFIS

Without tuning .1901 .0072


١٦٨

5.7.2 Comparing the performance (CD-MV-ANFIS) with other controllers

To support the usefulness of our work, the hybrid genetic algorithm (IGA-

GA) which is a combination of both (IGA) and (GA) is used for comparing

the results obtained from the proposed controller with those obtained by PID

controller introduced in [72] for a greenhouse (GH) system.

The most common performance criteria are IAE, ISE, MSE and ITAE

Performance criterion formulas are as follows [72]:

tt

dttedttytrIAE00

)()()( (5.21)

t

dtteISE0

2))(( (5.22)

t

dttet

MSE0

2))((1 (5.23)

t

dttetITAE0

)( (5.24)

The proposed CD-MV-ANFIS scheme demonstrated during the above criteria using the following three cases. Case (1): Using Genetic Algorithm.(GA)

It can be shows that the response of the proposed controller using the ITAE is smallest overshoot as seen in Figure (5.27). The error in case of IAE is biggest compared to other criteria. The controller reaches the steady after .09 second with .01 error. We see also as depicted from Table 5.6, the MSE is smaller than ISE, but both reach the steady state on the same time. The maximum overshoot equal 8%.

Case (2): Using Immune Genetic Algorithm.(IGA) In this case, we can see that the response of the proposed using the ITAE is also smallest overshoot and not exceed 7% as showed in Figure (5.28). This because using the AIS considers more adapted


١٦٩

technique than GA. The error in case of using AIS in all criteria is smaller than given by GA as depicted in Table 5.6.

Case (3): Using hybrid Genetic Algorithm AIS-GA (BIGA).

As showed in Figure (5.29), the responses of controller in all criteria are faster than given by AIS and GA at the same condition. We can also see that all error values are very small compared to AIS, and GA. Also the maximum overshoot within 3%, while this value equal 6%, and 8% based on AIS, and GA respectively as seen in Figure(5.29). The error in case of using AIS-GA in all criteria is smaller than given by AIS, and GA as depicted in Table 5.6.

Table 5.6 The performance of ANFIS controller optimized by GA, AIS, and (BIGA) method based on performance criteria

AIS-GA (BIGA)

AIS GA

0.001109 0.001772 0.002815 ITAE 0.000646 0.003772 0.017989 IAE 0.00527 0.002022 0.013478 ISE 0.000728

0.028087

0.00575 MSE


١٧٠

Figu

re.(5

.27)

Res

pons

e of

(CD

-MV

AN

FIS)

con

trol

ler

optim

ized

by

GA

met

hod

at

diff

eren

t per

form

ance

cri

teri

a .

The

RES

PON

SE o

f AN

FIS

CO

NTR

OLL

ER O

PTIM

IZED

BY

GA

0.9

0.951

1.051.

1

00.

010.

020.

030.

040.

050.

060.

070.

080.

090.

1

X2M

SEX2

ITAE

X2IS

EX2

IAE


١٧١

The

RE

SPO

NSE

of

AN

FIS

CO

NTR

OLL

ER

OP

TIM

IZE

D B

Y A

IS

0.9

0.951

1.051.

1

00.

010.

020.

030.

040.

050.

060.

070.

080.

090.

1

X2M

SE

X2I

TAE

X2I

SE

X2IA

E

Figu

re.(5

.28)

Res

pons

e of

(CD

-MV

AN

FIS)

con

trol

ler

optim

ized

by

AIS

met

hod

at

diff

eren

t per

form

ance

cri

teri

a .


١٧٢

Figu

re.(5

.29)

Res

pons

e of

(CD

-MV

AN

FIS)

con

trol

ler

optim

ized

by

AIS

IGA

)-G

A(B

m

etho

d a

t diff

eren

t per

form

ance

cri

teri

a .

The

RESP

ONSE

of

ANFI

S CO

NTRO

LLER

OPT

IMIZ

ED B

Y AI

S-GA

0.94

0.98

1.02

00.

010.

020.

030.

040.

05

X2M

SEX2

ITAE

X2IS

EX2

IAE


١٧٣

The detailed of comparison between the proposed controllers and hybrid (PID-NN) [72] hybrid GA-AIS can be explained as follows. The error between the proposed controller and PID using GA based on all performance criteria is showed in Figure (5.30). By comparing the performance using MSE, we see that the response using introduced cascaded ANFIS is very fast, smooth and with smaller overshoot equal 8%,but using PID; the response is very slow, and overshoot is very big and equal .75% as showed in Figure (5.30). Figure (5.31) shows the comparison performance for PID and introduced controller optimized by AIS (IGA) at different performance criteria. The overshoot not exceeds 5 percent using our controller, while this value reaches 25 percent using other controller. The introduced controller reaches the steady state faster than PID by 25 times using MSE, ITAE respectively. Figure (5.32) shows the comparison performance between PID and proposed controller optimized by AI-GA (BIGA) at different performance criteria. the results show that the performance of our controller is faster 20 times than PID controller in case of IAE, and faster 35 times for MSE, ISE and ITAE. Also our controller reaches steady state without error in all criteria, while the other reaches with 1 to 2 percent of errors. From this figure we showed that the response in case of our cascaded controller combine the merits of fasting response given by GA and small value of overshoot given by AIS. The error of the performance for each above controllers in case of optimization by GA, AIS, and AIS-GA at different criteria are show in Figure (5.33), Figure(5.34), and Figure(5.35) respectively. Comparing results from both BIGA method and the AIS and GA standalone methods, the hybrid method exhibits good results. It is shown that the hybrid AIS-GA method is much better in terms of Overshoot, Rising time and settling time. The percentage of error for each case at different criteria showed that the (BIGA) has the smallest values as seen from Table 5.7. The above results show that the performance of the proposed controller with (PID-NN) hybrid GA-AIS in[72] has superior features and good computational efficiency.


١٧٤

COMP

ARE

BETW

EEN

ANFI

S &

PID

CONT

ROLL

ER O

PTIM

IZED

BY

GA

0.50.60.70.80.911.1

00.0

10.0

20.0

30.0

40.0

50.0

60.0

70.0

80.0

90.1

PID-

MSE

PID-

ITAE

PID-

IAE

PID-

ISE

ANFI

S-MS

E

ANFI

S-IT

AE

ANFI

S-IA

E

ANFI

S-IS

E

Figu

re.(5

.30)

Com

pari

son

betw

een

PID

and

AN

FIS

cont

rolle

r o

ptim

ized

by

GA

met

hod

at

diff

eren

t per

form

ance

.


١٧٥

Figu

re.(5

.31)

Com

pari

son

betw

een

PID

and

AN

FIS

cont

rolle

r o

ptim

ized

by

AIS

m

etho

d a

t diff

eren

t per

form

ance

.


١٧٦

Figu

re.(5

.32)

Com

pari

son

betw

een

PID

and

AN

FIS

cont

rolle

r o

ptim

ized

by

AIS

-GA

(BIG

A)

met

hod

at d

iffer

ent p

erfo

rman

ce.

COM

PAR

E BE

TWEE

N A

NFIS

& P

ID C

ONTR

OLLE

R OP

TIM

IZED

BY

AIS-

GA

0.951

00.

010.

020.

030.

040.

050.

060.

070.

080.

090.

1

PID-

MSE

PID-

ITAE

PID-

IAE

PID-

ISE

ANFI

S-M

SEAN

FIS-

ITAE

ANFI

S-IA

EAN

FIS-

ISE


١٧٧

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

0 0.02 0.04 0.06 0.08 0.1 0.12

PID-ITAEANFIS-ITAE

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 0.02 0.04 0.06 0.08 0.1 0.12

PID-IAEANFIS-IAE

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

0 0.02 0.04 0.06 0.08 0.1 0.12

PID-ISEANFIS-ISE

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 0.02 0.04 0.06 0.08 0.1 0.12

PID-MSEANFIS-MSE

(a)

(c)

(b)

(d)

Figure(5.33) Comparison the performance criteria between PID and ANFIS controller optimized by GA method (a) ITAE (b) IAE (c) (c) ISE (d) MSE


١٧٨

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

0 0.02 0.04 0.06 0.08 0.1 0.12

PID-ITAEANFIS-ITAE

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

0 0.02 0.04 0.06 0.08 0.1 0.12

PID-IAEANFIS-IAE

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

0 0.02 0.04 0.06 0.08 0.1 0.12

PID-ISEANFIS-ISE

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

0 0.02 0.04 0.06 0.08 0.1 0.12

PID-MSEANFIS-MSE

(a)

(c)

(b)

(d)

Figure.(5.34) Comparison the performance criteria between PID and ANFIS controller optimized by AIS method (a) ITAE (b) IAE (c) (c) ISE (d) Mse


١٧٩

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

0 0.02 0.04 0.06 0.08 0.1 0.12

PID-ITAEANFIS-ITAE

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

0 0.02 0.04 0.06 0.08 0.1 0.12

PID-IAEANFIS-IAE

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

0 0.02 0.04 0.06 0.08 0.1 0.12

PID-ISEANFIS-ISE

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

0 0.02 0.04 0.06 0.08 0.1 0.12

PID-MSEANFIS-MSE

(a)

(c)

(b)

(d)

Figure.(5.35) Comparison the performance criteria between PID and ANFIS controller optimized by AIS-GA (BIGA) method (a) ITAE (b) IAE (c) (c) ISE (d) Mse


١٨٠

Another comparison with the nonlinear MIMO plant model controlled by simplified (ANFIS) controller by [76], the plant model described in eq(5.25) [70].

)1()1(

)1(1)1()1(

)1(1)1(

)()(

2

1

22

21

22

1

2

1

kuku

kykyky

kyky

kyky (5.25)

the GA was employed to determine the input and output scaling factors for

this controller, instead of the widely used trial and error method.

The total number of fitting parameters in the ANFIS structure is given by:

)1.(..),,( npmpnmpnf n for the first order sugeno fuzzy model. (5.26) npmpnmpnf ..),,( for the zero order sugeno fuzzy model. (5.27)

Where (n) is the number input variables, (p) number of fuzzy sets, and (m) is

the number of fitting parameters per membership function (MF). Although

the simplified (ANFIS) controller used zero order sugeno fuzzy model, the

proposed cascaded ANFIS (CD-MV-ANFIS) controller requires less number

of parameters to be tuned comparing to others as shown in Table 5.8.

Table 5.7 The performance of the proposed controller compared to PID at different criteria in case of GA, AIS, AIS-GA

AIS-GA (BIGA) AIS GA

PID ANFIS PID ANFIS PID ANFIS 0.149087 0.001109 0.047076 0.001772 0.237283 0.002815 ITAE 0.042391 0.000646 0.003913 0.003772 0.530543 0.017989 IAE 0.016304 0.00527 0.0003 0.002022 0.001413 0.013478 ISE 0.016522 0.000728

0.081196 0.028087

0.167174 0.00575 MSE


١٨١

As can be seen from Figures (5.36) a and b, the CD-MV-ANFIS controller has compared to simplified (ANFIS)controller [76] .The proposed controller has good performance with zero steady-state error and no overshoots at the beginning of each step change rather than for simplified (ANFIS)controller. Figures (5.36) (c), and (d) show a sharp control signals when the testing signal has changed its amplitude. This sharp control action is necessary to compensate for the interactions between the two channels of this nonlinear MIMO system, and consequently, to achieve the good tracking performance in Figure (5.36)(a),and (b). The mean square errors for both CD-MV-ANFIS and simplified ANFIS controllers are depicted in Figure.(5.37). It can be seen that the MSE has reached its near zero value from the first few generations as seen from Figure(5.37).Therefore, the selection of the maximum number of generations to be 50 seems to be adequate. This fact indicates the fast convergence to the optimal solution rather than that has been achieved by the GA in the simplified MIMO ANFIS controller using 300 generation. Therefore, from a comparative study with a simplified MIMO ANFIS [76], the proposed controller has shown its superiority in terms of the reduced training time and the control accuracy, forth more eliminate number of fuzzy rules.

Table 5.8 Comparing the proposed controller to other controllers Controllers No of

fuzzy No of premise parameters

No of consequent parameters

Total no of parameters

CD-MV-ANFIS 3 18 27 45 Simplified ANFIS 7 28 98 126


١٨٢

Samples (k)

Figure.(٥.36) Comparison between output responses for using CD-MV-ANFIS and simplified ANFIS controllers (a)and (b) output results in both controllers. (c), and (d) control signals.

(a)

(b)

(c)

(d) Samples (k)

Figure.(5.37) MSES for both CD-MV-ANFIS and simplified ANFIS controllers.

Samples(k)


١٨٣

5.8 Summary The two schemes (MV-ANFIS) and (CD-MV-ANFIS) proposed for a greenhouse (GH) system, tuned by immune genetic algorithm. The comparison between two schemes showed that each of them able to track the set points smooth based on mean square errors (MSEs). The changing of control signal was also very smooth, which increase the lifetime of actuators. It also reduces the operation cost of a GH production system to be compatible with scarcity of resources and the low of investment capacity of growth. The comparison with other controllers showed that our proposed schemes able to handle any imprecise knowledge with minimum numbers of tuned parameters. Finally, it is shown that the proposed controller has a great improvement on the output responses for all wide ranges of operations.

CHAPTER 6 Conclusions and Trends for Relevant Future Work

6. Conclusion

6.1 Summary and conclusion Recent publications in the area of industrial non-linear systems study multiple outputs when being merely juxtaposed evidently these are a constraint which is not applicable for the majority of practical control schemes, besides a set of limitations, e.g. empirical tuning of their parameters when the operating conditions of the controlled process are changed. This thesis presented two approaches for optimal operation and control non-linear industrial processes.

6.2 Contributions In response to the circumstances, this thesis contributes a methodology to design adaptive control system for a drum boiler turbine unit, and a Greenhouse (GH) system as a multiple output. Towards the above goal, this thesis introduced new Adaptive-neuro fuzzy inference systems (ANFIS) due to their transparency, nonlinear features, and self tuning of their parameters for controlling dynamics, uncertain and highly nonlinear systems. It proposes two control schemes for controlling these dynamical systems. The two schemes (one is a conventional and the other is a distributor) consider the interactions between the variables of the controlled process by developing a (MIMO) ANFIS control schemes. The proposed conventional multi-variable ANFIS (MV-ANFIS) controller includes the feedforward-feedback (FF-FB) control scheme, which is an extension of the general linear single-input single-output feedback control scheme, with both reference feedforward and disturbance feedforward actions, to the nonlinear multivariable case. The feedforward controller which is implemented using a set of multi-input-single-output (MISO) fuzzy inference systems that was designed from plant input-output data using a neural network paradigm. The process operating window is partitioned to take into account the process nonlinear characteristics. The Immune Genetic algorithm (IGA) method is a global search technique based on an analogy with biology in which a group of solutions were evolved through a natural selection and survival of the fittest. An Immune Genetic algorithm (IGA) is used to give adaptability to the fuzzy system to be adapted the changing situations. The feedback control path is implemented as a fuzzy PI-based decentralized (multi-loop) control. The feedforward (FF) control algorithms are the first order of Sugeno-type fuzzy inference that system comprises one fuzzy block with a set of inputs that are involved in fuzzy rules of which

Chapter 6: Conclusion and Trend for Relevant Future Work

184 comprising several AND-conditions, while the feedback (FB) control algorithm is a zero order Sugeno-type fuzzy inference system. Since the number of rules increases exponentially with the number of inputs, the conventional scheme which is proposed for controlling MIMO systems is degraded. This thesis proposes also a cascade distributed multi-variable (CD-MV-ANFIS) ANFIS controller to overcome the dimensionality problem of large-scale systems. The proposed scheme decomposes a complex model with input vector, XRn into distributed architecture of sub models each of which has input vector XR2 that reduces the number of fuzzy rules drastically. A relevant matlab programs and codes (not available in the original package) are devised for the implementation and testing of the proposed design approach. The thesis introduced an on-line approach using a new Blend Immune Genetic Algorithm (BIGA) for adjusting parameters of fuzzy controller. The effect of decreasing or increasing number of rules is presented also. In addition the performance of the proposed controllers is demonstrated through simulation experiments in two types of non-linear drum boiler turbine unit. Moreover the proposed (CD-MV-ANFIS) controller is applied also to the Greenhouse (GH) system as a different type of practical processes on environmental under variety of climate circumstances. Results show the feasibility and efficacy of the new proposed paradigm developed with immune genetic tuning (IGA). Compared with the conventional multi-variable control structure (MV-ANFIS) the cascade distributed multi-variable control structure (CD-MV-ANFIS) is a more promising scheme for controlling complex, uncertain, and nonlinear MIMO real processes. Several simulation examples are given to verify the performance of the proposed cascaded multivariable ANFIA (CD-MV-ANFIS) controller tuned by Immune Genetic Algorithm (BIGA). The performances of proposed method also compared with GA and artificial immune System (AIS) or (IGA) alone, it was shown that (CD-MV-ANFIS) hybrid GA-AIS controllers reveal clear differences between them. 6.3 discussions

Comparing the results obtained by the two proposed schemes with that obtained by previous researches we noticed that: Regarding to the proposed modeling technique; explained and introduced in chapter 2, for three “linear and non-linear processes” and that introduced by Multi-Layer Perception Network (AMLP) [75]. We see that in all cases the proposed MV-ANFIS model is very well and have smaller RMSE values as we can see in Table 6.1.


185

For MIMO modelling of drum-boiler based on proposed multivariable ANFIS(MV-ANFIS) scheme, the mean square errors(MSES) for pressure, power, and density of water were very small compared with that given by Multi-Layer Perception Network (AMLP) [75], see Table 6.2.

The performance of proposed multi-input multi-output (MIMO) ANFIS controller to compare the performance of fuzzy controller over a wide ranges of operations for third order drum boiler model. The mean square errors(MSES) between multi-input multi-output (MIMO) ANFIS and fuzzy at different lodes is depicted in Table 6.3, The average mean square errors at different set-point changes in Table 6.3 is showed in Table 6.4 We can show from the Table 6.3, Table 6.4 ,how can the proposed MIMO ANFIS gives best performance over a wide ranges of operations for third

Table 6.1 RMS and errors reduction for ANFIS and AMLPs networks

RMS error modeling

Modeling task 1 Modeling task 2 Modeling task 3 Linear Non-

linear Linear Non-

linear Linear Non-

linear AMLPs 4.00E-05 9.25e-7 1.07E-5 2.45e-6 8.032e-5 0.0013

ANFIS 3.61E-05 43.43e-8 3.43E-7 37.79e-9 5.338e-5 6.444e-4

%

Reduction 9.7342 53.04 96.802 98.46 33.539 50.429

Table 6.2 Root mean square error value in case of MV-ANFIS & NN modeling

RMS error *10-2

power pressure density NN 0.07 0.25 0.32

ANFIS 0.04 0.18 0.2 % Reduction 43 28 37.5


186 order drum boiler turbine unit. The small reduction of error can be achieved in case of pressure loop, while the maximum reduction given in case of drum level loop.

Table 6.3 The average Mean square errors for different set-point changes using Multi-loop ANFIS and fuzzy controller for third order model

Change of set point MSES of Multi-loop Fuzzy Controller 3 order model

MSES of Multi-loop ANFIS Controller 3 order model

Pre

ssur

e

pow

er D

rum

/l P

ress

ure

Pow

er

Dru

m/l

Pre

ssur

e

Pow

er

Dru

m/l

± 4 Bar ± 35 Mw ± 1 m 0.0177 0.8898 0.0021 0.0173 0.7728 0.0017

± 4 Bar ± 35 Mw ±.5 m 0.0688 0.8898 0.0003 0.0173 0.7899 0.0002

± 5 Bar ± 35 Mw ± .75 m 0.0549 0.8898 0.0040 0.0441 0.9412 0.0007

± 5 Bar ± 35 Mw ± 1 m 0.0632 0.8865 0.0021 0.0442 .72326 0.0017

± 12 Bar ± 55 Mw ± .5 m 0.1399 2.2572 0.0004 0.1199 1.2770 0.0002

± 12 Bar ± 55 Mw ± 1m 0.1222 2.2770 0.0019 0.1218 1.4706 0.0015

±32 Bar ± 62 Mw ± 1 mm 1.2291 3.0188 0.0013 1.1645 2.1395 0.0013

Table 6.4 The average Mean square errors for different set-point changes using Multi-loop ANFIS and fuzzy controller for third order model.

Average MSES Controller

power pressure Drum/l FUZZY

1.586986

0.242257

1.729E-03

MIMO ANFIS 1.15918

0.218443

1.043E-03

% Reduction

between ANFIS and FUZZY

26.96

9.83

39.66


187 In case of seven orders model included critical drum water level, the proposed MIMO controller is very successful to track all set-point with less over shoot especially in drum level changes. The mean square errors(MSES) between MV-ANFIS and fuzzy at different lodes is depicted in Table 6.5, also The average mean square errors at loads in Table 6.5 is showed in Table 6.7. In case of seven orders model included critical drum water level, the proposed MIMO controller is very successful to track all set-point with less over shoot especially in drum level changes. We can also see, although there is no reduction of error in case of pressure loop, the maximum reduction can be achieved in drum level loop.

The average mean square errors for the performance of C-MV-ANFIS controller when controller parameters tuned by Immune Genetic Algorithm (IGA) as detailed in chapter 4 was smaller than others tuning as depicted in Table 6.9.

Table 6.5 Mean square errors for different set-point changes using Multi-loop ANFIS and fuzzy controller for seven order model.

Change of set point MSES of Multi-loop Fuzzy Controller seven order

model

MSES of Multi-loop ANFIS Controller seven order

model

Pre

ssur

e

Pow

er

Dru

m/l

Pre

ssur

e

Pow

er

Dru

m/l

Pre

ssur

e

Pow

er

Dru

m/l

± 4 Bar ± 35 Mw ± 85 cm 0.0019 0.0139 2.2823 0.0019 0.0140 0.6676

± 12 Bar ± 35 Mw ± 135 cm 0.0015 0.0031 1.2088 0.0015 0.0031 1.1909

± 19 Bar ± 75 Mw ± 135 cm 0.3006 4.5264 5.1307 0.3012 4.5263 4.2155


188

Regarding to the comparison between the proposed MV-ANFIS, LQR, and

fuzzy controllers that disused in chapter 4, the average mean squared errors

for three cases are depicted in Table.6.7. From this table we showed that the

all mean square errors associated for the proposed MV-ANFIS controller are

very small compared to that given by other controllers.

Table.6.7 The average MSES of the proposed controller with different controllers at different ranges of operation

LQR FUZY MV-ANFIS

7.03E-01 8.73E-01 1.34E-01 Pressure

1.66E-01 1.83E-01 4.96E-03 Power

4.48E-05 1.19E-04 3.13E-05 Drum/level

Case(1),

Case(2), and

Case(3)

Table 6.6 The average Mean square errors for different set-point changes using Multi-loop ANFIS and fuzzy controller for seven order model.

Average MSES Controller

power pressure Drum/l FUZZY 1.033E-02 4.000E-03 3.221E+00

MIMO ANFIS

1.037E-02

2.200E-03

9.412E-01

% Reduction

-

45

70.77788


189 The average mean square errors for the performance of CD-MV-ANFIS controller when controller parameters tuned by Immune Genetic Algorithm (IGA) as detailed in chapter 4 was smaller than others tuning as depicted in Table 6.8.

By comparing the results of controlling the outputs of third order drum-boiler model with proposed MV-ANFIS Controller, and adaptable nonlinear controller (ANC) [58], exact feedback linearization (EFL), and [35] were explained in chapter 4 and with MIMO fuzzy controller produced by [43] and [42] that tested on the same model with ( same input variables). We notice that all mean squared values for proposed controller are very small compared to the given by other controller at the same operation conditions. The CD-MV-ANFIS controller for three order model explained in chapter 4 solved the problems of huge number of rules, premise parameters, and consequence parameters, where these parameters are very large by using the MV-ANFIS controller.

Table 6.8 Average MSES and % of errors for two model based on tuning algorithm.

Average MSEs and % of errors with different

cases based on tuning tools

Adapting

parameters

AMSEs %error

Without tuning 4.080E-01 7.077E-01

Using genetic 2.010E-01 5.247E-01

3 order

model

Immune genetic 8.033E-02

4.263E-01

Without tuning 8.457E-01 3.214E-01 Using genetic 8.005E-01 2.536E-01

7order model Immune genetic 6.680E-01

1.125E-01


190 The detailed comparison between two controllers was explained in chapter 4, despite of the total parameters to be tuned in case of using CD-MV-ANFIS controller is very small compared to that in case of MV-ANFIS controller, the average mean squared errors were nearly equals in two controllers. In this thesis the challenging to controlling this type was already done as explained in details in chapter 4 by introducing also the two controllers mentioned above. Here also the rules number and total parameters given by CD-MV-ANFIS is very small compared to that for MV-ANFIS controller, besides the average of MSES errors in all outputs at different set-point very small in case of CD-MV-ANFIS. The performance of results is very good using different fuzzy sets with parameters tuned by Immune Genetic algorithm for MV-ANFIS controllers as explained in chapter 4, and chapter 5. To evaluate the performance of power plant under control of new control strategy, different cases (different working conditions) are studied and compared to linear quadratic regulators (LQR), Dimeo and Lee, Boiler-Turbine control system design using an Immune Genetic algorithm [27]. Also the proposed controller compared to fuzzy controller based on inverse model of boiler-turbine system [37].The results showed the capability of the introduced controller to track all set-points without overshoot, besides all control signals within the acceptable range. The mean square errors of temperature and humidity for green house system (GH)using CD-MV-ANFIS, and MV-ANFIS controller based on immune genetic type are smaller than that given by genetic, and without tuning for temperature, and humidity. Also the MSES based on (BIGA) is the best in case of temperature and humidity using MV-ANFIS controller compared to other tuning. Comparing the MSES for both temperature and humidity based on controller type, we show that the MSES associated to CD-MV-ANFIS are the best. To support the usefulness of our work, a comparison with PID controller tuned by blend immune genetic algorithm (BIGA) [72] are also examined. The examination result using proposed controller showed based on the most performance criteria, (ITAE), (IAE), (ISE), and (MSE) as seen in Table 6.9. Based on genetic algorithm (GA) using MSE, the maximum overshoot not exceed 6 percent, while this value using PID controller reaches 75 percent and steady state error equal 9 percent.


191

Based on artificial immune system (AIS), the overshoot not exceeds 5 percent using our controller, while this value reaches 25 percent using other controller. The introduced controller reaches the steady state faster than other by 25 times using MSE, ITAE respectively. Based on hybrid AIS and GA (AIS-GA), the results show that the performance of our controller is faster 20 times than PID controller in case of IAE, and faster 35 times for MSE, ISE and ITAE. Also our controller reaches steady state without error in all criteria, while the other reaches with 1 to 2 percent of errors. Comparing results from both BIGA method and the AIS and GA standalone methods, the hybrid method exhibits good results. It is shown that the hybrid AIS-GA method is much better in terms of Overshoot, Rising time and settling time. Another comparison was made with the nonlinear MIMO plant model controlled by simplified (ANFIS) controller [76]. Although the simplified (ANFIS) controller used zero order sugeno fuzzy models, the proposed cascaded ANFIS controller required less number of parameters; in terms of premise and consequent parameters. The number of tuned parameters in our controller is smaller than that gives from above controller by 87 parameters; this is due to the minimizing of used rules. Comparing results of our controller shows the capability to track the set points without overshoot, while the overshoot reaches 25 percent using a simplified ANFIS controller. The performances of proposed controller comparing with earlier work have superior features, stable convergence characteristic and good computational efficiency. The experimental results have shown the effectiveness of the proposed controller and capability in different wide range operations.

Table 6.9 Comparison the performance between PID and CD-MV-ANFIS controller optimized by GA, AIS, AND (BIGA) method based on minimum error for common performance criteria

AIS-GA (BIGA) AIS GA

PID ANFIS PID ANFIS PID ANFIS

5.61E-02 1.94E-03

3.31E-02 8.91E-03

2.34E-01 1.00E-02


192 Finally, by comparing the two proposed approaches 1 and 2 for drum boiler turbine units and the greenhouse system (GH), we can reach to the following conclusion as follow:

In case of using the two approaches for controlling the third and seven orders drum boiler turbine units and a greenhouse system:

For the third order drum model

We observe that although the CD-MV-ANFIS gave a better performance for pressure and power loops, it was failed to obtain a better performance in drum water level rather than the given performance by MV-ANFIS controller as depicted in chapter 4 Table 4.19

For the seven order drum model

We observe that the MV-ANFIS controller gave the best performance in term of MSES in all loops (pressure, power, and drum/level loops) as depicted in chapter 4 Table 4.20

For a greenhouse system (GH)

In this case, the performance of the introduced CD-MV-ANFIS for temperature and humidity for a greenhouse system was better than the performance of the proposed MV-ANFIS controller in case of tuning with and without genetic. On the other leg, the MV-ANFIS controller gave the best performance based on immune genetic algorithm (IGA) as described in Table 5.5 chapter 5. 6.4 Future work

Although good results have been obtained by using the proposed approaches, their stability and robustness have not been yet analysed mathematically. Such an analysis together with further experimentation in a wide range of complex processes would be worth pursuing to prove conclusively the general validity of the proposed schemes. It is necessary to implement the applied schemes practically on a small drum boiler unit on laboratory as a first step towards the real time application of these schemes on power plant. Also, we suggest studying the application of the blend immune genetic algorithm (BIGA) to reduce the number of fuzzy rules of the applied controllers to reduce the computational time.

١٩٣

Appendex A,B,C

Appendix A 1.1 FFPU Static Models The static model of the FFPU is used to calculate equilibrium points, determine operating windows, and to generate set-points. The static equations can be solved in different ways. Some of them are: • Direct static model. Static equations solved to calculate the process output signals,with input signals as independent variables. • Inverse static model. Static equations solved to calculate the process input signals, with the output signals as independent variables. • Mixed static model. Static equations solved to calculate a mixture of process inputs and outputs signals, with the remaining input and output signals as independent variables. In steady-state the state variables are constant, thus,

0

0

Ltt

PtE

(1)

Substitution into the dynamic model equations yields:

38/9

21 15.00018.09.00 uPuu (2)

EPu 8/92 )16.073.0(0 (3)

38/9

21 15.00018.09.00 uPuu (4) Puu )19.01.1(1410 23 (5) The algebraic model equations become: 5.65/600 awVTVv efssftw (6)

)/1/()/1( wswfs vv (7)

21 sss KPK (8)

)1/()(

*)19.01.1(((

3

22101

kurkPukkukkkw

fw

sffbe

(9)

Substitution of numerical values into the algebraic equations gives:

5.659/6013073.00 esf wa (10) 00154.0/1/00154.0/1 sfs ppa (11)

6.258.0 pp s (12) 0958.251431.214746.08537.059166.45 321 upuuwe (13)

١٩٤

Appendex A,B,C

1.2 Direct static model The direct static model solves the static equations to determine the process outputs (E, P, L) and state variables (E, P, f given the values of the input signals (u1, u2, u3). Since L = 0 in steady state, it is only necessary to determine E, P, and (E, P, f From (2) and (3):

312

2 15.09.00018.0

16.073.0 uuu

uE

(14)

From (4):

19.01.1141

2

3

uup (15)

The working fluid (steam-water) density R is determined by solving the second order equation formed by substituting equation (4) into (6):

sw

sf

sw

swefsfw pv

pppv

pvawVTpVv

1

601

5.65/0 21 (16)

where s and we are given by equations (8) and (9), respectively. Substitution of numerical values for constants in (16) yields:

s

sf

s

sef p

ppp

pwp00154.01

6000154.01

00154.05.659

13073.00 2

(17)

Where s and we are given by equations (12) and (13), respectively. 1.3 Inverse static model The inverse static model solves the static equations to determine the process inputs ( u1,u2,u3 ) and state variables ( E,P, f ) given the values of the output signals ( E , P , L ). Equations (2), (3), and (4) may be rewritten in matrix form as:

pEp

uuu

pp

p

19.019.0

0

1411.10073.00

15.00018.09.08/9

3

2

18/9

8/9

(18)

with sequential solutions:

١٩٥

Appendex A,B,C

8/9

8/9

2 73.016.0

pEpu

(19)

141

19.01.1 23

puu (20)

9.015.00018.0 3

8/92

1upuu (21)

The fluid (steam-water) density, f , is calculated with (17), with s and we given by equations (12) and (13), respectively. Since (17) provides two solutions for the fluid density, only the value with a reasonable physical meaning is selected.

١٩٦

Appendex A,B,C

1.4 Open loop responses for Third order drum boiler turbine unit The outputs responses of third and seven orders drum boiler-turbine model to step changes in the input fuel flow, throttle valve position and feedwater respectively described in case of low load and for full load for Figure (A.1) to Figure (A.6).

Figure (A.1) System response to 1% step change in fuel flow (low load) three order drum boiler turbine model

y2(MW)

Figure (A.2) System response to 1% step change in control valve position (low load) three order drum boiler turbine model

y1(Bar) u1

u2

u3

u1

u2

u3

y2(MW)

y3(m)

y3(m)

y1(Bar)

Time (sec)

Time (sec)

١٩٧

Appendex A,B,C

y2(MW)

u1

u2

u3 y3(m)

y1(Bar)

y2(MW)

u1

u2

u3 y3(m)

y1(Bar)

Figure (A.٣) System response to 1% step change in feedwater flow three order drum boiler turbine model

Figure (A.4) System response to 1% step change in fuel flow (full load) three order drum boiler turbine model

Time (sec)

Time (sec)

١٩٨

Appendex A,B,C

Figure (A.٥) System response to 1% step change in control valve position (full load)three order drum boiler turbine model

y1(Bar)

y2(MW)

u1

u2

u3

y3(m)

y1(Bar) u1

u2

u3

y2(MW)

y3(m)

Time (sec)

Time (sec)

Figure (A.6) System response to 1% step change in feedwater flow (full load) three order drum boiler turbine model

١٩٩

Appendex A,B,C

Appendix B

1.5 Open loop responses for seven order drum boiler turbine unit The outputs responses of seven order drum boiler-turbine model to step changes in the input fuel flow, throttle valve position and feedwater respectively described in case of low load and for full load for Figure (B.1) to Figure (B.6). The varaiables of seven order modelare depicted in Table 1

Table 1 The varaiables of seven order drum boiler model average quality of steam in complete system

cs drum steam pressur P

time constant associated with state x1 TC1 electrical output powe Po

time constant associated with state x2 TC2 normalized fuel mass flow rate u1

state to limit high frequency response to d

2 cs /dt2

x1 normalized throttle valve position u2

state to limit high frequency response to d

2 cs /dt2

x2 normalized feedwater mass flow rate

u3

state to account for shrink and swell phenomena effect

x3 steam mass flow rate Ws

state to account for shrink and swell phenomena effect

x4 total volume of drum and risers Vt

volume below the drum water level VW density of fluid in complete system

drum Water Level Xw density of fluid in drum s

specific volume of water vw

٢٠٠

Appendex A,B,C

y1(Bar) u1

u2

u3

u1

u2

u3

y2(Mw)

y3(cm)

y1(Bar)

y2(Mw)

y3(cm)

Time (sec)

Time (sec)

Figure (B.1) System response to 1% step change in fuel flow (low load) seven order drum boiler turbine model

Figure (B.2) System response to 1% step change in control valve position (low load) seven order drum boiler turbine model

٢٠١

Appendex A,B,C

y1(Bar) u1

u2

u3

y2(Mw)

y3(cm)

u1

u2

u3

y1(Bar)

y2(Mw)

Time (sec

y3(cm)

Time (sec)

Time (sec)

Figure (B.3) System response to 1% step change in feedwater flow (low load) seven order drum boiler turbine model

Figure (B.4) System response to 1% step change in fuel flow (full load) seven order drum boiler turbine model

٢٠٢

Appendex A,B,C

u1

u2

u3 y3(cm)

y1(Bar) u1

u3

y2(MW)

y3(cm)

y1(Bar)

y2(Mw)

u2

Time (sec)

Time (sec)

Figure (B.5) System response to 1% step change in control valve position (full load) seven order drum boiler turbine model

Figure (B.6) System response to 1% step change in feedwater flow (full load) seven order drum boiler turbine model

٢٠٣

Appendex A,B,C

Appendix C

The variables of a Grernhouse system (GH)

Value Meaning of Symbol Symbol

22.2 Ventilation rate m3[air]/ s VR

26 Water capacity of the fog system g[h2 o]/ s qfog

Heat provided by the greenhouse heater W qheater

28 Interior humidity ratio g [h2o]/ kg[ dray air] Win

4-8 Exterior humidity ratio g [h2o]/ kg[ dray air] Wout

Evapotranspiration rate of the plants g[h2o]/ s E(Si,win)

30 Indoor air temperature oC Tin

32-35 Outdoor air temperature oC T out

250-300 Solar radiation W /m2 S i

4000 Greenhouse volume m3 V

Floor area m2 A f

1000 Surface area m2 A s

Building’s solar heating efficiency, dimensionless -- a

25 Heat transfer coefficient W / k UA

1006 Specific heat of air at constant pressure J /(kg[air]K) C p

2257 Latent heat of vaporization g[ h2 o ]/ s ٢ λ

1.2 Air density kg /m3 ρ

0.1295 Shading and leaf area factor, dimensionless -- α

0.15 Thermodynamic constants Kg/min/m٢ β T

State vector x

Control vector u

Disturbance vector v

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1

مستخلص الرسالة

لمعالجـة األنظمــة )MV-ANFIS( حـاكم متكیــف عـصبي مـبهمتـم تـصمیم .عالقات تداخل طبیعیة فیما بینهاالتي تتأثر ب

المـبهمالعـصبى الحـاكم المتكیـف تحـت مـسمىوتم أیضا تقدیم حاكم آخـر تقـــسیم الحـــاكم الـــسابق إلــــى ى علـــامعتمـــد) CD-MV-ANFIS(التسلـــسلي

تـــم ضـــبط و..ورة جذریـــةعـــدد القواعـــد الغیمیـــة بـــصعملیـــات بـــسیطة لتقلیـــل جینــى منبــعم عــن طریــق خــوارزین المقتــرحینالبــارامترات المختلفــة للحــاكم

"Immune Genetic Algorithm".

Drum boiler"تـــم تطبیـــق النظـــامین الــــسابقین علـــى الغالیـــات وturbine units" وكذلك على الصوب الزجاحیة، بمحطات إنتاج الطاقة

"Greenhouse system(GH) "الخطیةأنظمة ما تباره باع..

2

3

موجز الرسالة

”Multi-variable ANFIS Controller“تصمیم حاكم متكیف عصبي مبهم ب الرسالة تتعلقر طرقا مالئمة للتعامل مع یوفت فىویعتمد الحاكم على المنطق المبهم .. مة الالخطیةظللتحكم فى األن

ات الحاكم باستخدام خوارزم جینى منیع بارامترحیث ضبطت ..خطیةالیر غنماذج العملیات

"Immune Genetic Algorithm".. وتم تطبیق طریقة التصمیم المقترحة على نظامین صناعییننظام الغالیة فى محطات تولید الكهرباء و""”Greenhouse systemهما نظام الصوب الزجاجیة

“Drum boiler turbine unit in electric power generation plants” "CD-MV-ANFIS Controller" تسلسلىمبهم عصبىمتكیف أیضا حاكم قدم البحث و

النظام المقترح الحاكمات المعقدة ذات بتحویل فى تقلیل عدد القواعد الغیمیةوقد ساهم هذا الحاكم nRX إلى السابقة ا والتي تنتميالدخل المتعدد ن من متغیرین دخل یتكوو إلى نموذج ذ

2RXفقط متكرر بصورة متسلسلة مما یقلل عدد القواعد الغیمیة بصورة جذریة .

یتمتع الحاكم المقترح بثالث میزات هامة أهمها خاصیة الشفافیة والضبط وقلة سعة المتجه و nRXمن 2الىRX ،خیرة الحاكم المقترح نظام واعد فى التحكم فى النظم تجعل الخاصیة األ

.الحقیقیة متعددة الدخل والخرج بسهولة

Basic function of the mean"ویم إیجاد وتحدیث معامالت نظام االستدالل الغیمى باستخدام

least-squares "عن طریق efficient recursive procedure بدال من استخدام محددات لمعامالت التي یستحیل معها الوصول إلى نتائج عند تعذر الحصول على معكوس مصفوفة ا

-Gradient descent back"بینما یستخدم ، المصفوفة أو أن قیمة المحدد تساوى صفرا

propagation "للحصول على بارامترات دوال الدخل للقواعد الغیمیة

خطیةلالمة اجین من األنظذ نموتم تطبیق النظامین المقترحین علىو

Bell and Astrom models( unitsDrum boiler turbine.( ج األول ذالنمو

فى حالة اقل حمل (حیث تم االستعانة بقیم متغیرات الدخل والخرج فى كل ظروف التشغیل المختلفةوذلك لتدؤیب )عملیات ااتدرج بین أقل وأقصى حمل- ظروف التشغیل العادیة–أقصى حمل -للشبكة

، للمنطق الغیمى المبهم) القواعد الغیمیة( لحصول على القیم االبتدائیة لمعامالت دوال الخرجالنظام ل . باستخدام الخواریوم الجین المنیعاوالتي یتم ضبطها أوتوماتیكی

النظم الالخطیة، متغیرة مع الزمن، متعددة الدخل والخرج والتى تتغیر حالتها بصفة عامة و یعتبر من المشكلة األساسیة فى تلك النظم ذات ظاهرة التمدد واالنكماش هى أنه وتعتبرمع ظروف التشغیل

4

دینامكیات مستوى الماء فى غالیتها یحتوى على دالة تكاملیة والتى ینتج عنها خاصیة االتزان الحرجومن ثم تحتاج تلك األنظمة إلى تحكمات ذات تكنولوجیا ،نتیجة لتغیر األحمال في الشبكة الكهربائیة

تم عمل مقارنة بین النظامین المقترحین واألنظمة األخرى التى طبقت على الغالیات والتى .متطورة .أثبتت مدى فاعلیتها وقابلتها للتطبیق

m syste)GH(Greenhouseج الثانىذالنمو

كاحد االنظمة العملیة التى تسهم اسهاما " Greenhouse system"تم تطبیق الحاكم المقترح على درجة الحرار وكذلك الرطوبة ( فى توفیر المحاصییل الهامة تحت الظروف المناخیة المختلفةكبیرا

حیث اظهر الحاكم المقدم كفائته فى توفیر ،الالزمة المطلوبة فضال عن تحقیق عائد مربح للمزارعین .المناخ المالئم للنباتات المختلفة مقارنة بما تم استخدامه من حاكمات سالفا

: كمایلى أبوابستةوتشتمل الرسالةعلى

على مقدمة عامة وعرض مختصر ألهم ما سبق نشره عن الحاكمات المتكیفة : حتوي الباب األول ی .و تعریف للمسألة موضوع البحث والخواریزم الجینى المنیع الغیمیة المبهمة

ة الألنطمةالالخطیة متعددبتصمیم الحاكم المتكیف الغیمى المبهم للتحكم فى :ویختص الباب الثانى MV-ANFIS“ للنظام والتي تتأثر بحكم عالقات تداخل طبیعیة فیما بینها والكخرجات المدخالت

Controller” . حیث تم تصمیمه وتطبیقه أوال على بعض األمثلة ذات الدخل الوحید والخروج الوحید على نظم الغالیات ةة تم تطبیقیثم على أنظمة متعددة الدخول والخروج وبعد االطمئنان على كفائت

:فیما بعد

CD-MV-ANFIS" التسلسلي بتقدیم الحاكم المتكیف الغیمي المبهم :ویختص الباب الثالث

Controller"الحاكمات المعقدة ذات الدخل المتعدد إلى نموذج والذي ساهم إلى حد كبیر بتحویل ا یقلل عدد القواعد الغیمیة بصورة ذات دخل یتكون من متغیرین فقط متكرر بصورة متسلسلة مم

. جینى منیعم وتم ضبط بارامترات الحاكم باستخدام خوار یز.جذریة

:ویختص الباب الرابع

MV-ANFIS" " استخدام الحاكم المتكیف الغیمى المبهم للتحكم فى الألنطمة الالخطیةب

Controller التسلسلي وكذلك الحاكم المتكیف الغیمي المبهم "CD-MV-ANFIS Controller"

. حیث طبقا على نموزجین من الغالیات البخاریة من الرتبة الثالثة والسابعة

مستوى تدینامیكیا نظرا النظاهرة التمدد واالنكماش السابعة تبدو بها ج من الرتبة ذحیث أن النمو تبعا لمتطلبات حرج ینتج عنها خاصیة االتزان الوالتي على دالة تكاملیة تحتوى هذه األنظمة فيالماء

5

واألبحاث المنشورة حول هذه األنظمة تتفادى التعامل مع هذا النموذج نظرا لصعوبة .الشبكة الكهربیة .ج من الرتبة الثالثة ذ وطبقت ایضا على النمو.تصمیم حاكم متكیف لمثل هذه الظروف

:ویختص الباب الخامس

-CD-MV" . و "MV-ANFIS Controller" المقترحین باستخدام الحاكمین السابقین ANFIS" Controller"

نظمة العملیة حد األاك "Greenhouse system" الصوب الزجاجیة ى علماه تطبیقحیث تم النتائج بما تم مقارنةوتم لمختلفة افى توفیر المناخ المالئم للنباتاتكبیرا التى تسهم اسهاما خطیة الال

.س النوع من هذه الصوبسالفة النشر على نف حاكماتاستخدامه من :السادسویختص الباب

بعرض المیزات التي تم الحصول علیها باستخدام الحاكمات المقترحة مقارنة بما تم نشره في هذا .فضال عن المقترحات التى یمكن إتباعها في األبحاث المستقبلیة،المجال

تعریف بالباحـث

سـعد محمد حافظ ھویدى /مھندس: مـــســاال االلكترونیةھندسة كلیة ال (الھندسة الكھربیة ماجستیر )جامعة المنوفیة–قسم االلكترونیات الصناعیة -بمنوف

١/٧/١٩٦٨: ـالدـ المی تاریخ بحیرة - الدلنجات – كفر الھوایدة: محل المیـــالد

اثنینعول ی و- متزوج: جتماعیةالحالة اال مصري: سیةـــــالجن

مسلم: انةــــــالدی

االلكترونیة ھندسة كلیة ال ١٩٩١ مایو دور - بكالوریوس الھندسة الكھربیة:ي ل الدراسـالمؤھ

)جامعة المنوفیة–قسم االلكترونیات الصناعیة -بمنوف

لكترونیات الصناعیة قسم اال-االلكترونیةھندسة كلیة ال-ماجستیر الھندسة الكھربیة

.٢٠٠٥یة المنوفجامعة

٢٠٠٧ عام ١٢ القادة التابع لوزارة الكھرباء والطاقة دفعة دإعداخریج معھد : الخبرات السابقة

جمیع الشركات التابعة للشركة القابضة للكھرباء بوفي العلوم اإلداریة محاضر بالمعھد

تحت رعایة وزارة الدولة للتنمیة اإلداریة٢٠١٠خریج معھد القادة الحكومیین عام

شركة –مدیر عام التعاون مع جھاز تنظیم مرفق الكھرباء وحمایة المستھلك : الیةـالوظیفة الح

كھرباء البحیرة

mail-e( : com.yahoo@hewaidy_aads( نىوالبرید اإللكتر

[email protected]

)عمل ( ٠٤٥ / ٣٣٣٦٥٠٢ : اتفـــــالھ

)منزل (٠٤٥ /٣٧٦٢٧٠٠

)محمول( ٠١٠ / ١٦٣٦٧٦٢١

جامعة طنطا ةـــة الھندســــكلی

قسم ھندسة الحاسبات و التحكم اآللي

مبھم تحت ضبط عصبيتصمیم حاكم متكیف منیعجینيخوارزم

الدكتوراهرجة دلحصول علىل كمتطلب بحث مقدم

) اآللىھندسة الحاسبات والتحكم( في الھندسة الكھربیة من

افظ ھویدىسـعد محمد ح/المھندس ) ٢٠٠٥- نظم التحكم األلى وااللكترونیات الصناعیةھندسة (ماجستیر الھندسة الكھربیة

تحت إشراف

ـيـمد فهمـمود محـمح/ أستاذ دكتور قسم هندسة الحاسبات والتحكم اآللي

جامعة طنطا–كلیة الهندسة

سید أحمدطلعت فهیمد محـم/ أستاذ دكتور تحكم اآللي قسم هندسة الحاسبات وال


ليـدي الطبیـارق األحمـط /دكتورأستاذ مساعد

قسم هندسة الحاسبات والتحكم اآللي جامعة طنطا– كلیة الھندسة

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المنــاقشة والحكــم على الرســالة

٢٠١٣ ینایر ٣ :التـــاریخ

جامعة طنطا–كلیة الھندسة :المكــــان

ــــــــنةـاللجـــــ محمود محمد فهمي أمین ./د.أ

هندسة الحاسبات والتحكم اآلليبقسم أستاذ متفرغ جامعة طنطا- كلیة الهندسة

محمد مبروك شرف/د.أ بقسم هندسة االلكترونیات الصناعیة والتحكم اآللي أستاذ متفرغ

فیةجامعة المنو- االلكترونیة بمنوف لهندسة كلیة ا

لحمید سالما السید عبد /د.م.أ األستاذ المساعد ورئیس قسم هندسة الحاسبات والتحكم اآللي

جامعة طنطا- كلیة الهندسة

طارق األحمدى عبد العزیز الطبیلى/ د.م.أ قسم هندسة الحاسبات والتحكم اآلليباألستاذ المساعد

جامعة طنطا- كلیة الهندسة ٢٠١٣

جامعة طنطا ةـــة الھندســــكلی

قسم ھندسة الحاسبات والتحكم اآللي

مبھم تحت ضبط عصبيتصمیم حاكم متكیف منیعجینيخوارزم

مقدم من سـعد محمد حافظ ھویدى /ھندسم

ماجستیر الھندسة الكھربیة ) ٢٠٠٥-نظم التحكم األلى وااللكترونیات الصناعیةھندسة (

جامعة المنوفیة-كلیة الهندسة االلكترونیة بمنوف

رسالة دكتوراه الفلسفة فى الهندسة الكهربیة

)هندسة الحاسبات والتحكم اآللى(

تحت إشراف

محـمد طلعت فهیم سید أحمد/ أستاذ دكتور قسم هندسة الحاسبات والتحكم اآللي


محـمود محـمد فهمــي/ ستاذ دكتور أ قسم هندسة الحاسبات والتحكم اآللي


طـارق األحمـدي الطبیـلي/ أستاذ مساعد دكتور

قسم هندسة الحاسبات والتحكم اآللي جامعة طنطا– كلیة الھندسة

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Documents

Tanta University Faculty of Engineering Computer and Control Engineering Department Adapitve Neuro-Fuzzy Controller Design Tuned by an Immune Genetic Algorithm By Eng. Saad Mohame