Lv Hongli Duang Peiyong - Direct Conversion of PID Controller to Fuzzy Controller

8/13/2019 Lv Hongli Duang Peiyong - Direct Conversion of PID Controller to Fuzzy Controller

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Direct Conversion of PID Controller to Fuzzy

Controller Method for Robustness

Lv Hongli Duan Peiyong Cai Wenjian Jia LeiInformation and Electric Engineering

College

School of Electrical and Electronic

Engineering

School of Control Science and

Engineering

Shandong Jianzhu University Nanyang Technological University Shandong University

Jian, Shandong,250101, China Singapore, 619798 Jian, Shandong,250061, China

[email protected] [email protected] [email protected]

Abstract - A new fuzzy control strategy, converted

directly from the PID controller, was applied to control

the Heating, Ventilating, and Air-Conditioning (HVAC)

systems in this paper. It took full advantages of mature

technologies of PID parameters tuning to improve the

design of fuzzy controllers. The mathematical analyticalexpression of parameters between fuzzy controllers and

linear gains coefficients of conventional PID controllers

was got based on the structure analysis of fuzzy

controllers. And the fuzzy controller was designed

through gains tuning of PID controller based the

analytical relations. Because HVAC systems are typical

nonlinear time-variable multivariate systems with

disturbances and uncertainties, then this new fuzzy

controller was applied into temperature control in HVAC

systems. The simulation test results compared with the

conventional PID control showed that the proposed fuzzy

controller is effective and this algorithm has less

overshoot, shorter setting time and better robustness etc.

I. INTRODUCTION

Fuzzy logic control technique based-on the concept of the

fuzzy algorithm by Zadeh in 1973 has been successfully

applied in many engineering areas since the pioneer work of

Mamdani in 1974[1, 2]. Fuzzy controllers possess

advantages of strong robustness, better global control

effects etc. and no need mathematical model. The fuzzy

controller is essentially time-variable nonlinear system with

variable gains in nature and only at the certain time it

behaves the linear PID type controller with constant gains.

But up to date fuzzy controller design is still more a matter

of art than technology and can not play the main role in

industrial processes because it is difficult to grasp the fuzzycontrol technologies for common technicians and skilled

workers.

In the process industries modern process control problems

are dominated by nonlinear, time-varying behaviour, dead

time, disturbance and uncertainties with the development of

technologies in practical engineering[3] and most lpants in

industrial automation and process are controlled by the well-

established PID controllers until today[4]. But the linear

PID algorithm might be difficult for process with complex

and time-variant, poorly defined dynamics. Conventional

PID controllers have gone through a technological evolution

because many sophisticated algorithms have been used to

improve its work under difficult conditions. Especially

fuzzy logic inferences and neuron network based on self-

tuning schemes of PID controllers have also been proposedto enhance the control performance. Qiang Bi et al gave an

advanced auto-tuning PID controller then applied it into

HVAC systems successfully[5]. Hanxiong Li proposed an

improved robust fuzzy-PID controller with optimal fuzzy

reasoning, which was introduced to overcome inconsistent

inference and losing robustness. But they can not change the

linear essence of PID controllers.

A novel idea to design PID controller-based fuzzy

controller is attempted to be proposed in order to absorb the

advantages of existing two combination of fuzzy and PID

controllers in this paper. At first the mathematical analytical

expressions of parameters between the fuzzy control and

PID controller are given based on the structure analysis of

fuzzy controller. So we get the mathematical relation ofparameters of fuzzy controller and linear gains of PID

controllers. Then the fuzzy controller makes good use of

gains tuning of PID controller to be designed based the

analytical relations. Then we get the newest satisfactory

design of fuzzy controller based on the PID control

parameters tuning. Furthermore, the simulation results show

the effective performance of this fuzzy controller and

experiment tests results indicate that the proposed fuzzy

control approach is effective for the temperature control of

air handling unit in HVAC systems.

II.DESIGNOFNOMINALFUZZYCONTROLLER

ue

re

Fuzzy

controller

PID

controller

Process

DIP KKK ,,

Parameters

Fig. 1 fuzzy controller based on PID tuning

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Authorized licensed use limited to: Norges Teknisk-Naturvitenskapelige Universitet. Downloaded on December 4, 2009 at 08:28 from IEEE Xplore. Restrictions apply.


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It is assumed that the process under control can be

modelled as the following first order plus dead time

(FOPDT) dynamics, and all the three plant parameters can

be obtained a priori:

( ) 1

sKeG s Ts

= + (1)

Where K is the open-loop process gain, is theeffective dead time and T is the overall time constant. For

this kind of plant, a conventional PID control strategies was

the most often used, and then it is easy to get the gain

coefficientsDIP KKK ,, of its PID controller respectively. In

order to design the PID parameters based-on fuzzy

controller, at first the simplest structure of two-input single-

output nominal fuzzy controller is given. At any given time

instance nwith a sampling time Ts, the two input variables

of fuzzy controller, error state variable and error change are

defined as ( ) ( ) ( )e n y n r n= and ( ) ( ) ( 1)e n e n e n = . And

its output variable )(tu is the control signal of process.(1) The membership functions of two input variables

,e e used triangular shapes and the membership functionsof output variables u used singleton fuzzy sets. The

membership functions of input variables ,e e are definedas the following triangular shape membership functions

fuzzy sets , , ,Pe Ne P e N e , that is:1 1

1( ) ( 1) 1 1

2

0 1

P

e

e e e

e

= +


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Then the fuzzy controller can be transformed into

( ) ( ) ( ) ( )P I D

u n K e n K e n dn K e n= + + (8)It is a PID controller in style, but it is a fuzzy controller at

a certain sampling time in nature. Then we can take good

use of these equations to design the fuzzy controller on base

of parameters tuning of PID controllers. First of all, since

the gains tuning of PID controller is used to service for

fuzzy controller, we regard the error normalized factor

Ge as a free variable for a while, and (7) can be changedinto following equal styles:

2

2

4

2

4

( 4 )

P P I D

I

D I

P P I D

I

K K K KG e Ge

K

K KGu

K K K K Ge

KG u

Ge

=

=

=

(9)

III. DESIGN AND TUNING OF NORMALIZEDFACTORS BASED ON PID PARAMETERS

The parameters of one typical fuzzy controller are

generally composed of two kinds, one is design parameters,

including membership functions, rules, inference algorithms

and defuzzification operation, and the other kind of

parameters is tuning parameters, including all the

normalized factors because they change with the different

controlled processes. In fact, the identification of fuzzy

controller is the determining process of these parameters

through PID gain parameters in this paper.

At first we design nominal fuzzy controller according to

the general structure of fuzzy controller. The fuzzy data

base and rules, the fuzzification and defuzzificationalgorithm are chosen and the fuzzy inference operators are

decided accordingly.

Secondly we tune the design parameters of fuzzy

controller, ,Gei G ei , Gu and G u , based on the

relationship between the normalized factors of fuzzy

controllers and gains of PID controller shown in (9). We

suppose the initial error normalized factor, which is marked

by 0Ge , is fixed. Then they can directly be used to tune

normalized factors in fuzzy controller off-line firstly. In

order to make fuzzy controller better fit for the dynamical

process, furthermore convenient to be applied into industrial

plant, according to the designing formulate (9), the concrete

design is given as follows:When

PK is increasing in PID controller, the output

response will speed and the steady state error will reduce.

Accordingly in (9), the system response arises from increase

ofPK turns into very comparatively relaxative and more

recipient, in stead of simple change of proportional gain.

G e will increase, Gu will increase and G u do notchange. Similarly, When

IK is increasing in PID controller,

G e will decrease, Gu will increase, and G u will increase

in fuzzy controller; WhenD

K is increasing, G e will

decrease, Gu will increase, and G u do not change.As a result, the above design and tuning based on the PID

controller gain factors, the fuzzy controller achieved

primary design and then it can work in process on line. In

order to be applied into industrial process control

conveniently, sum up the above design and tuning ofproposed fuzzy controller, the concrete design guideline is

given as follows:

Step 1: Design conventional PID controller for process

plant on base of mature design algorithems;

Step 2: Design nominal fuzzy controller for process plant

and confirm its design parameters, that is, choose fitting

fuzzy algorithms, including fuzzification, defuzzification,

inference operations etc. It is better to realize the

compositive device electronics for general fuzzy controller;

Step 3: On base of equations (9) and initial error

normalized factor 0Ge , design and tune fuzzy controller

according to gains of PID controller, the tuning parameters

of fuzzy controller, the normalized factors are got;Step 4: Apply the designed well fuzzy controller into

process plant, only change the normalized factors of fuzzy

controller on-line with the transformation of process

parameters.

IV. SIMULATION EXAMPLE

The simulation study is conducted to verify the proposed

fuzzy controller design algorithm based on the parameters

tuning of the PID controller. Considering the following this

kind of FOPDT process0.80.3

( )0.9 1

seG s

s

=

+ (10)

At first, we get the gain parameters of its PID controller,that is

1.875, 2.08, 0.09PP I D

I

KK K K

T= = = =

Secondly, the fuzzy controller of process (10) is designed

according to the algorithm given in Section 3 and its PID

controller. Then on base of design for standard and

universe fuzzy controller, only the tuning parameters of

conventional fuzzy controller need to be design and

tuned. Thirdly, when the gain parameters of its PID

controller in first step was brought into (9) and initial

error normalized factor0Ge is temporarily chosen to 1

for convenience, according to the experiments and

experience, The tuning parameters of fuzzy controller,

the normalized factors were got according to the

controlled process (10), that

is 0.45, 0.08, 2.08G e Gu G u = = = . The simulation

result in figure 3 showed that it is similarly available to

apply the proposed fuzzy controller and PID controller. But

the fuzzy controller has extraordinary stronger disturbance

rejection capability than PID controller.

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0 20 40 60 80 1000

0.2

0.4

0.6

0.8

1

1.2

1.4

time(s)

y(t)

FC

PID

Fig. 3 control response of process (10)

In order to further verify the dynamical performance of the

designed fuzzy controller and check its robustness, we used

the same fuzzy controller to control other FOPDT process.

When model time constant T change, the dynamical

performance was shown in figure 4; When model gain k

change, the dynamical performance was shown in figure 5;When model time delay change, the dynamicalperformance was shown in figure 6. In order to illuminate

controller effects, in every control process, the unit pulse

disturbance was added into process at t=20 second. The

simulation results of dynamical responses from figure 4 to 6

showed further validities of the proposed fuzzy controllers.

At the same time, the designed PID controller (13) was used

to control corresponding processes. Compared with the

control effect of PID controller, the fuzzy controller based

on the PID controller parameters behaved better dynamical

performance and strong robustness.

V. EXPERIMENTALTESTINTHEHVACSYSTEMS

Considering the HVAC systems, we only choose

temperature control as an example. Then an air-handling

unit (AHU) is composed of cooling coil, air dampers, fans,

chilled water pump and valves etc. The schematic diagram

of AHU in HVAC system is shown as in Figure 7, which

consists of cooling coil, air dampers, fans, chilled water

pumps and valves. There are two physical loops in the

cooling coil unit (CCU): chilled water loop and air loop.

The dry-bulb temperature, web-bulb temperature and

airflow rate of the on-coil air are aiT , aiwbT and am& ,

respectively. Likewise, the off-coil dry-bulb and wet-bulb

air temperatures descend to aoT and aowbT , through heat

transfer with chilled water in the cooling coil pipes. The off-coil temperature aoT and chilled water flow rate chwm& are

the process output to be controlled and manipulated

variables, respectively. The on-coil temperature of the

chilled water is assumed as a constant, and the airflow rate

am& varies in corresponding to cooling load demand of

conditioned space, these two variables are considered as

disturbances to the process. Thus the output aoT can be

described as:

0 10 20 30 40 50 60 70 80 90 1000

0.2

0.4

0.6

0.8

1

1.2

1.4

y(t)

time

FC t=1.4

FC t=0.4

PID t=1.4

PID t=0.4

Fig. 4 in fuzzy control systems

0 10 20 30 40 50 600

0.2

0.4

0.6

0.8

1

1.2

1.4

y(t)

time

FC k=0.5

FC k=0.1

PID k=0.5

PID k=0.1


0 10 20 30 40 50 60 70 80 90 1000

0.2

0.4

0.6

0.8

1

1.2

1.4

y(t)

time

FC delay=1.3

FC delay=0.4

PID delay=1.3

PID delay=0.4


( , , , )ao chw a ai chwiT f m m T T = & & (11)

Where f is a nonlinear time varying function between the

system output and the state variables. In steady-state, as the

transient response of the dynamics for air and chilled water

loop are very difficult to model accurately, it can be

approximated in a small region, respectively, by a FOPDTmodels [8]

and given by

( )

( ) 1

chwL sao chw

chw chw

T s K e

m s T s

=+&

(12)

where chwK , chwT , chwL , aK , aT and aL are the process

gain, time constant and time delay for chilled water loop and

air loop respectively. Before the real process testing, a

simulation study is conducted to verify the proposed fuzzy

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controller design. Consider a heat exchange model

described by (12). Its operating ranges of system parameters

, ,p sK T L on low, middle, high level are -0.3, -0.8, -1.6; 0.9,

1.1, 1.2; 0.8, 0.8, 0.9 responsively. Then the PID controller

based on low level model is designed, the parameters

, ,P I D

K K K are determined as 1.1, 1.22 and 0.09 respectively

and fuzzy controllers are designed on base of the designed

PID controller. Simulation tests and comparisons is clear to

show that a better performance is achieved through

proposed fuzzy controller, whereas it is difficult to apply

one set of PID controller parameters to obtain good

performance for the whole operation range.

A pilot centralized HVAC systems is showed as in figure 8.

The system has three chillers, three zones with three AHUs,

three cooling towers and flexible partitions up to twelve

rooms. All motors (fans, pumps and compressors) are

equipped with VSDs. The cooling coils for system are two

rows with the dimension of 382525 cm . The experiment

is conducted under the following conditions: The chilled

water supply temperature is fixed; the cooling load variation

is achieved through the air and water flow rates. The

experiments result in Figure 7 showed that it is available to

apply the proposed fuzzy control strategy to control off-coil

dry-bulb temperature aoT of AHU systems. Compared with

PID controller, the novel fuzzy controller design technology

has better robustness.

Fig.8Pilot plant of Centralized HVAC system

Fig.9Experiment result in HVAC labs

VI. CONCLUSION

In this paper, a new approach to design fuzzy controller

was firstly proposed. It take full advantages of mature

technologies of PID controller to improve the performance

of fuzzy controller and it will be regarded the new

relationship and combination of fuzzy and PID controller.The gains tuning of PID controller were used to design

normalized factors of fuzzy controller so that the fuzzy

controller can be more easily understood and can be applied

in practical industrial process on large scale. The simulation

and experiment results in HVAC systems gave the

comparison between both of them, and shown that this novel

design of fuzzy controller appeared good performance.

ACKNOWLEDGMENT

The paper was supported by Shandong province science

foundation grant Z2006G07.

REFERENCES

[1] L. A. Zadeh, Outline of a new approach to the analysis of complexsystems and decision processes, IEEE trans. SMC, vol. 3, no. 1, pp.28-44, 1973.

[2] E. H. Mamdani, Application of fuzzy algorithms for simple dynamic

plant,Proc. Inst. Elect. Eng., vol. 121, no. 12, pp.1585-1588, 1974.

[3] R. J. P Defiguerredo and G. Chen,Nonlinear feedback control systems:

an operator theory approach, New York, Academic, 1993.

[4] Astrom, K. J. and T. Hagglund, PID controllers: theory, design, and

tuning (2nd ed.), Research Triangle Park, NC: Instrument Society ofAmerica, 1995.

[5] Qiang Bi, Wen-Jian Cai, Qing-Guo Wang et al, Advanced controller

auto-tuning and its application in HVAC systems, Control Eng.Practice, Vol.8, pp.633-644, 2000.

[6] Hanxiong Li, An improved robust fuzzy-PID controller with optimal

fuzzy reasoning,IEEE trans on SMC, vol. 35, no. 6, pp.1283-1294,2005.

[7] Xu J, Hang C, Liu C, Parallel structure and tuning of a fuzzy PID

controller, Automatica,Vol. 36,pp.673-684,2000.

[8] He Ming, Wenjian Cai, Multiple Fuzzy Model-based Temperaturepredictive control for HVAC systems, Information science, vol.169,

pp.155-174, 2005.

Exhaust

Air

ControlDamper

Outside

Air

Chilled

Water

Return Fan

FilterCooling Coil

Supply Fan

(VSD)

ControlValve

MixedAir

Return Air

Supply Air

Fig.7 Air Handling Unit

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Lv Hongli Duang Peiyong - Direct Conversion of PID Controller to Fuzzy Controller