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A Novel Neuro-Fuzzy based Control for Non-linear Systems
G.Srinath1
M.E. Control& Instrumentation,
Department of E&I,
Kongu Engineering College, Perundurai
9943244394, [email protected]
S.Janarthanan2
Assistant Professor (Sr.G),
Department of E&I,
Kongu Engineering College, Perundurai
9344668801, [email protected]
Abstract
The control of non-linear systems is one of the tedious process in any industry. This paper
presents a novel strategy for the control of such
systems by means of various intelligent controllers.
This proposed method combines the Neural Networks
and Fuzzy techniques, which is one of the suitable
controllers for highly non-linear process control. In
case of conventional control algorithms, it is difficult
to attain the required control quality, as it has
restrictions due to peak overshoot. In this project, a
two input Fuzzy PID control, is applied for a single
tank conical system, which is used in chemical and
process industries such as pulverizing andsedimentation. The proposed controller mode has
three features; uniform boundaries in case of
unknown disturbances with improved applicability,
the increased convergence rate of neural network
learning, and finally the one-one adaptation which
produces an universal approximation in case of ANFIS. The designed controllers are testified for a
single conical system using simulation and the
performance charts are compared for the selection of
the optimal control strategy.
KEYWORDS: ANFIS, Fuzzy PID, non-linear systems,
conical tank
I . INTRODUCTION
The selection of the optimal controller plays an
important role in the control of such non-linear
processes. The Proportional-Integral-Derivative (PID)
controller, as shown in Figure.1, is the most widely usedtype and was first proposed by Ziegler-Nichols. This
type of controller tuning was proposed since the
controller structure is simple and easier to understand the
parameters, than other controller types.
Figure.1Basic block diagram of a Conventional PID
Many researches have been carried out in the
design and selection of the optimal controller for each type of
linear and non-linear systems, such as PID controller with largedead time, integrating processes and first order process with
dead time.
A PID type Fuzzy controller, as shown in Figure.2
which uses information from the fuzzy regions of a nonlinear
process, like the continuously stirred tank reactor (CSTR) for
pH titration is proposed by Qin et al. Since the
introduction of the fuzzy sets by Zadeh, and the introduction of
the industrial application by Mamdani, fuzzy control systems
have played a major role in the engineering systems.
Figure.2 Basic block diagram of a Fuzzy PID
controller
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Non-linear systems
Many physical quantities, such as a vehicle’s
velocity, or electrical signals, have an upper bound.When that upper bound is reached, linearity is lost. The
differential equations governing some systems, such assome thermal, fluidic, or biological systems, are
nonlinear in nature. It is therefore advantageous to
consider the nonlinearities directly while analyzing and
designing controllers for such systems. Mechanical
systems may be designed with backlash – this is so a
very small signal will produce no output (for example,
in gearboxes). In addition, many mechanical systems
are subject to nonlinear friction. Relays, which are part
of many practical control systems, are inherently
nonlinear. Finally, ferromagnetic cores in electrical
machines and transformers are often described with
nonlinear magnetization curves and equations. In levelcontrol systems, which are highly non-linear ,due to the
process dead-time, knowledge based inference system
play a vital role by fine tuning the controller parameters
that are required
II.FUZZY CONTROLLERS FOR NON- LINEAR
SYSTEMS
G.K. Mann et al. (1999) proposed a fuzzy PID
controller [1] with the conventional two input PI or PD
controller as given by Mamdani. The complexity of a
fuzzy PID controller lies in the defining the fuzzy rule
base. The distinction of each fuzzy control is given byvarious rules that are framed for the process. The fuzzy
controller developed can be of one input, two input, or
three input types. In the case of two input configurations,
only PI and PD controller elements are considered for
the process. This leads to difficulty in the input variable
sum of error analysis for steady state of more control.
Also, for designing a fuzzy PID controller, the error e is
considered as the input that is required for deriving the
PID structure.
T.K.Radhakrishnan et al. [2] proposed that a real-time control of liquid level in a conical tank is analyzed.
The conical level system is a non-linear system as its
cross-section varies with height. Nithya et al. [3]
proposed the soft computing based controllers are being
developed for non-linear systems, in real time
implementation.
III THE CONICAL SYSTEM
The conical tank system, as in Figure.3, is
essentially a system with non-linear dynamics[3], which
is described by the first order differential equation.
Figure. 3 A Conical tank
F 0 -Inlet flow of the liquid to the tank,
R max --Top radius of the tank, in meter
r -- Inner radius of the tank, in meter
H max -- total height of the cone, in meter
h -- Height of liquid in the tank, in meterF1 -- outlet flow of the liquid from the conical tank
V= πr2h/3
h- Height of the conical tank, in cm
r- Radius of the tank, in cm
On applying the steady state values, and by solving the
equations
=
The dead time of the process is to be determined by
analyzing the two times t1 and t2 of the process, for the step
response curve. The time corresponds to the 35.3% and
85.3% of the response curves. The time constant and time
delay are determined as
T=0.67(t2 –t1 )
TD=1.3t1 -0.29t2
In a conical tank, the main task of the controller
is to maintain the process under stable conditions whatever
the disturbance may occur. The non-linearity is caused due to
the shape of the tank. The non-linear dynamics of a single
conical tank is given by a first order differential equation. At
a fixed inlet flow rate and a output flow rate, the system ismade to attain the steady state.
The transfer function of the first order system is
obtained, [3]as
=.
.
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IV. CONTROLLER DESIGN FOR THE
NONLINEAR SYSTEMThe controller selection and design is vital since
the nonlinear process control is complex. Theconventional PID control is generally designed first to
verify the performance with other knowledge based
controllers.
A. Conventional PID controllerThe simulink model of the PID controller is
designed for the system as in Figure 4
Figure. 4 Conventional PID controller
The values of Kp , Ki ,Kd are considered as 1,0.1, and
10 respectively.
B. Fuzzy PID controllerThe Direct Action fuzzy PID is the most widely used
as it is easy to implement with sufficient number of
rules that cover a wide range of specifications. The use
of IF-THEN rules provides the non-linear transfer
elements for a non-linear process control. The two inputFLC is considered for this process as the error (e) and
the change in error (de) effectively tend to linearise the
high non-linearity.
UPID (n) =KPe(n) +KITs∑nq=0e(q)+(KD /Ts )∆e(n)
∆UPID (n) =KP∆e (n) +KITs∑nq=0e (q) + (KD /Ts) ∆
2e(n)
In the above equations KP,KI,KD stands for the
proportional, integral and the derivative gains
respectively. The Membership Functions (MF) are
referred as MN, SN, LN, ZE, LP, SP, MP. The number
of rules that are framed are 9, instead of the actual 49
required. Thus the process is operated in such a way
that the error, which is the deviation between the Set
Point (SP) and the Process Variable that is attained.
1. IF (e is SP) AND (de is LP),THEN Kpid is ZE
2. IF (e is MP) AND (de is LN),THEN Kpid is SP
3. IF (e is SN) AND (de is SN),THEN Kpid is LN
4. IF (e is SP) AND (de is LN), THEN Kpid is ZE
5. IF (e is SP) AND (de is MP), THEN Kpid is SP
6. IF(e is MP) AND (de is SN),THEN Kpid is ZE
7. IF(e is MP) AND (de is SP), THEN Kpid is LP
8.
IF (e is SP) AND (de is MN),THEN Kpid is SP9. IF ( e is SP) AND(de is LP),THEN Kpid is ZE.
The surface generated in the Mamdani Fuzzy
should be a linear as shown in Figure.5 for the two
input fuzzy structure as in Figure.6
Figure.5 Surface view of Mamdani Fuzzy
Figure.6 Two Inputs Fuzzy PID
The controller is simulated as in Figure 7 and the
corresponding responses are generated. The gain
values of KPI and KPD are 1.5 and 0.3 respectively.
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Figure.7 Fuzzy PID controller model
C. ANFIS controllerThe disadvantages of a FLC, slower response
for a high non-linear system, can be overcome by
adapting a Neuro-Fuzzy technique. The Neural
Network (NN) is used for high reliability and more
accuracy of the process, without affecting the stability
of the system even when the external disturbances tend
to impact the process. The ANFIS structure consists of
five layers[4] including a hidden layer, two inputs e and
∆e the input and output MFs, weighted average of the
output, as shown in Figure.8
The performance can be further improved by
adding the hidden layer neurons. The trained and tested
data outputs are the inputs of the ANFIS controller,provided the testing error is obtained minimal.[5] The
number of rules used in this controller design is 7 and
the epochs are selected as the training is efficient, such
that the error in the output is substantially reduced for
any non-linearity obtained.
Figure. 8 ANFIS Structure
The Simulink model of the proposed controller is
obtained as in Figure 9, with the same structure as that of
a Fuzzy PID controller, but the difference is only the
structure of the Fuzzy and the ANFIS.
Figure.9 ANFIS controller model
Figure.10 Surface view of Sugeno Fuzzy for ANFIS
V. RESULTS AND ANALYSIS
The step response of all the controllers are obtained
and the performance analysis (tr, ts, Mp) is determined .
The gains KP,KI,KD are calculated on the basis of error
and change in error.The ANFIS model obtains the
output of the FLC and thus the weighted average of the
output is calculated. Of all the controllers, the neuro-
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fuzzy controller has a better response than the other two
controllers, as shown in Figure.11.
Figure.11 Response of all controllers
Table.1 provides a better view of the performance
analysis ( the rise time , peak overshoot , settling time)of
all the controllers .
Table.1 Performance analysis of Controllers
CONTROL %MP RISE
TIME
Tr, sec
SETTLING TIME,ts sec
CONV’
PID18 144 320
FUZZY PID 0 123 275
ANFIS 0 18 40
VI. CONCLUSION
By comparing the performance of the controllers,
the ANFIS controller has a faster settling time and risetime. The controller also has high tolerance for
external disturbances that tend to act on the system ,thus the stability of the non-linear process is
maintained for the given set point. Further, by adding
the hidden neurons, the ANFIS can be linearised for
the two input fuzzy controller.
REFERENCES
1. George K.I. Mann, Bao-Gang Hu,Raymond G.
Gosine , “Analysis of Direct action fuzzy PID
controllers”, IEEE transactions on systems, man
and cybernetics,VOL.29 No.3,June1999.
2. T.K.Radhakrishnan et al, “Development and
tuning of Fuzzy controller for a conical level
system”, IEEE transactions ,September 2004.
3. Nithya et al, “Soft computing based controllers
Implementation for non-linear process in real
time”, Proceedings Of The World Congress On
Engineering And Computer Science Vol II,2010
4. G.Shahghholian and A.Movahedi,“Modeling and
controller design using ANFIS method for a Non-
linear liquid level system”, International Journal
Of Information And Electronics
Engineering,Vol1,No.3,November 20115. T.Thyagarajan and V.R.Ravi , “ A Decentralized
PID Controller for Interacting Nonlinear
Systems”, pgs 297-302,Proceedings Of ICETECT ,
September 2011
6. Yajun Zhang et al. , “A Nonlinear Control
Method Based on ANFIS and Multiple Models
for a class of SISO Nonlinear Systems and its
Application”, IEEE Transactions Of Neural
Networks, Vol 22, Pgs 1783-1795 ,November
2011
7. Omar. F. Lufty et al., “A Genetically Trained
Simplified ANFIS controller to Control Nonlinear
MIMO systems”, pgs 349-355, Proceedings Of
ICECCE , June 2011