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8/2/2019 Sathyabama Final

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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

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