Fuzzy Remote Control of a Dc Drive

8/13/2019 Fuzzy Remote Control of a Dc Drive

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FUZZY REMOTE CONTROL OF A DC DRIVE

BY

UDIT GUPTA

(DEPARTMENT OF INSTRUMENTATION &CONTROL ENGINEERING)

NATIONAL INSTITUTE OF TECHNOLOGY

JALANDHAR


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ABSTRACT

In this paper, a Fuzzy Logic Controller has been proposed for the control of a DCdrive system from a remote point. The mode of communication is obtainedthrough frequency modulation technique. The proposed scheme has beendesigned for a typical Industrial environment. The anticipated signal to noise ratio(SNR) is high - therefore, the drive is required to track noisy reference signalswhich demands alternative forms of control methods which should be immune to

noise as well as plant parameter variations. Generally, the state-of-the-arttechniques for the design of a controller is to make the response of the controllerindependent of the system parameter variations. The prime aim of the controller isto minimise the error between the actual and the desired output parameters. Tomeet the above specifications a fuzzy logic controller is employed whose responseis compared with a conventional PI controller. The gain parameters of both thecontrollers are tuned to their optimum values with the help of computer

simulations. A personal computer(PC-486) is used for supervisory control and dataacquisition (SCADA). Specially designed FM transmitter and receiver circuits areemployed to obtain the reference speed signal for the drive system from a remotepoint of the laboratory. The results obtained by both the controllers have beencompared under the loading conditions by giving step variations in the referencespeed. The comparison confirms the validity and accurate performance of theproposed technique


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STATEMENT OF PURPOSE

In this paper, a fuzzy remote control of a DC drive has been realised. Thepower converter is a single phase full wave bridge thyristorised rectifiercircuit employing several thyristors. The speed of the motor is fedbackwith the help of a tachogenerator. The reference speed signal istransmitted from a distant place with the help of frequencymodulation(FM) transmitter and the signal is received near the personal

computer(PC) and fed into it. Now this is the PC which compares thedesired speed signal received and the actual speed signal fromtachogenerator and obtains the error signal. This error signal is processedby open loop controller, PI controller and also with fuzzy controller. For allthe controllers the respective gains are properly tuned. Once it is tuned itis fixed throughout. In a particular period of operating time, a slowvariation in the reference speed is given from the transmitter side forobserving the accurate speed tracking. Again in a small duration of time asudden variation in the reference speed is given from the transmitter sideagain for examining the response for fast response. Also 20% and 40%variation in the input voltages are given for a particular desired speed. Theresults are compared with the simulation results


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PROPORTIONAL AND INTEGRAL CONTROLLER

In this type of controller the error signals are obtained from the reference speedsignals and the actual speed signals. The output of this controller consists of twocomponents; one proportional to the actuating signal and the other proportional toits integral .The output of this controller be given as

where ,

KP is the proportional gain,

Kiis the integral gain.

e(k-1) is the previous error signal.


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P-I CONTROLLER CONTD.

The block diagram representation of a PI controller is as follows in Fig

proportional-integral controller increases the type number by unity and thereby eliminating the steady state error. The output due to

the second component of the controller at any instant is area under the error signal curve upto that instant. But this controller may

lead to oscillatory response of slowly decreasing or even increasing amplitudes, which is undesirable. Thus this controller provides a

counter torque which will reduce the error signal as well as make the system stable.

Thus the values of these constants, proportional(Kp) as well as integral(Ki) constants should be tuned such that the system

reduces the error very fastly and the overshoot of the error is minimum, although the time taken be somewhat a significant value, butthose should be the optimum values.


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FUZZY LOGIC CONTROLLER

In order to automate a plant a direct policy of heuristic control is not easy toimplement in terms of quantitative statements. The starting point is the fuzzy set, asintroduced by Prof. Lofti Zadeh, a collection of objects of a certain universe having somecommon properties, characterised by a function of membership as i(x) *0,1+, whichmeans that degree of membership of an element 'x' in the fuzzy set i ranges from 0 to 1.0,both inclusive. The elementary operations on the fuzzy sets are union, intersection andcomplement. These are obtained as follows.

Let us consider two fuzzy sets A and B of an universe of discourse X, characterised bythe membership function Aand B. The resultant membership functions are as follows.

AUB(a)=MAX( A, B)

AnB(a)=MIN( A, B)

A'(a)=1- A

B'(a)=1- B.

To establish a relation between two fuzzy sets A and B belonging to two different universe ofdiscourses U and V, the definition of fuzzy conditional expression or linguistic implication hasbeen established.

If x is A then y is b.

where

fuzzy sets A and B are termed as antecedent and consequent.

R(u,v)= A*B(u, v)= MIN[ A(u); B(v)],


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BASIC STRUCTURE OF A FUZZY LOGIC CONTROLLER

A fuzzy controller ,whose basic structure is shown in Fig.2.10.,

A fuzzy controller whose basic structure is shown by the figure is defined by a certain number M of

conditional expressions, where the antecedent carries informations related to the system variablesto be controlled and the consequent initialises the control variables based on a principle that maybe obtained from the inferential rules of composition. Since the fuzzy controller is able tomanipulate only linguistic variables, the operations of fuzzification for the input variables anddefuzzification for the output variables are required and thus allowing the fuzzy controller tooperate in the control chain.

The fuzzification is made by establishing both the variation domains and the membershipfunctions of the input variables to the controller. The system performance will be affected by boththe shapes and the number of membership functions, which are written based on the knowledge

of well experienced people, according to the heuristic criterion.The defuzzification is accomplished with preference by the centroid or the height methods.

The height method requires to evaluate the centroid of every output and the their average value,weighted by the proper degrees of pertinence as follows.


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The most significant variables entering the fuzzy controller have been selected as the speed error and its time variation. And

the controller output is the control signal, established through an heuristic logic. To proceed on the way of input fuzzification,

previous items need to be transduced from the level of assertions to the level of conditional instructions typical of fuzzy logic.

Here the error

ERR=ref - fb

and rate of error

DERR = ERR - ERRP

(2.37)

where

ERRP is the previous error.

A linguistic value has been attributed to every level in the following way and these two fuzzy sets have their three members as

follows.

EP = error positive : EN = error negative : EZ = error zero : DP = positive rate of error : DN = negative rate of error : DZ = zero

rate of error

The control is attributed to the following

LP = large positive : MP = medium positive : Z = zero control : MN = medium negative : LN= large negative.

The membership functions for the error(ERR) and its rate(DERR) are obtained as follows.

EP(ERR) = ge ERR

EN(ERR) = -ge ERR EZ(ERR) = 1-abs(ge ERR)

DP(DERR) = gr DERR

DN(DERR) = -gr DERR

DZ(DERR) = 1-abs(gr DERR)

such that 0


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The following fuzzy control rules are used in this controller.

Rule 1:-If ERRis EP And DERRis DP Then dUis LP.

Rule 2:-If ERRis EP And DERR is DZ Then dUis MP.

Rule 3:-If ERRis EP AndDERRis DN ThendUis Z.

Rule 4:-IfERRis EN And DERR is DP Then dUis Z.

Rule 5:-If ERRis EN And DERRis DZ Then dUis MN.

Rule 6:-If ERR is EN And DERRis DN Then dUis LN.

Rule 7:-If ERR is EZ And DERRis DP Then dUis MP.

Rule 8:-If ERRis EZ And DERRis DN Then dUis MN.Rule 9:-If ERRis EZ And DERRis DZ Then dUis Z.

To enable the fuzzy controller to operate for any given input use is made of the compositional rule of inference

dU = (ERR DERR) o R

where "o" denotes the MAX-MIN product. In evaluating the control rules, Zadeh AND and Lukasiewicz OR logic are used. It is desirable to use ZadehAND for individual rules and Lukasiewicz OR for the control rules for which the linguistic outputs of dUbe same.

The inference engine of the fuzzy logic controller matches the antecedents of the rules in the fuzzy rule base with the input state linguistic termsand performs the implications from the consequent of the rules. For a given error and its rate, the firing strengths a i; i=1 to 9 of the rules 1 to 9 areobtained as follows, for an example let us consider Rule 1.

Rule 1:-If ERRis EP And DERRis DP Then dU is LP.

a1= EP(ERR) And DP(DERR)= MIN( EP, DP)The control output (dU) be MP in Rule 2 and Rule 7, thus

a10= MAX(a2, a7)

a10= MAX(IN( EP, DZ),MIN( EZ, DP)).

Likewise the control output(dU) be MN in Rule 5 and Rule 8, thus

a11= MAX(a5,a8)

a11= MAX(MIN( EN, DZ),MIN( EZ, DN)).

And the control output(dU) be Z in Rule 3, Rule 4 and Rule 9, thus

a12= MAX(a3,a4,a9)

a12= MAX(MIN( EP, DN),MAX(MIN( EN, DP),MIN( EZ, DZ))).

Using a defuzzification procedure, in which normalisation of the grades of membership of the members of the fuzzy set being defuzzified to a sum ofunity, the defuzzified output be

dU=(-dU1 LN- dU2 MN+dU3 MP+dU4 LP)/( LN+ MN+ Z+ MP+ LP)

where dU1,dU2,dU3,dU4and dU5are the values of the control outputs for which the membership values are unity. Now by substituting the values aparticular control output for a given values of error and its rate is obtained as follows.

dU=(- LN- 0.5* MN+0.5* MP+ LP)/( LN+ MN+ Z+ MP+ LP)

This control output(dU) signal is nothing but a correction in the error signal. Hence the net error output, in otherwords the net control signal be

Vc(k) = Vc(k-1)+gu dU

The fuzzy controller is to be tuned for the optimum values of the gains ge,grand gusuch that the response is the fastest.


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SIMULATION RESULTS


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SIMULATION RESULTS(CONTD.)


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RESULTS AND CONCLUSION

This section provides a comparative study of the results obtained bythe different types of controller used such as PI and fuzzy logiccontroller. Since it is to establish the supremacy of the fuzzycontroller over the other optimal conventional controllers

therefore these controllers are compared with the unoptimisedfuzzy controller. The comparative results are given both for trackingas well as step change in the reference speed signal at thetransmitter end.

Figures which follow compares the results for a PI and fuzzycontroller for tracking frequency of 0.4Hz for a sinusoidal reference

speed input. The step response is obtained by providing large andsmall step changes in the reference speed signal again in thetransmitter end .In the case of fuzzy controller it is seen that thereis a better damping effect and the steadystate is obtained muchfaster as compared to its conventional counterparts.


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CONCLUSION

From the above results it is seen that the difference in the comparativeperformance is small but the better control action of the fuzzy controller isobvious. This proves the superiority of the fuzzy controller over the openloop controller as well as proportional and integral controller. And alsofuzzy controller is almost independent of system parameters because itsprincipal aim is to minimise the error. The above observations may also

lead to an interesting conclusion that the fuzzy controller has the propertyof adaptive and nimbleness to respond quickly to the error and adjustitself accordingly.

In addition to above features the control of the reference speed from aremote place with the help of

a most noise immune technique as FM system made this piece of job

compatible with industrial environments where the unavoidable noise ismost prone to occur.There are many other places of job where

the drive system has to be controlled from a centralised control room.Forthis also the proposed system will

give an excellent performance.


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FUTURE SCOPE

` Envisioned on the performance exhibited by an experienced human operator it is believed that acontroller should be designed to have abilities to learn from experience and to use the knowledge gainedduring the training process.

In this case the grades of the error and its derivative and that of the control output are tuned manually.This could have been done automatically with the help of Artificial Neural Networks(ANN) as follows. It issomewhat similar to the human brain of an adaptive distributed architecture.

The basic concept behind the neural network approach is to generate an approximation to theclassification regions from input-output measurements and to use them as rules to calculate the

appropriate control signal. Control knowledge and information are embedded during its training. Thetraining involves the error signals between the plant output signals and the desired signals, as the inputsto the neural network. The neural network controller contains four units as pre-processing, neural networkclassifier, look up table and drive unit. The pre-processing unit will scale the error signal into the range of[-1,+1] and partition it into several groups. Each group clusters those error signals for which an appropriatecontrol action would correct. These errors are inputted to the neural network classifier which is a feedforward three layer backpropagation network which consists of the input layer with several inputsdepending upon the number of trajectories to be followed. After the learning process it performs theclassification and/or mapping. Outputs of the neural network classifier will be rounded off to "1" or "0",where "1" indicates the abnormal case and the look up table then increase or decrease the control signal

based on the output decision from the classifier. Now the control signal fed into the drive circuit to controlthe output of the thyristor converter circuit and hence the speed of the motor. Inparticular if the scalederror e is between -0.05 and +0.05 the plant is assumed to be stable and hence no control action isneeded.


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Fuzzy Remote Control of a Dc Drive