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  1. 1. Safina Al Nisa, Lini Mathew, S Chatterji / International Journal of Engineering Research andApplications (IJERA) ISSN: 2248-9622 www.ijera.comVol. 3, Issue 3, May-Jun 2013, pp.1137-11461137 | P a g eComparative Analysis of Speed Control of DC Motor Using AITechniqueSafina Al Nisa, Lini Mathew, S ChatterjiDepartment of Electronics, Women College, M.A Road Srinagar, India Kashmir UniversityDepartment of Electrical, NITTTR, Chandigarh, India, Punjab UniversityDepartment of Electrical, NITTTR, Chandigarh, India, Punjab UniversityAbstractThis paper presents a comparativestudy of various controllers for the speed controlof DC motor. The Proportional IntegralDerivative (PID) controller is one of the mostcommon types of feedback controllers used indynamic systems. This controller has beenwidely used in many different areas such asaerospace, process control, manufacturing,robotics, automation etc. As PID controllersrequire exact mathematical modelling, theperformance of the system is questionable ifthere is parameter variation. Further two morecontrollers are proposed namely; Fuzzy LogicController and FOPID Controller. Theperformances of the three controllers arecompared. Simulation results are presented andanalysed for all the controllers. It is observedthat Fuzzy Logic based controller gives betterresponse than PID and FOPID controller for thespeed control of dc motor.Keywords - Proportional-Integral-Derivativecontroller, Fuzzy Logic controller, FOPIDcontroller, DC motor speed control.I INTRODUCTIONDC motor is a power actuator whichconverts electrical energy into mechanical energy.DC motor is used in application where wide speedranges are required. The greatest advantage of dcmotors may be speed control. The term speedcontrol stand for intentional speed variation carriedout manually or automatically. DC motors are mostsuitable for wide range speed control and aretherefore used in many adjustable speed drives.Since speed is directly proportional to armaturevoltage and inversely proportional to magnetic fluxproduced by the poles, adjusting the armaturevoltage and/or the field current will change therotor speed. DC motors have been widely used inmany industrial applications such as electricvehicles, steel rolling mills, electric cranes, androbotic manipulators due to precise, wide, simple,and continuous control characteristics.Proportional-Integral-Derivative (PID) controllerhas been used for several decades in industries forprocess control applications. At the same time PIDcontroller has some disadvantages namely; theundesirable speed overshoot, the sluggish responsedue to sudden change in load torque and thesensitivity to controller gains KI and KP. Theperformance of this controller depends on theaccuracy of system models and parameters.Therefore there is need of a controller which canovercome disadvantages of PID controller.Emerging intelligent techniques have beendeveloped and extensively used to improve or toreplace conventional control techniques becausethese techniques do not require a precise model.Fuzzy logic has rapidly become one of the mostsuccessful technologies for developingsophisticated control systems. The reason for whichis very simple. Fuzzy logic addresses suchapplications perfectly as it resembles humandecision making with an ability to generate precisesolutions from certain or approximate information.It fills an important gap in engineering designmethods left vacant by purely mathematicalapproaches (e.g. linear control design), and purelylogic-based approaches (e.g. expert systems) insystem design.DC motor can also be controlled by a non-conventional control technique known asfractional-order PID (FOPID) control, a generalisedversion of integer order control. Dynamic systemsbased on fractional order calculus have been asubject of extensive research in recent years. Infractional order proportional-integral derivative(FOPID) controller, I and D operations are usuallyof fractional order; therefore, besides setting theproportional, derivative and integral constants KP,KI, KD, we have two more parameters; the order offractional integration 𝛌 and that of fractionalderivative 𝛍. Determining an optimal set of valuefor a given process plant. This has been solved byusing N-integer tool box. The values of KP, KI, KD,𝛌 and 𝛍 are selected by hit and trial method.II MODEL OF DC MOTORDC motors are most suitable for widerange speed control and are therefore used in manyadjustable speed drives. Fig 1 shows a separatelyexcited DC Motor. Ra is the armature resistanceand La is the armature inductance of separately
  2. 2. Safina Al Nisa, Lini Mathew, S Chatterji / International Journal of Engineering Research andApplications (IJERA) ISSN: 2248-9622 www.ijera.comVol. 3, Issue 3, May-Jun 2013, pp.1137-11461138 | P a g eexcited dc motor. Rf is the field resistance and Lf is the inductance of the field winding.Fig. 1 Separately Excited DC Motor ModelA linear model of a simple DC motor consists of an electrical equation and mechanical equation as determinedin the following equations (1) and (2).Va = Eb + IaRa + La(dIa/dt) (1)Tm = Jmdωdt + Bm ω + TL (2)where Va is the armature voltage (in volt) Eb is back emf the motor (in volt) Ia is the armature current (in ampere) Ra is the armature resistance (in ohm) La is the armature inductance (in Henry) Tm is the mechanical torque developed (in Nm) Jm is moment of inertia (in kg/m²) Bm is friction coefficient of the motor (in Nm/ (rad/sec)) ω is angular velocity (in rad/sec) Ta = Armature Time Constant , Ta = La RaAfter simplifying the above equations, the overall transfer function is obtained as shown in Fig. 2.The following specifications of DC motor are used:TABLE1SPECIFICATIONS OF DC MOTORBy making use of the above motor constants the SIMULINK block diagram of dc motor obtained is as shown inFig.3.Symbol MagnitudeRa 0.5ΩLa 0.02HVa 200VJm 0.1 Kg.m2Bm 0.008 N.m/rad/seck 1.25 V/rad/sec
  3. 3. Safina Al Nisa, Lini Mathew, S Chatterji / International Journal of Engineering Research andApplications (IJERA) ISSN: 2248-9622 www.ijera.comVol. 3, Issue 3, May-Jun 2013, pp.1137-11461139 | P a g eFig. 3 SIMULINK Block Diagram of DC MotorIII. PROPORTIONAL-INTEGRAL-DERIVATIVE CONTROLLERFig.4. shows the SIMULINK block diagram of speed control of dc motor using PID controller. Step input isgiven to the controller. The error signal is given to the PID controller. Subsystem signifies the motor model asshown in Fig.3 and output is obtained at scope3.Fig.4 SIMULINK Block Diagram of Speed Control of Dc Motor Using PID ControllerBefore going into the procedure of controllertuning, it is important to look at what is the aim ofthe controller tuning. If possible, we would like toobtain both of the following for the control system:• Fast responses, and• Good stabilityUnfortunately, for most practical processes beingcontrolled with a PID controller, these two cannotbe achieved simultaneously. In other words:• The faster responses, the worse stability, and• The better stability, the slower responses.For a control system, it is more important that it hasgood stability than being fast. A PID controller isdesign for separately excited DC Motor usingMATLAB. The system as shown in Fig.4 is tunedfor the following parameters for the PID controllerto get desired speed:KP = 315.42, KI = 770.27, KD = -0.7927Major problems in applying a conventional controlalgorithm in a speed controller are the effects ofnonlinearity in a dc motor. The nonlinearcharacteristics of a dc motor such as saturation andfriction could degrade the performance ofconventional controller. Therefore there is need ofa controller which can overcome disadvantages ofPID controller.IV FUZZY LOGIC CONTROLLER(FLC)A Fuzzy Logic Controller (FLC) wasproved analytically to be equivalent to a nonlinearPI controller when a nonlinear defuzzificationmethod was used. The foundations of fuzzy logichave become firmer and its impact within the basicsciences - and especially in mathematical andphysical sciences - has become more visible. Fuzzycontrollers have been proposed for physicalsystems which do not lend themselves too easy andaccurate mathematical modelling and crispvariables, and therefore, cannot be tackled bytraditional strict analytic control design techniques.Instead, control variables are represented by fuzzyvariables which let the level of uncertainty of thevariables to be modelled in a systematic way. Inaddition, the expert knowledge of a typical operatorof such a process is embodied in a set of linguisticor rule-based engines which constitutes the core ofa fuzzy controller.The objective is to implement FLC forcontrolling the speed of a dc motor. The goal ofdesigned FLC in this study is to minimize speederror. The bigger speed error the bigger controllerinput is expected .In addition, the change of speedof error plays important role to define controllerinput. Consequently FLC uses error (e) and changein error (ce) for linguistic variables which aregenerated from control rules. The output variable isthe change in control variable of the motor drive.The output variable from FLC is given to the planti.e DC motor. A fuzzy logic controller has fourmain components:a) Fuzzificationb) Inference Engine
  4. 4. Safina Al Nisa, Lini Mathew, S Chatterji / International Journal of Engineering Research andApplications (IJERA) ISSN: 2248-9622 www.ijera.comVol. 3, Issue 3, May-Jun 2013, pp.1137-11461140 | P a g ec) Rule Based) DefuzzificationFig.5. shows SIMULINK block diagram of speedcontrol of dc motor using FLC. Speed shows thecontrolled speed. A Fuzzy PID controller isincorporated in the block diagram as a subsystem.Error (e) and change in error (ce) are the two inputsof the FLC and the output is u, which is fed to themotor.Fig. 5 SIMULINK Model for Speed Control of DC Motor Using Self Tuned Fuzzy PID ControllerTo perform computations, inputs and outputs must be converted from numerical or “crisp” value into linguisticforms. The terms such as “Small” and “Big” are used to quantize the input and output values to linguistic values.In this paper, the linguistic terms used to represent the input and output values are defined by seven fuzzyvariables as shown in Table 2 and Table 3.TABLE 2FUZZY LINGUISTIC TERMS USED FOR INPUT VARIABLESTABLE 3FUZZY LINGUISTIC TERMS USED FOR OUTPUT VARIABLESFuzzy membership functions are used as tools to convert crisp values to linguistic terms. A fuzzymembership function can contain several fuzzy sets depending on how many linguistic terms are used. Eachfuzzy set represents one linguistic term. In this paper, five fuzzy sets are obtained by applying the five linguisticterms. The number for indicating how much a crisp value can be a member in each fuzzy set is called a degreeof membership .One crisp value can be converted to be “partly” in many fuzzy sets, but the membership degreein each fuzzy set may be different. In order to define fuzzy membership function, designers can choose differentshapes based on their preference or experience. The popular shapes are triangular and trapezoidal because theseshapes are easy to represent designer’s idea and require low computations time. Fig.6. Membership FunctionEditor Window for the Error in SpeedTerm DefinitionNL Negative LargeNS Negative SmallZE ZeroPS Positive SmallPL Positive LargeTerms DefinitionsPVS Positive Very SmallPS Positive SmallPMS Positive Medium SmallPM Positive MediumPML Positive Medium LargePL Positive LargePVL Positive Very Large
  5. 5. Safina Al Nisa, Lini Mathew, S Chatterji / International Journal of Engineering Research andApplications (IJERA) ISSN: 2248-9622 www.ijera.comVol. 3, Issue 3, May-Jun 2013, pp.1137-11461141 | P a g eFig. 6 Membership Function Editor Window for the Error in SpeedSimilarly memership function for change in error (ce) and output variables can be obtainrd.Instead of using mathematical formulas, a FLC uses fuzzy rules to make a decision and generate the controleffort. The rules are in the form of IF-THEN statements.For example, IF the error(e) is equal to negative low(NL) and change in error is negative low (NL) Then the change in speed is positive very small (PVS). Thesolutions are based on experiences of a designer or the previous knowledge of the system.The efficiency can beimproved by adjusting the membership functions and rules.Table 4, Table 5 and Table 6 shows the rule base forKP, KI and KD.Table 4Fuzzy Rule Table for KPTable 5Fuzzy Rule Table for KITable 6Fuzzy Rule Table for KDce/e NL NS ZE PS PLNL PVS PMS PM PL PVLNS PMS PML PL PVL PVLZE PM PL PL PVL PVLPS PML PVL PVL PVL PVLPL PVL PVL PVL PVL PVLce/e NL NS ZE PS PLNL PVL PVL PVL PVL PVLNSPMLPML PML PL PVLZE PVS PVS PS PMS PMSPSPMLPML PML PL PVLPL PVL PVL PVL PVL PVLce/e NL NS ZE PS PLNL PM PM PM PM PMNS PMS PMS PMS PMS PMSZE PS PS PVS PS PSPS PMS PMS PMS PMS PMSPL PM PM PM PM PM
  6. 6. Safina Al Nisa, Lini Mathew, S Chatterji / International Journal of Engineering Research andApplications (IJERA) ISSN: 2248-9622 www.ijera.comVol. 3, Issue 3, May-Jun 2013, pp.1137-11461142 | P a g eThe rule editor window for the Fuzzy Controller for DC Motor is as shown in Fig.7.There are 25 rules in totalcombining all the above rulesFig. 7 Rule Editor Window for Fuzzy Controller of DC MotorV FRACTIONAL ORDER PIDCONTROLLERA. Fractional CalculusTo study the fractional order controllers,the starting point is of course the fractional orderdifferential equations using fractional calculus.Fractional calculus extends the classic concepts ofdifferential and integral calculus to an arbitraryorder. For the definition of the generalized operatoraD_t (where a and t are the limits and _ is the orderof the operation), the Riemann-Liouville (RL) andthe Gr ¨unwald-Letnikov (GL) definitions aregenerally applied. The RL definition is given by (_> 0): aD_aDt∝f t =1Γ(n−1)dndtnf(Γ)(t−Γ)α−n+1tadΓwhere 𝛤(x) is the gamma function of f(x)The GL definition is (α∈ℝ) uAnd [x] represents the integer part of x.The classical PID controller can be generalized intoa fractional order PID controller, the socalled PIλDμ, whose integro-differential equationcan be expressed as:u t = Kpe t +1TID−λe t + TDDμe(t) (3)where KP is the proportional gain, TI is the integraltime constant, TD is the derivative time constant, 𝛌is the (non-integer) order of the integrator and μ isthe (non-integer) order of the derivative action. Thecorresponding transfer function is expressed asC S =U(S)E(S)= KP(1 +1TISλ + TASλ) (4)KI = KP /TI and KD = KP · TD, we obtainC s = KP +KISλ + Kdsλ(4.27)It turns out in any case that in thePIλDμcontroller, there are five parameters to tuneand, most of all, the physical meaning of the twoadditional parameters is not clear. Indeed, the effectof changing these two parameters on the obtainedperformance is not well understood.B. Controller SchemeThe control scheme considered is shownin Fig.8 where C and P are the controller and theprocess transfer functions respectively, x is theprocess output, y is the measured output, u is thecontrol variable, r is the reference signal and e =r−y is the control error. Then, d denotes the loaddisturbance signal and n denotes the measurementnoise signal. It is worth stressing that theperformance of the control system in general isevaluated by considering all the input-outputrelationships between the three inputs r, d and n,and the three outputs y, x and u.Fig. 8 Control scheme of FO PIDFor the purpose of the description made in thefollowing sections, denote as S the sensitivityfunctionS(s) =11+C S P(S)(5)as T the complementary sensitivity functionT s =C s P(s)1+C s P(s)(6)and as L the open-loop transfer functionL(s) = C(s) P(s)C. Design of FOPID Controller for SpeedControl of Dc MotorFig.9 shows the SIMULINK model forspeed control of separately excited dc motor usingFOPID Controller. Subsystem shows the model ofseparately excited DC Motor as shown in Fig.1.
  7. 7. Safina Al Nisa, Lini Mathew, S Chatterji / International Journal of Engineering Research andApplications (IJERA) ISSN: 2248-9622 www.ijera.comVol. 3, Issue 3, May-Jun 2013, pp.1137-11461143 | P a g eFig. 9 SIMULINK Model of Speed Control ofMotor using FOPIDTo design a fractional controller, there aretwo approaches possible. The first one isplacements of pole and second is by experimentalresults. The method of experimental results is usedfor design of controllers. The method involvesstudying the closed loop response of system byvarying a tuning parameter. An appropriate valueof tuning parameter is chosen depending on theclosed loop performance requirements of thesystem i.e. overshoot, settling time, rise time, etc.Fractional PID controller design involves followingsteps:A. Determination of proportional gain KP:The value of proportional gain KP isadjusted to get minimum steady state errorpossible. With increase in KP, the settling timedecreases but the steady state value remainsunchanged. A value of KP is chosen as:KP = 221.59B. Determination of KI and λ:When integral time TI is increased keeping KP =221.59, it is observed that the controlled responsebecome more and more oscillatory in nature. NowKI is kept constant at 2.2375 x 103and integralorder λ is changed. The peak value and oscillatorynature of the response increases with increasingvalue of λ.. The integral order λ is chosen so as tohave less oscillation in the controlled response, lesssettling time and KI is selected to have low possiblepeak value.The values chosen are:λ = 0.87, KI = 2.2375 x 103C. Determination of KD and 𝛍:The increase in derivative time KD causes the initialresponse to set point change becomes faster andalso the peak value decreases. The value ofderivative order 𝛍 is varied, which affects the peakvalue and also speed of the response. 𝛍 is chosen tohave faster response but to avoid any peakovershoot. The values chosen for the derivativegain and derivative order are:KD = 2.4785, 𝛍 = 0.42VI SIMULATION RESULTSThe speed vs time response of DC motor using PIDcontroller is shown in Fig.10.This output responseshows that there are initial oscillations in speed andafter a settling time of 4 seconds,the motor attainsthe rated speed.Fig. 10 SPEED VS TIME RESPONSE OF SPEED CONTROL OF DC MOTOR USING PID CONTROLLERThe speed vs time response of DC motor usingFuzzy- PID controller is shown in Fig.11. The model can besimulated to visualize and analyse the result. This output response shows that after 2.7 seconds the motor attainsthe rated speed of 157.07rad/s.
  8. 8. Safina Al Nisa, Lini Mathew, S Chatterji / International Journal of Engineering Research andApplications (IJERA) ISSN: 2248-9622 www.ijera.comVol. 3, Issue 3, May-Jun 2013, pp.1137-11461144 | P a g eFig. 11 Speed VS Time Response of Fuzzy Tuned PID Controlled DC MotorThe speed vs time response of DC motor using FOPID controller is shown in Fig.12Fig. 12 Simulation Results of Separately Excited DC Motor Using FOPID ControllerAfter analysing the above three graphs, the comparative table is made and results are analysed and discussed.Table 7 shows the comparative analysis of the three controllers.Table 7The Comparative Analysis of the ControllersThe performance specifications of the controlledsystem using the fractional controller are betterthan that of the controlled system using classicalPID controller. In general, the system with theinteger order PID controllers takes more time tosettle than with fractional order PID controller.Oscillations in FOPID are less as compared toconventional PID. Settling time is less in FOPID ascompared to PID controller. When these twocontrollers are compared with FLC, it is observedthat FLC is more efficient among the threecontrollers.FLC parameter controller has less risingand settling time as compared to other twocontrollers. Steady state error is also less in FuzzyLogic Controller. FLC has better dynamic responseproperties and steady-state properties.VI CONCLUSIONIn present work, performance comparisonof PID controller with that of fractional order PIDcontroller and Fuzzy Logic controller is presented.Performance comparison are simulated and studied.The time response characteristics of the threesystems are analysed. The effectiveness of thefractional order PID controller and PID controllerand Fuzzy Logic controller is evaluated in terms of:i. Rise-timeii. Settling-timeiii. Steady state valueComparing the step responses with the onesobtained (in simulation) with the three controller,Specifications PID FOPID FLCRise time 3sec 1sec 0.7secSettling time 4 sec 3sec 2.7secSteady statevalue156.3 156.5 157.07
  9. 9. Safina Al Nisa, Lini Mathew, S Chatterji / International Journal of Engineering Research andApplications (IJERA) ISSN: 2248-9622 www.ijera.comVol. 3, Issue 3, May-Jun 2013, pp.1137-11461145 | P a g ethe better performance of the system with theFuzzy Logic controller was observed. Fractionalorder PID controller for integer order plants offerbetter flexibility in adjusting gain characteristicsthan the PID controllers, owing to the two extratuning parameters i.e. order of integration and orderof derivative in addition to proportional gain,integral time and derivative time. Fine-tuned Fuzzycontroller presents smaller overshoot and settlingtime than conventional PID controller and FOPIDcontroller. The three parameters "KP", "KI", "KD"of conventional PID control need to be constantlyadjusted in order to achieve better controlperformance. In case of fractional PID fiveparameters needs to be tuned to achieve betterperformance. Fuzzy self-tuning PID parameterscontroller can automatically adjust PID parametersin accordance with the speed error and the rate ofspeed error-change, so it has better self-adaptivecapacity. The reason for getting a smooth controlleroutput in the PID-like FLC case is because of thefact that PID-like FLC updates the controller outputby making comparison of the error and the changein error in angular displacement of the motor shaft.REFRENCES[1] Zhang G and Funji Furusho Fungi, “SpeedControl of Two-Inertia System by PI/PIDControl”, IEEE Transaction on IndustrialElectronics, Vo1. 47, pp. 603-609, June,2000.[2] I-Hai Lin P and Ellsworth Chris, “Designand Implementation of a PC-BasedUniversal Fuzzy Logic ControllerSystem”, Proceedings of InternationalIEEE/IAS Conference on IndustrialAutomation and control, pp. 399-408, 06August, 2002.[3] Zadeh L.A., “Fuzzy Logic: Issues,Contentions and Perspectives”, IEEEInternational Conference on Acoustics,Speech, and Signal Processing, VI, pp.VI/183, Vol. 6, 19 April, 1994.[4] Prommeuan S., Boonpiyathud S andSuksri T, “Fuzzy Logic Based onLabVIEW for Speed Control of Two-Inertia System”, Proceedings ofInternational Joint Conference by theInstitute of Control, Robotics and Systems(ICROS) and the Society of Instrumentand Control Engineers (SICE) onIndustrial Electronics, pp. 2867-2870,August, 2009.[5] Tipsuwan Y., Mo-Yuen Chow, “Fuzzylogic Microcontroller Implementation forDC Motor Speed Control”,Proceedings of International IEEEConference on Industrial ElectronicSociety, Vol. 3, pp. 1271-1276, 29November, 1999.[6] Sousa G.C.D and Bose B.K, “A Fuzzy SetTheory Based Control of a Phase-Controlled Converter DC Machine Drive”IEEE Transaction on IndustrialApplications, Vol. 30, pp. 34-44, January,1994.[7] Katbab A., “Fuzzy Logic and ControllerDesign-a Review”, Proceedings of IEEEConference on Visualize the Future, pp.443-449, March, 1995.[8] Wen J. Sheng Wang C. Hsu; Chang Y.De; Teng C. Cheng., “Intelligent Controlof High-speed Sensorless Brushless DCMotor for Intelligent Automobiles”,Proceedings of IEEE Conference onSystem, Man and Cybernetic, pp. 3394-3398, October, 2008.[9] N. Barakat., “Speed Control of a DCMotor using a Feedforward ComputedTorque Control Scheme”, Proceedings ofIEEE Conference on Intelligent Control,pp. 432-437, September, 1996.[10] Khoei A., Hadidi Kh. and Yuvarajan S.,“Fuzzy-Logic DC-Motor Controller withImproved Performance”, Proceedings ofIEEE Conference on IndustryApplications, Vol. 3, pp. 1652-1656,October, 1998.[11] Altayef J. A. and Zhu Qun-xiong, “Real –Time DC Motor Position Control by(FPID) Controllers and Design (FLC)Using LabVIEW Software Simulation”,Proceedings of International Conferenceon Computer and Automation Engineeringheld in Singapur, Vol. 2, pp. 417-420, 26February, 2010.[12] Mrad F., DandachS H., Azar S.and DeebG., “Operator-Friendly Common SenseController with Experimental Verificationusing LabVIEW”, Proceedings of IEEEInternational Symposium on Control andAutomation, pp. 1051-1055, June, 2005.[13] Huibin Z., Jianxun Jin and Jun Cheng,“Virtual Instrument Based Fuzzy Control,System form PMLSM Drive” Proceedingsof IEEE International Conference onApplied Superconductivity andElectromagnetic Devices, pp. 299-303, 25September, 2009.[14] Khuntia S.R., Mohanty K.B., Panda S andArdil C, “A Comparative Study of P-I, I-P, Fuzzy and Neuro-Fuzzy Controllers forSpeed Control of DC Motor Drive”,Proceedings of International Journal onElectrical and Computer Engineering, Vol.5, pp. 287-291, 2010.
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