Review of ANFIS-based control of induction motorsrepository.um.edu.my/14597/1/Jounal of Intelligent & Fuzzy Systems.pdf · Review of ANFIS-based control of induction motors ... an

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Journal of Intelligent & Fuzzy Systems 23 (2012) 143–158DOI:10.3233/IFS-2012-0502IOS Press

143

Review of ANFIS-based controlof induction motors

M.K. Masood∗, Wooi Ping Hew and Nasrudin Abd. RahimDepartment of Electrical Engineering, University of Malaya, Kuala Lumpur, Malaysia

Abstract. This paper reviews the use of Adaptive Neuro-Fuzzy Inference Systems (ANFIS) for vector-controlled induction motordrives. While conventional schemes do not deal well with the highly nonlinear nature of motor control, fuzzy logic with itsadjustability and neural networks with their adaptability have been shown to be excellent alternatives. ANFIS combines theadvantages of fuzzy logic and neural networks and yields excellent results when used at various stages of the motor controlprocess. The most prominent use of ANFIS with motor drives has been for parameter estimation, speed control and torque andflux control. The merits and demerits of these methods are examined. This paper is intended to serve as a reference for researchersconsidering the use of ANFIS for the control of motor drives.

Keywords: ANFIS, induction motor, flux, parameter, torque

1. Introduction

Motor drives, which consist essentially of an elec-tric motor driving a mechanical load, find widespreadapplication in industry. Traditionally, DC motors havebeen used for variable speed drives due to their sim-ple design, easy operation and excellent performance.However, the need for a cheaper, low maintenancealternative lead to the use of AC motors. Unlike DCmotors, the stationary and rotating parts of AC motorsare not connected. They are therefore brushless andpractically maintenance-free. Also, they can work involatile environments without producing sparks or cor-roding. This, combined with their low cost, is why ACmotors constitute 90% of all industrial motors [1]. Theyare used in industrial machinery, fans, blowers, vac-uum cleaners, air conditioners and a plethora of otherapplications.

∗Corresponding author. M.K. Masood, Department of ElectricalEngineering, University of Malaya, Kuala Lumpur, Malaysia. Tel.:+60 193764751; E-mail: mkm [email protected].

Vector control came to the fore as a method promis-ing the excellent performance of a DC motor whileusing the relatively inexpensive AC motors. FieldOriented Control (FOC) used stator currents to con-trol the torque of the motors. With the introductionof Direct Torque Control (DTC), however, improvedresponse with reduced complexity was made possible.

Combination of FOC and DTC with artificial intel-ligence (AI) opened an immensely promising avenuefor motor control. Fuzzy logic, with its adjustablemembership functions, provided a way to incorpo-rate human expert knowledge in the control process.Neural networks offered the advantage of a trainingmechanism, a trait that would prove very useful inconfronting the nonlinearity that besets modern motorcontrol methods. The culmination of this trend was thecombination of fuzzy logic and neural networks intoneuro-fuzzy controllers, the most popular configurationof which uses the Adaptive Neuro-Fuzzy Inference Sys-tem (ANFIS). This paper, besides a brief review of theuse of Fuzzy Logic and Neural Network, examines theuse of ANFIS for different aspects of vector controlledinduction motor drives. Specifically, the use of ANFIS

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144 M.K. Masood et al. / Review of ANFIS-based control of induction motors

for parameter estimation, speed control and torque andflux control is reviewed. The advantages of ANFIS usefor different stages of the motor control process are laidout.

2. Principles of vector control

Induction motor drives require frequency variationto vary the rotor speed. Also, at low frequencies, themotor impedance drops and the current shoots up. Tolimit this current, we need to be able to vary the voltagesupplied to the motor as well [2]. With the developmentof microprocessors, microcomputers, digital signal pro-cessors (DSPs) and increasing advancements in powerelectronics, it is now possible to achieve this variation infrequency and voltage, so as to achieve speed control.However, due to the fact that the control is nonlinearand multivariable, significant effort had to be directedto reducing the complexity of the control algorithms.

The complex space vector description is a commonlyadopted method of depicting the variables of the induc-tion motor. If we consider the reference frame to be fixedto a frame F rotating with an angular speedωf , the equa-tions of the induction motor in per-unit form are [3–8]:

Vsf = RsIsf + TNdψsf

dt+ jωfψsf (1)

0 = RrIrf + TNdψrf

dt+ j(ωf − ωm)ψrf (2)

ψsf = LsIsf + LmIrf (3)

ψrf = LrIrf + LmIsf (4)

dωm

dt= 1

Tm[Im(ψ∗

sf Isf ) −mL] (5)

Where Vs is stator voltage, Is is stator current, [ψs]is stator flux linkage, Ir is rotor current, ωm is themechanical angular speed, mL is the load torque, Lmis the magnetizing inductance, TN is 1/2πf where fis nominal frequency and Tm is the mechanical timeconstant.

There are two fundamental approaches to control-ling an induction motor: scalar and vector control. Inscalar control, only the magnitude and frequency ofvoltages, currents and flux linkages is controlled. Whileit gives satisfactory performance with low-cost and low-performance drives [9], the speed and torque responsefor higher speed drives is poor because the stator fluxand torque are not directly controlled. In vector control,both the magnitude and phase of the motor variables

is controlled. In space vector notation, this translatesto the control of both the magnitude and position ofthe space vectors of voltage, current and flux linkage.While scalar control is restricted to the steady state,vector control provides the correct orientation of spacevectors both in the steady and transient state [10].

Vector control became prominent with the proposi-tion of Field-oriented control (FOC) by Hasse [11] andBlaschke [12]. FOC was an attempt to mimic the decou-pled control of the field and torque that was possible inseparately-excited DC machines. The rotor winding ininduction motors is not physically

T = 3

2Np

Lm

σLsLr||ψr||||ψs|| sin δsr (6)

connected to the stator and the rotor current is induced,not directly supplied by an external source. Due to this,independent control of torque and the magnetic field(and thus the flux) is not straightforward in inductionmotors [13–15]. FOC involves the transformation ofthe three phase stator currents into an asynchronouslyrotating two axis d-q reference frame. The stator currentis the torque control quantity. If the rotor flux amplitudeis kept constant, the following equation depicts howtorque is controlled by the stator current, isq :

T = Lm

Lrψrisq (7)

The current-controlled inverter is well suited toimplementing FOC [16].

In 1985, Takahashi and Noguchi [17] presentedthe strategy of Direct Torque Control. They proposedthe simultaneous, not merely independent, control oftorque and flux. The need for current loops was elimi-nated and torque and flux were controlled in the mannerof a closed loop system [18–23]. DTC requires theknowledge of stator resistance only and thus greatlydiminishes sensitivity to parameter variations. The needfor a speed sensor does not arise. Also, the need for coor-dinate transformation between the stationary frame andsynchronous frame is removed [24]. The expression fortorque that forms the basis of DTC is [25]:

σ = 1 − L2m

LsLrψr (8)

Where Np is the pole-pair number, δsr is the spatialangle between stator and rotor fluxes and σ is as in (8).

By keeping the stator flux constant, a fast torqueresponse can be obtained by changing the angle δsrquickly.

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M.K. Masood et al. / Review of ANFIS-based control of induction motors 145

A voltage source inverter is well suited to the imple-mentation of DTC-based drives [26, 89]. A six pulsevoltage source inverter consists of six non-zero activevoltage switching space vectors and two zero vectors,giving a six sector formation as shown in Fig. 1. Con-sider the relationship between the voltage vector andstator flux:

Vs = dψs

dt(9)

Depending on the magnitude and position of the volt-age vector applied, the stator flux vector moves with aparticular speed in the direction of the voltage vector.A zero vector makes the flux vector remain stationary.Thus, the stator flux can be controlled with the applica-tion of suitable voltage vectors in each sampling period.

Conventionally, DTC has used hysteresis compara-tors to select voltage vectors from a switching table. Inevery sampling period, the actual and reference torqueand flux values are compared. The errors are fed to atwo-level hysteresis comparator. Depending on whetherthe errors are positive, negative or zero, the hysteresiscomparators output 1, 0 or −1. This information, alongwith the position of the stator flux, is used to select theappropriate voltage vector from the switching table. Theblock diagram of this scheme is shown in Fig. 2.

The conventional scheme, while providing fasttorque response, has a few drawbacks. With only sixactive voltage vectors, the torque and flux errors arenon-zero for a large portion of the control process,leading to torque and flux ripples [16]. The problem iscompounded by the variation of switching frequency.To remedy these issues, Space Vector Modulationwas proposed to synthesize the voltage vectors, as is

Fig. 1. Six active voltage vectors of two-level voltage source inverter.

demonstrated in [27, 28]. This method allowed for aconstant switching frequency and a significant reduc-tion in torque ripple.

3. Intelligent control

Fuzzy logic provided a viable alternative to modelnonlinear relationships that posed difficulties in vec-tor control. In [29], a fuzzy logic controller (FLC)replaced the hysteresis comparators for a direct selfcontrolled induction motor drive. Using errors betweenactual and estimated torque and flux values, the FLCdetermined the switching states of the inverter for eachsampling period. Not only was the response faster thanthat of conventional DTC, the flux regulation was vastlyimproved as well. The FLC has been extensively usedwith switching tables. In [30], a FLC determined the

Fig. 2. Conventional DTC scheme block diagram.

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duration within one sampling period for which a torqueincreasing vector selected from the switching table wasapplied. For the remaining duration, a torque decreasingvector was applied. As a result, the average value of thevoltage vector could be from a wider range than the con-ventional seven voltage vectors. In [31–33], two FLCswere employed to calculate the optimum duty cycle persampling period within which to apply the voltage vec-tor. If in a particular sampling period, the inverter statewas to be changed, one fuzzy logic controller selectedthe optimum duty cycle. If, in subsequent samplingperiods, the inverter state was to remain the same, asecond FLC selected an increment to the duty cycle.Only one FLC worked per sampling period and thus,the reduction in torque ripple came without a signif-icant increase in computational burden compared toconventional DTC.

The use of FLC to regulate torque in [34] resultedin excellent torque tracking. To reduce the steady stateerror observed with FLC use, a PI-Fuzzy scheme wasproposed in [35]. In addition to the reduction of thesteady state error, this method provided a fast responseand low overshoot. Another variant of a PI-fuzzyscheme was attempted in [36]. The torque componentof the voltage vector was provided by an FLC, whilea PI controller gave the flux component. With the fluxestimated using PI flux magnitude control, the induc-tion motor drive was made insensitive to DC drift. Theissue of DC drift was addressed in [37] as well, wherethe error between the stator flux estimated by integrat-ing back emf and low-pass filtered flux was input to anFLC. The absence of a complex observer or estimatorreduced the computational burden. Also, the estimationwas more accurate than methods used in works such as[38, 39], where the FLC used stator current error as theinput. A noteworthy application was the placing of aPID-like fuzzy controller with another fuzzy controllerfor speed control in a vector controlled drive, yield-ing high performance albeit with a small number ofparameters to be adjusted [91].

The combination of FLC that outputs the voltagevector with space vector modulation has yielded goodresults, as has been demonstrated in [40, 41]. Con-stant switching frequency, reduced torque ripple andstator current distortion have been achieved through thismethod. A slightly different approach was presented in[42], where the FLC was used to calculate the phasecorrection only.

In [43], two FLCs were used, one to provide voltageamplitude and the other for the angle of the voltage vec-tor for direct torque control. Combined with a variable

gain PI controller, this configuration gave fast speedresponse, reduced torque ripple and offered rapid loaddisturbance rejection. In [44], the FLC was used withfuzzy adaptive gains for speed control of a FOC drive.While the FLC provided the torque producing current,a sliding mode controller output the flux producingcurrent. The FLC was shown to be robust against keyparameter variations.

While fuzzy logic’s ability to mimic human expertsis tremendously useful, it lacks the adaptive capabil-ity that would eliminate the need for extensive trialand error. Neural networks, with their learning capa-bility, have thus found widespread use in the control ofplants that vary with time or where the model of the sys-tem is partially known. Extensive research has thereforebeen conducted with the objective of finding the mostsuitable ANN training algorithms for vector control.The use of neural networks has been examined for twolevel inverters [45], three level inverters [46–48] andeven a five level inverter [49]. ANNS have proven use-ful at various stages of control. In [50], an ANN wasused to estimate the feedback signals in an inductionmotor drive. In [51], using parallel recursive predictionerror and backpropagation training algorithms, ANNwas used to tune the stator resistance for DTC. Besidesdemonstrating that the ANN could deal with large resis-tance variations and still estimate accurately, it was alsoproved that more neurons in the hidden layer provideda better approximation.

ANN use in speed control has been especiallyvaried, as is evident in [52–56]. In [57], an ANN wasused for modeling. Using the Maximum Likelihood(ML) estimation method and free acceleration responsedata, nonlinear models of the induction machine werecreated. In [58], a neural network was used as a stateselector for a direct torque controlled induction motordrive. The errors between actual and estimated torqueand flux were fed to a comparator. The comparatoroutputs, along with the stator flux angle, were made theinputs of a neural network, which output the switchingstates of the inverter. Using a reference switchingstate vector, an error vector was generated which wasused to tune the weights of the ANN. Four trainingalgorithms were compared: backpropagation, extendedkalman filter [90], adaptive neuron model and parallelrecursive prediction error. While this work did presenta comparative analysis of the algorithms, it did notshow neural networks to offer better results than con-ventional DTC. This issue recurred in [59]. An ANNtrained with the Levenberg Marquardt method and usedalong with a modified switching table produced torque

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responses from the motor not significantly differentfrom conventional DTC. However, the ANN controllerwas more stable and had the advantage of adaptability.In [60], the pattern recognition capability of a GeneralMapping Regressor, a type of neural network, was usedto replace the hysteresis comparators in conventionalDTC scheme. In addition to drastic reduction intorque ripple, response faster than even fuzzy logicbased DTC was achieved. A recent development wasthe use of wavelet networks [61]. In field orientedcontrol, it is often difficult to continuously modifythe neural network offline to improve performance.To overcome this, a wavelet function was introducedin neural networks. A wavelet network allows foronline parameter tuning. This network was used forstator estimation identification and shown to be moreaccurate than conventional neural networks.

With all their advantages, neural networks are nota preferred solution if the training data is insuffi-cient to cover all operating modes [62]. To overcometheir respective disadvantages, fuzzy logic and neuralnetworks have been combined into neuro-fuzzy con-trollers. In so doing, the fuzzy logic ability to takeaccount of human expert knowledge is paired withthe learning ability of neural networks. The Adap-tive Neuro-Fuzzy Inference System (ANFIS) is themost popular neuro-fuzzy configuration. Its structuralflexibility, adaptability and simple mathematical repre-sentations have made it an excellent choice of controllerin motor control.

4. Function of the ANFIS

An ANFIS makes an intelligent choice of the param-eters of the membership functions (the antecedent

parameters) and the coefficients of the output equation(the consequent parameters), thus eliminating a greatdeal of trial and error that normally plagues fuzzy con-trol. The basic ANFIS architecture is shown in Fig. 3. Asquare node represents an adaptive node while a circlenode has no parameters. The functions of each layer aredescribed below:

Layer 1: This layer contains square nodes whichreceive the input and produce the degree of member-ship to each linguistic variable, which are representedby membership functions that are usually triangular orbell-shaped. For example, the membership value of aninput x to a linguistic variable Ai (represented by abell-shaped function) of node i, is given by:

O1i = µAi (x) = 1

1 +[(

x−ciai

)2]bi (10)

The parameters Ai, bi and ci are the premiseparameters.

Layer 2: The nodes in this layer provide the firingstrength of each rule. A preferred choice of doing so isby multiplication [63]. For example,

O2i = wi = µAi (x).µBi(y) (11)

Layer 3: The firing strengths are normalized in thislayer. The output of each node in this layer is

O3i = wi = wi

wi + w2(12)

Layer 4: The output of each node in this layer is:

O4i = wifi = wi(pix+ qiy + ri) (13)

Wherepi, qi and ri are called consequent parameters.

Fig. 3. Basic ANFIS architecture.

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Layer 5: All incoming signals are summed in thislayer to obtain the crisp output.

O5i =

∑i

wifi =∑i

wifi

∑i

wi(14)

Training the ANFIS controller essentially involvestuning the premise and consequent parameters. Thehybrid learning algorithm [64], which combines gra-dient descent and the least squares estimate (LSE), is apopular method due to its rapid convergence.

In the forward pass of the hybrid learning algorithm,premise parameters remain fixed and the consequentparameters are upgraded by the least squares estimate.In the backward pass, consequent parameters remainfixed and the premise parameters are updated by gradi-ent descent.

5. ANFIS estimators

A good model of the induction motor is one thatincorporates the variation of parameters over a widerange of operating conditions. This section examinesthe use of ANFIS to accomplish this.

To derive a dynamic model of the induction machine,the three-phase voltages and currents of the stator androtor (denoted by s and r subscripts, respectively) aretransformed into the more workable two-axis, d–q co-ordinate system. The voltage equations are:

Vqs = Rs.Iqs + dλqs

dt+ ωs.λds (15)

Vds = Rs.Ids + dλds

dt− ωs.λqs (16)

0 = Rr.Iqr + dλqr

dt+ (ωs − ωr).λdr (17)

0 = Rr.Idr + dλdr

dt− (ωs − ωr).λqr (18)

Whereλ is the flux linkage andω the angular velocity.The flux linkages depend on the currents and induc-

tances. When the machine becomes saturated, themutual and leakage inductances become nonlinear anddependent on the currents that flow through the induc-tances. The stator and rotor flux linkages also dependnonlinearly on all currents. To calculate the flux deriva-tives in the voltage equations, we need to apply thechain rule. The resulting derivatives are called incre-mental inductances [65]. For example, the q-xis statorincremental inductance is given in (19).

∂λqs

∂t= ∂λqs

∂Iqs

dIqs

dt+ ∂λqs

∂Ids

dIds

dt

+∂λqs∂Iqr

dIqr

dt+ ∂λqs

∂Idr

dIdr

dt(19)

In a similar manner, the d-axis stator incrementalinductance and the rotor incremental inductances canbe calculated. The dynamic machine model is obtainedby substituting these equations in the voltage equations.The resulting model would contain 21 parameters, eachvarying with the operating conditions. In [66], a sim-plified model which ignores the cross-coupling effectsbetween the d and q axis, and thus assumes the incre-mental inductances to be influenced only by their ownaxis currents, was proposed. The simplified model isgiven in (20). The model reduces the number of param-eters to be estimated to 11. These are

Rs,Rr, Lls, Llr, Lm,Llqs, Llqr, Lmq, Llds, Lldr, Lmd.

In [66], parameter estimation through neural net-works was tested. The main shortcoming of thisapproach was the absence of intuitive modeling inneural networks. As a remedy, an ANFIS estimatorwas used in [67, 68]. Each parameter to be estimatedrequires its own ANFIS model, since the ANFIS canhave only one crisp output.

⎡⎢⎢⎢⎢⎣

Vqs

Vds

0

0

⎤⎥⎥⎥⎥⎦ =

⎡⎢⎢⎢⎢⎢⎢⎣

Rs ωs.(Lls + Lm) 0 ωs.Lm

−ωs.(Lls + Lm) Rs −ωs.Lm 0

0 (ωs − ωr).Lm Rr (ωs − ωr).(Llr + Lm)

−(ωs − ωr).Lm 0 −(ωs − ωr).(Llr + Lm) Rr

−(ωs − ωr).Lm 0 −(ωs − ωr).(Llr + Lm) Rr

⎤⎥⎥⎥⎥⎥⎥⎦

∗

⎡⎢⎢⎢⎢⎣

Iqs

Ids

Iqr

Idr

⎤⎥⎥⎥⎥⎦

+

⎡⎢⎢⎢⎢⎣

Llqs + Lmq 0 Lmq 0

0 Llds + Lmd 0 Lmd

Lmq 0 Llqs + Lmq 0

0 Lmd 0 Llqs + Lmq

⎤⎥⎥⎥⎥⎦ ∗ d

dt

⎡⎢⎢⎢⎢⎣

Iqs

Ids

Iqr

Idr

⎤⎥⎥⎥⎥⎦ (20)

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Fig. 4. ANFIS speed controller.

Data for modeling must contain transient responsesfrom various operating conditions because the param-eters depend nonlinearly on operating conditions. Thatis why, free acceleration data is used to create themodels [66]. The measurements are obtained by apply-ing three phase power to the motor while it is atstandstill without load. When the motor starts, thestator and rotor are saturated with current. As therotor accelerates, the stator voltages, stator currentsand rotor angular velocities are recorded. Hall effectsensors can be used for the voltage and current mea-surements. An encoder can get the rotor angularposition. Angular velocity can be calculated using aDSP.

Now, the slip of the motor is given by:

s = ωsyn − ωr

ωsyn(21)

Where ωsyn is the velocity of the stator field, alsocalled the synchronous velocity. As the rotor speedvaries from zero to just below the synchronous speed,the slip varies from one to zero. Therefore, a thoroughrepresentation of parameter variation with rotor speedcan be obtained from this test procedure.

The training data set is prepared by selecting ashort time duration (In [66], this duration is 0.05

Fig. 5. Speed response of onlinee tuned ANFIS speed controller tostep increase in load.

seconds) within which the parameter variation isinfinitesimal. Average values of the stator voltages androtor angular velocity (i.e. the ANFIS inputs) and theeleven parameters to be estimated (the ANFIS out-puts) are measured for each duration. The resultinglist of parameters for successive durations constitutesthe training data to be used to create the ANFISmodel.

To test the model, varying values of stator current androtor angular velocity are provided to the model and theoutput of the ANFIS is examined. This is compared toactual measured values of the parameters. In [67], errors

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as low as 0.000341% were obtained with the ANFISestimator.

6. ANFIS use in speed control

FOC methods have two primary disadvantages: sen-sitivity to motor parametric variations and flux errorsat low speeds [68]. These are problems PID controllersdo not deal with well, leading to deterioration in per-formance. This is where artificial intelligent controllershave proven to be excellent alternatives to speed control.The ANFIS controller can be trained to accommodatea wide range of operating conditions.

In [69, 70], the conventional PI speed controller wasreplaced by an ANFIS controller. The controller usedspeed error and the rate of change of speed error asinputs. The inputs were normalized before being fed tothe ANFIS controller, according to equations (22) and(23).

εω = ω∗ − ω

ω∗ × 100% (22)

εω = εω(n) − εω(n− 1)

T× 100% (23)

Where εω is the normalized speed error and εω isthe rate of change of speed error. Figure 4 shows theblock diagram of the speed controller.

To train the controller, the hybrid learning algorithmwas used. The speed controller was combined with anANFIS speed estimator. Excellent current and speedresponse was achieved. However, while works such as[69, 70] used the torque producing current componentiqs as the speed controller output, it is very difficult topractically generate current values to be used as offlinetraining data for the ANFIS controller. To address thisproblem, an online tuning method was used in [71] toupdate the ANFIS weights based on the error betweena reference model of motor speed and actual motorspeed accelerations. The motor speed acceleration iscalculated as the slope of motor speed.

Taking the specific requirements of the IM drive intoconsideration, the motor speed slope was expressedas:

y =(

1 − exp

( −(ω)2

2 ∗ 0.012

))∗ 1000 ∗ sign(ω) (24)

Where y is the reference motor speed slope,(dωdt

)∗

The ANFIS weights were tuned so as to make theactual speed slope follow the reference. The objectivefunction to be minimized was:

E = 1

2

(y − dω

dt

)2

(25)

This model was implemented using a DSP. The tran-sient response showed no overshoot and a small settlingtime. Also, limiting the input membership functions tothree made for low computational burden. The con-troller was tested with sudden load disturbance, towhich it showed a negligible amount of speed devia-tion, as is shown in Fig. 5. Additionally, the ANFIScontroller forced the speed to follow the reference farmore closely than a PI controller that was tuned to haveminimum overshoot and settling time. This is shown inFig. 6.

The use of two controller inputs, as has been donein [72–76], leads to a large number of membershipfunctions and rules. An improved scheme, proposed in[77] and experimentally verified in [78], utilized onlythe speed error as input to the ANFIS controller. TheANFIS used one input with three membership func-tions. The normalized speed error was input to the

a

b

Fig. 6. (a) Response to sinusoidal speed reference for PI controller.(b) Response to sinusoidal speed reference for ANFIS controller.

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Fig. 7. Torque and flux control using ANFIS.

Fig. 8. Architecture of ANFIS controller.

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ANFIS controller and the reference torque was gener-ated. The command current was calculated using (40).

i∗q(n) = T ∗e (n)

2

3

2

P

Lr

Lm

1

λ∗dr

(26)

Where T ∗e is the command torque, P is the number

of poles of the motor, Lr is the rotor inductance, Lm isthe magnetizing inductance and λ∗

dr is the rotor’s d-axisflux linkage.

Training of the controller was done using an unsu-pervised on-line self tuning method. The objectivefunction that the algorithm sought to minimize is givenin (27).

E = 1

2

(ω∗ − ω

)2 (27)

Comparison of the speed response of this one inputscheme with the conventional two-input one showed nosignificant decrease in performance. The increased sim-plicity of the design was thus shown to be a satisfactorytradeoff.

On-line training of the ANFIS controller was alsoexamined in [79]. Here again, the objective functionwas as in (41). The weights of the controller wereadjusted using (42).

wr(k + 1) = wr(k) − γ∂E(k)

∂wr(k)(28)

Where γ is the learning rate, E is the objective func-tion and wr is the weight of the r-th rule. However,this algorithm converges slowly, leading to an unsatis-factory learning rate. Therefore, a modified algorithmsuggested in [80] was used. This is based on local gra-dient PD control:

wr(k + 1) = wr(k) +O3Nr

(kpem(k)

+ kdem(k))

(29)

WhereO3Nr is the firing strength of r-th rule and em(k)

is the tracking error. The parameters kp and kd weredetermined using a genetic algorithm to rapidly elimi-nate the tracking error. The response of the drive wastested by a slow reverse of the reference speed. Bar-ring small speed oscillations, the controller eliminatedthe speed tracking error and the drive remained stableunder full load torque.

7. ANFIS use in torque and flux control

The use of ANFIS to directly generate voltage vectorsaccording to toque and flux values was first proposedin [81]. The block diagram of this scheme is shown inFig. 7.

Reference torque and flux values are compared withactual estimated values. The errors are fed to the ANFIScontroller, which outputs the reference voltage vectoramplitude and phase.

The architecture of the ANFIS controller is shown inFig. 8. Layer 5 outputs the voltage vector amplitude anduses an increment angle (described later in this section)to calculate the phase of the voltage vector.

To train the controller automatically, the hybrid learn-ing algorithm was used. The consequent parametersthat define the ANFIS output were tuned using least-square estimation and the antecedent parameters weretrained using the backpropagation method. Referencevalues of voltage vector, obtained from a PI con-troller, combined with torque and flux error values

Fig. 9. (a) Tuning surface for manual training of ANFIS for Torque.(b) Tuning surface for manual training of ANFIS for Flux.

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a

b

Fig. 10. (a) Torque response with conventional DTC. (b) Torqueresponse with ANFIS controller.

were used to allow the controller to learn the pat-tern. The Kalman filter is also an appropriate optionof learning algorithm, as has been demonstrated in[82].

For low-speed motor operation, a manual tuningprocedure was suggested in [83]. The antecedentparameters defining the membership functions are cho-sen on the basis of calculation time. While an extensionof membership functions only marginally improvesthe performance, the calculation time is considerablyincreased. The width of the membership functions isdetermined by the product of the weights and the errorinputs. By locating the minimum value of this prod-uct, effective tuning can be accomplished. The tuningsurface, shown in Fig. 9, is constructed by comparingthe effects of various weight values with the torque andflux errors, separately. In [83], it is suggested to first

a

b

Fig. 11. (a) Flux trajectory with conventional DTC. (b) Flux trajec-tory with ANFIS controller.

identify the optimal weights for least flux error andthen for the torque error. The vector adder in Fig. 8outputs the amplitude and angle of the voltage vec-tor. For each sampling period, the average value of allthe voltage vectors obtained from the ANFIS output iscalculated.

To calculate the increment to the angle of the volt-age vector, a selection table is constructed. Considerthe equations for stator flux and torque for a statorflux coordinate system [84], as shown in (44) and(45):

λs = 1

TN

t∫0

vs cosφdt + λs0 (30)

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Fig. 12. ANFIS control scheme with phase correction as output.

Fig. 13. Architecture of ANFIS for use with a three level inverter.

T = λs

(vs sin φ − ωsλs

rs

)(31)

Where vs is the stator voltage and φ is the angleincrement �.

Consider the case when the flux error is zero and thetorque error is either positive or negative. No changein flux is required and therefore the cosφ term in (44)should be made zero. Thus, φ = ± π/2 would be a

prudent choice for the angle increment. This will makethe torque value to become:

T = λs

(±vs − ωsλs

rs

)(32)

When both torque and flux errors are either positiveor negative, an intermediate value is chosen. For exam-ple, when both torque and flux errors are positive, theangle increment is chosen to be π/4.

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Table 1Stator flux angle selection table

eλ P Z N

eτ P Z N P Z N P Z N

�π4 0 −π

4π2

π2 −π

23π4 π − 3π

4

In this manner, a selection table is constructed.Table 1 shows the table used in [84].

A number of advantages have been achieved usingthis control method. Firstly, while conventional DTC islimited to eight switching vectors, the ANFIS controlcombined with space vector modulation enables anynumber of voltages to be synthesized. This shows inthe reduction of torque ripple, as shown in Fig. 10. Thisalso allows for a smooth stator flux trajectory, as shownin Fig. 11. Besides the scheme described above, twovariants have been documented:

1. Phase correction as ANFIS output:In [85], the ANFIS controller was trained to output

only the angle increment. Figure 12 shows the blockdiagram of this control scheme.

The ANFIS controller’s output is given by:

Ag =

n∑i=1WiCi

n∑i=1Wi

(33)

The amplitude calculator of Fig. 13 utilizes Equa-tions (34) and (35).

Vsα = 3

2cos

(Ag + k

π

3

)(34)

Vsβ = 3

2sin

(Ag + k

π

3

)(35)

2. Two ANFIS controllers for three-level inverters:Three-level voltage source inverters consist of four

switches in each inverter leg. They allow for higher volt-age ratings compared to two-level inverters and producehigher quality currents [1]. Three switching states areused per inverter leg and therefore a total of 27 statesare available [86]. Each state corresponds to a switchingvector, of which three are zero-state vectors. The volt-age vectors are classified into four groups [87]: ZeroVoltage Vectors (V0, V1, V2), Low Voltage Vectors (V1,V2, V3, V4, V5, V6,V8, V9, V10, V11, V12,V13), Inter-mediate Voltage Vectors (V21, V22, V23, V24, V25, V26)and High Voltage Vectors (V15, V16, V17, V18, V19,V20).

In [88], the use of two separate ANFIS controllerswas proposed. Both controllers use the torque and flux

a

b

Fig. 14. (a) Stator current response with conventional DTC. (b) Statorcurrent response with ANFIS controller with three level inverter.

errors, but one controller outputs the low voltage vec-tors, while the other covers the intermediate and highvoltage vectors. This scheme is depicted in Fig. 13.This scheme reduced harmonic distortion in currents,in comparison to conventional DTC using a two-levelinverter. This is depicted in Fig. 14.

8. Conclusion

This paper has reviewed the use of ANFIS to controlinduction motor drives. The main features of ANFISare structural flexibility, adaptability and simple math-ematical representation. It has been used with bothField Oriented Controlled and Direct Torque Con-trolled drives at various stages of the control process.The most recurring use, though, has been for model-ing, parameter estimation, and speed, torque and fluxcontrol. The control schemes used by researchers are

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examined, the methods explained and the advantagesoffered by ANFIS over conventional control methodsare presented.

ANFIS has proven to be tremendously accurate inthe modeling of motor parameters, enabling the incor-poration of a wide range of operating conditions inthe model. In speed control, ANFIS controllers havebeen shown to give excellent transient response withprecise speed tracking. ANFIS-based torque and fluxcontrollers significantly reduced torque ripple, gener-ated smooth flux trajectories and reduced stator currentdistortion. This paper is intended to serve as a refer-ence to the most recurring use of ANFIS in inductionmotor control. The application of ANFIS to remedycommon control problems may give an insight as tohow it may address problems of a similar nature. Withthe constant advancement of simulation software andhardware such as microprocessors and DSPs, intelli-gent control schemes such as ANFIS are expected tobecome the most effective control choices, not least inthe control of variable frequency drives.

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