modelling & simulation of an anfis controller for an ac … a. kusagur1 & s. kodad & b....

ISSN 1 746-7233, England, UKWorld Journal of Modelling and Simulation

Vol. 8 (2012) No. 1, pp. 36-49

Modelling & Simulation of an ANFIS controller for an AC drive

Ashok Kusagur1,2∗, Shankarappa Fakirappa Kodad3, Sanker Ram4

1 Research Scholar, EEE Department, JNTU, Hyderabad-85, Andhra Pradesh 534305, India2 Professor & Head of the Department, HMSIT, Tumkur-4, Karnataka 591501, India

3 Principal, Krishnamurthy Institute of Technology & Engineering , Hyderabad, Andhra Pradesh 534305, India4 Department of EEE, JNTUCE, Kukatpally, Hydarabad-85, Andhra Pradesh 534305, India

(Received April 20 2010, Accepted March 1 2011)

Abstract. This paper presents the modelling, design & simulation of an adaptive neuro fuzzy inference strat-egy (ANFIS) for controlling the speed of the induction motor. Various advanced control techniques has beendevised by various researchers across the world till date, one technique being the use of fuzzy concepts inthe control algorithm. These fuzzy based controllers develop a control signal which yields on the firing of therule base, which is written on the previous experiences & are then fired to get the final output. As a resultof which, the outcome of the controller is also random & optimal results may not be obtained. To avoid this,selection of the proper rule base depending upon the situation can be achieved by the use of an ANFIS con-troller, which becomes an integrated method of approach for the control purposes & yields excellent results.In the designed ANFIS scheme for the speed control of IM, neural network techniques are used to select aproper rule base, which is achieved using the back propagation algorithm. This integrated approach improvesthe system performance, cost-effectiveness, efficiency, dynamism, reliability of the designed controller. Thesimulation results show the effectiveness of the method developed & has got very good dynamic responses.

Keywords: ANFIS, Fuzzy Logic, ANN, Simulink

1 Introduction & literature survey

In the modern day world, the AC motors play a vital role in the industrial sector especially in the fieldof electric drives. Without proper controlling of the speed, it is virtually impossible to achieve the desiredtask for any industrial application. AC motors, particularly the squirrel-cage induction motors (SCIM), en-joy several inherent advantages like simplicity, reliability, low cost and virtually maintenance-free electricaldrives. However, for high dynamic performance industrial applications, their control remains a challengingproblem because they exhibit significant non-linearities and many of the parameters, mainly the rotor resis-tance, vary with the operating conditions. Different control techniques to control the speed of the IMs havebeen developed by various researchers across the world. To name a few of them, being the classical or theconventional control, DTC & the FOC control, vector control, scalar control, PID control, the sliding modecontrol method, the fuzzy control, neural network control, hybrid control, etc., which had lot of advantages aswell as dis-advantages.

In this context, the fuzzy logic concepts coupled with artificial neural networks (hybrid control) playa very important role in developing the controllers for the plant, which might yield excellent results. Here,follows a brief review of the literature relating to the work done by various authors on the fuzzy logic coupledwith ANNs, i.e., the Adaptive Neuro Fuzzy Inference System (ANFIS) w.r.t. the speed control of AC drivesystems. In the last few years, fuzzy logic has met a growing interest in many motor control applications dueto its non-linearities handling features and independence of the plant modeling. The fuzzy controller (FLC)

∗ Corresponding author. Tel.: +91 9844795560. E-mail address: [email protected].

Published by World Academic Press, World Academic Union

World Journal of Modelling and Simulation, Vol. 8 (2012) No. 1, pp. 36-49 37

operates in a knowledge-based way, and its knowledge relies on a set of linguistic if-then rules, like a humanoperator. Ashok et al. [9] developed a novel design of a Takagi-Sugeno fuzzy strategy for induction motorspeed control, which yielded excellent results, especially in the settling times of the various responses. Here,a hybrid control was used for the speed control purposes. AI based design of a fuzzy logic scheme for speedcontrol of induction motors using SVPWM technique was proposed by the authors Ashok et al. in [7].

Abdul and Asghar[6] presented a soft starter applied to a IM system, which was based upon artificialneural networks (ANN) and adaptive neuro fuzzy inference system (ANFIS). The latter one was used to im-plement the feedback estimator while the former controller was used to adjust the firing angle of SCR’s underdifferent loading conditions. The presented soft starter was implemented using DSP and with neural networkstools and their performance was compared. The ANN based performance was found to be satisfactory in termsof the firing angle of the SCR’s.

Miloudi et al.[11] presented a new control technique of controlling the speed of IM using 2 methods,viz., variable gain PI (VGPI) controller and a direct torque adaptive neuro fuzzy controller (DTANFC) in[11] and compared them. First, a VGPI speed controller was designed to replace the classical PI controller.Then, DTNFC for a voltage source PWM inverter fed IM drive was presented. Simulation of the DTNFC-IMdrive using VGPI for speed control showed promising results compared to the VGPI one. In the latter case,the motor reached the set speed rapidly and without overshoots, trapezoidal commands under no load weretracked with zero steady state error and almost no overshoots, load disturbances were rapidly rejected by thedesigned controller.

Neuro-fuzzy robust controllers for AC drive systems using predictive controllers was developed byYashuhiko et al.[4] which reduced the plant and observation noise in the IM drive systems. Then, the pre-dictive linear controller was changed using FL such that the controller makes the system to respond quicklyand vice-versa, thus making the controller insensitive to plant noise. Further, a variable structure PI controllerusing FL for drive systems was implemented by them using neural networks, which showed very promisingexperimental results compared to the predictive ones.

Bimal et al.[2] extended the work done in [5] to a stator flux-oriented electric vehicle induction motor driveand then implemented the fuzzy controller by a dynamic back propagation neural network-based controller.The principal advantage of their proposed control was the fast convergence with adaptive step size of thecontrol variable. An adaptive speed control of hybrid fuzzy-neural network for a high performance IM drivewas presented by Mokhtar and Sofiane[15]. The 3-layered NN using a back propagation algorithm was usedto provide RT adaptive estimation of the motor’s unknown parameters and another 3-layered NN was usedto produce an adaptive control. The performance and robustness of the IM drives under non-linear loads,parameter variations and uncertainties was highly improved in their case. Simulation results showed excellenttracking performance.

Farzan[14] developed a sensorless adaptive neuro-fuzzy speed controller for IM drives in his paper. AnANN was adopted to estimate the motor speed and to provide a sensorless speed estimator system. The per-formance of the proposed ANFIS controller was evaluated for a wide range of operating conditions of theIM and also showed robustness to the parameters variations. A model reference adaptive flux observer basedneuro-fuzzy controller for an IM drive was presented by Uddin[12] in his paper. In order to provide a highperformance speed tracking, an improved self-tuned NFC was utilized by him. The performances of the pro-posed IM drive was investigated at various operating conditions and found to be robust and suitable for highperformance industrial drive applications.

Consoli et al.[3] dealt with the design and experimental realization of an MRAC based speed controller forindirect field oriented IM drive based on Fuzzy laws (for the adaptive process) and a Neuro-Fuzzy procedure(to optimize the Fuzzy rules). In their work, the variation of the rotor time constant was compensated by per-forming a fuzzy fusion of 3 simple compensation strategies. A prototype based on an IM drive was assembledand used to practically verify the features of the proposed control strategy. Rezvan and Mehran[13] applied theFuzzy based General Regression Neural Network (FGRNN) concept to the speed control of IMs. A GeneralRegression Neural Network (GRNN) was adopted to estimate the motor speed and to provide a sensorlessbased speed estimator system. The performance of the proposed FGRNN speed controller was evaluated for

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38 A. Kusagur1 & S. Kodad & B. Ram: Modelling & Simulation of an ANFIS controller for an AC drive

a wide range of operating conditions and the response time was also very fast despite the fact that the controlstrategy was based on bounded rationality.

A number of works done by various researchers[2, 4–6, 11, 13], i.e., their achievements were mentioned inthe previous paragraphs. Couple of drawbacks / disadvantages exist in the works done by the researchers in[2, 4–6, 11, 13], which are:(1) At steady state, the operation will oscillate about the optimum point.(2) Speed control performance of IM is affected by parameter variations and non-linearities.(3) Oscillations in the response curves exist even during the steady state.

Further, commenting on the speed response curves in [2, 4–6, 11, 13], it stabilized above 0.5s and hence tooklot of time. The rise times was found to be larger in some cases. The speed curve in [6] took more than 5s toreach the set value. Here, the parameters were measured by using the approximation method, which may be arandom process. The speed curve in [11] took more than 0.5s to reach the set value. Here, the gains vary alonga particular tuning curve. The speed curve in [4] took more than 2s to reach the set value.

The speed curve in [2] nearly 10s to reach the set value. At steady state, the operation will oscillate aboutthe optimum point. In this paper, at every decrementation of flux, a pulsating torque is likely to develop whichis not acceptable to electric drives. The speed curve in [15] nearly 1s to reach the set value. The authors haveused the minimum fuzzy rules in this case.

In [12], the speed curve took more than 0.8s to reach the set value and the authors used the minimumfuzzy rules in their work. One of the problem associated with their work was the detuning of the controllerwhich was required due to rotor time constant variations. In [13], the speed curve took more than 0.6s to reachthe set value. The principal advantage of neuro-fuzzy control (ANFIS), i.e., fast convergence with adaptive stepsize of the control variable, is retained. The neural network adds the advantage of fast control implementationand computation. Such a neuro-fuzzy control combines the advantages of fuzzy and neural controls.

ANFIS which tunes the fuzzy inference system with a back propagation algorithm based on a collectionof input-output data is implemented here. Mihoub et al.[10] proposed a ANFIS controller to obtain a highdynamic performance in AC machines. In their work, they used fuzzy controller first and then the neuro-fuzzycontroller. Finally, they proved that the latter one is better than the former one in terms of the dynamism.An ANN was adopted to estimate the motor speed and to provide a sensorless speed estimator system byevaluating for a wide range of operating conditions such as start ups, step changes in the reference speeds,unknown load torque with parameter variations. An IM spindle motor drive using synchronous PWM anddead time compensatory techniques with an ANFIS controller was proposed by Faa and Rong for advancedspindle motor applications by performing an real time experiment. Since the control characteristics and motorparameters for the high speed IM drive were time varying, they proposed an ANFIS scheme to control therotor speed. The plant here was identified by a fuzzy NN identifier to provide the sensitivity info of the drivesystem to the adaptive controller using a back propagation algo to train the network online.

In the previously mentioned works by the various authors, the achievements, the advantages and the dis-advantages were deeply discussed. The research direction in the research area was to minimize the transientresponse and to improve the dynamic characteristics. But, in all the above mentioned cases, there were oneor other drawbacks. One of the parameter in the works done by various authors, being the settling time of theresponses and the proper selection of the rule base in the fuzzy control strategy, which was not yielding goodresults. The responses had taken a lot of time to reach the final steady state value.

In this paper, a sincere attempt is made to reduce the settling time of the responses and make the speedof response very fast by designing an efficient controller using ANFIS control strategy, which is the maincontributory work of this paper. The proper rule base was selected using an intelligently developed backpropagation algorithm. Here, we have formulated this complex control strategy for the speed control of IM,which has yielded excellent results compared to the others mentioned in the literature survey above. Theresults of our work have showed a very low transient response and a non-oscillating steady state response withexcellent stabilization and we have tried to improve the dynamic performance of the developed controller bydeveloping a sophisticated adaptive neuro fuzzy algorithm.

The structure of the research work (flow/organization of the paper) presented in this paper is organized inthe following sequence. A brief review of the literature survey of the related work was presented in the previous

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paragraphs in the introductory section. Section 2 presents the mathematical modelling of the induction motor.Review about the adaptive neuro fuzzy inference scheme used in the design of the controller is presented inSection 3. The design of the ANFIS controller is presented in Section 4. The Section 5 shows the developmentof the simulink model for the speed control of the induction motor. The simulation results and the discussionon it are presented in the Section 6. This is followed by the conclusions in the concluding section, the appendixand the author biographies.

2 Modelling of the induction motor

In this section, we present the mathematical model of the induction motor. In the control of any powerelectronics drive system (say a motor); to start with, a mathematical model of the plant is required. Thismathematical model is required further to design any type of controller to control the process of the plant.The mathematical model can be obtained by various methods, viz., from first principles, system identificationmethods, etc. This mathematical model may be a linear/non-linear differential equation or a transfer function(in s or z-domain) or in state space form. The induction motor model is established using a rotating (d, q)field reference (without saturation) concept[16] by using the power circuit of the 3− φ induction motor, whichis shown in the Fig. 1. The specs of the IM are given in the appendix.

2. Modelling of the Induction Motor In this section, we present the mathematical model of the induction motor. In the control of any power electronics drive system (say a motor); to start with, a mathematical model of the plant is required. This mathematical model is required further to design any type of controller to control the process of the plant. The mathematical model can be obtained by various methods, viz., from first principles, system identification methods, etc. This mathematical model may be a linear / non-linear differential equation or a transfer function (in s or z-domain) or in state space form. The induction motor model is established using a rotating (d, q) field reference (without saturation) concept [11] by using the power circuit of the 3-

induction motor, which is shown in the Fig. 1. The specs of the IM are given in the appendix. φ

Fig. 1 : Power circuit connection diagram for the IM

An induction motor model is further used to predict the voltage required to drive the flux and torque to the demanded values. This calculated voltage is then synthesized using the space vector modulation. The stator & rotor voltage equations are given by [11]

sd s sd sd d sdV R idt qλ ω λ= + − , (1)

sddsqsqssq λωλdtdiRV ++= , (2)

rqdArdrdrrd λωλdtdiRV −+= , (3)

rddArqrqrrq λωλdtdiRV ++= , (4)

where Vsd and Vsq, Vrd and Vrq are the direct axes & quadrature axes stator and rotor voltages [11]. The squirrel-cage induction motor considered for the simulation study in this paper and has the d and q-axis components of the rotor voltage zero. The flux linkages to the currents are related by the Eq. (5) as

0 00 0

;0

0 0

sd sd s m

sq sq

0s m

rd rd m r

rq rq m r

i L Li L L

M Mi L Li L L

λλλλ

⎡ ⎤ ⎡ ⎤ ⎡ ⎤⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥ ⎢ ⎥= =⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥ ⎣ ⎦⎣ ⎦ ⎣ ⎦

. (5)

The electrical part of an induction motor can thus be described by a fourth-order state mathematical model which is given in Eq. (6), by combining equations (1) - (5) as [11]

⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜

⎝

⎛

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

+

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

×−

=

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

rq

rd

sq

sd

rm

rm

mr

ms

rq

rd

sq

sd

srm

rq

rd

sq

sd

VVVV

LLLL

LLLL

iiii

ALLL

iiii

0000

0000

12 , (6)

5

Fig. 1. Power circuit connection diagram for the IM

An induction motor model is further used to predict the voltage required to drive the flux and torqueto the demanded values. This calculated voltage is then synthesized using the space vector modulation. Thestator and rotor voltage equations are given by [16].

Vsd = Rsisd +dλsd

dt− ωdλsq, (1)

Vsq = Rsisq +dλsq

dt+ ωdλsd, (2)

Vrd = Rrird +dλrd

dt− ωdAλrq, (3)

Vrq = Rrirq +dλrq

dt+ ωdAλrd, (4)

where Vsd and Vsq, Vrd and Vrq are the direct axes and quadrature axes stator and rotor voltages[16].The squirrel-cage induction motor considered for the simulation study in this paper and has the d and

q-axis components of the rotor voltage zero. The flux linkages to the currents are related by the Eq. (5) asλsd

λsq

λrd

λrq

= M

isdisqird

irq

; M =

Ls 0 Lm 00 Ls 0 Lm

Lm 0 Lr 00 Lm 0 Lr

. (5)

The electrical part of an induction motor can thus be described by a fourth-order state mathematicalmodel which is given in Eq. (6), by combining Eqs (1) ∼ (5) as [16].


40 A. Kusagur1 & S. Kodad & B. Ram: Modelling & Simulation of an ANFIS controller for an AC driveisdisqird

irq

=1

L2m − LrLs

×

A

isdisqird

irq

+

Ls 0 Lm 00 Ls 0 Lm

Lm 0 Lr 00 Lm 0 Lr

Vsd

Vsq

Vrd

Vrq

, (6)

where, A is given byLrRs ωdAL2

m − ωsLrLs −LmRr −LrLm(ωs − ωdA)−(ωdAL2

m − ωsLrLs) LrRs LrLm(ωs − ωdA) −LmRr

−LmRs LsLm(ωs − ωdA) LsRr ωsL2m − ωdALrLs

LsLm(ωs − ωdA) −LmRs −(ωsL2m − ωdALrLs) LsRr

. (7)

By superposition, i.e., adding the torques acting on the d-axis and the q-axis of the rotor windings, theinstantaneous torque produced in the electromechanical interaction is given by

Tem =32

(P

2

)(λrqird − λrdirq). (8)

The electromagnetic torque expressed in terms of inductances is given by

Tem =32

(P

2

)Lm(isqird − isdirq). (9)

The mechanical part of the motor is modeled by the equation[16].

dωMech

dt=

Tem − TL

Jeq=

32

(P2

)Lm(isqird − isdirq)− TL

Jeq, (10)

where

Jeq = Equivalent MI, ωdA = ωslip = ωs − ωm, ωm =P

2ωmech,

ωd = ωs, Ls = Lsl + Lm, Lr = Lrl + Lm.

3 Review of adaptive neuro fuzzy inference scheme

In this section, a brief review of the ANFIS concepts to control various system parameters of the plant ispresented.

The concept of neural networks started in the early-1900’s as an effort to describe how the human mindperformed in the olden days. As years rolled by, these neural networks started playing a very important role inthe various engineering applications. Neural networks have been applied successfully to speech recognition,image analysis and adaptive control, in order to construct software agents or autonomous robots and in thecontrol of machines. ANNs are a family of intelligent algorithms which can be used for time series prediction,classification, and control and identification purposes. Neural networks have an ability to train with variousparameter of induction motor.

As a non-linear function, they can be used for identifying the extremely nonlinear system parameterswith high accuracy. Recently, the use of neural networks, to identify and control nonlinear dynamic systemshas been proposed because they can approximate a wide range of non-linear functions to any desired degreeof accuracy. Moreover, they have the advantages of extremely fast parallel computation and fault tolerancecharacteristics. Also there have been some investigations into the application of NNs to power electronics andac drives, including speed estimation. This technique gives a fairly good estimate of the speed and is robust toparameter variation. However, the neural network speed estimator should be trained sufficiently with variouspatterns to get good performance[14].

Fuzzy logic is one of the successful applications in the control engineering field which can be used tocontrol various parameters of the real time systems. This logic combined with neural networks yields very



significant results. Neural networks can learn from data. However, understanding the knowledge learned byneural networks has been difficult. To be more specific, it is usually difficult to develop an insight aboutthe meaning associated with each neuron and each weight. In contrast, fuzzy rule based models are easy tobe understood because it uses linguistic terms and the structure of IF-THEN rules. Unlike neural networks,however, fuzzy logic by itself can not learn. The learning and identification of fuzzy logic systems need toadopt techniques from other areas, such as statistics, system identification. Since neural networks can learn,it is natural to merge these two techniques. This merged technique of the learning power of the NNs withthe knowledge representation of FL has created a new hybrid technique, called as the term ’neuro fuzzynetworks’[14].

Since ANFIS design starts with a pre-structured system, DOF for learning is limited, i.e., the MF ofinput and output variables contain more information that NN has to drive from sampled data sets. Knowledgeregarding the systems under design can be used right from the start. Part of the system can be excludedfrom the training. Hence, this ANFIS process is more efficient. The rules are in the linguistic forms and sointermediate results can be analyzed and interpreted easily. The modification of rules is possible during thetraining and optimization can be done manually. Further the ANFIS strategy supports the TS based systems.To start the ANFIS learning; first, a training data set that contains the desired input/output data pairs of targetsystems to be modeled is to be required. The design parameters required for any ANFIS controller are viz.,Number of data pairs, Training data set and checking data sets, Fuzzy inference systems for training, Numberof epochs to be chosen to start the training, Learning results to be verified after mentioning the step size[1].

In this context, the general ANFIS control structure algorithm for the control of any plant is presentedhere as follows[12]. This structure contains the same components as the FIS, expect for the NN block. Thestructure of the network is composed of a set of units (and connections) arranged into five connected networklayers, viz., l1 to l5.Layer 1: This layer consists of input variables (membership functions), viz., input 1 and input 2. Here, tri-angular or bell shaped MF can be used. This layer just supplies the input values xi to the next layer, wherei = 1 to n.Layer 2: This layer (membership layer) checks for the weights of each MFs. It receives the input values xi

from the 1st layer and act as MFs to represent the fuzzy sets of the respective input variables. Further, it com-putes the membership values which specify the degree to which the input value xi belongs to the fuzzy set,which acts as the inputs to the next layer.Layer 3: This layer is called as the rule layer. Each node (each neuron) in this layer performs the pre-conditionmatching of the fuzzy rules, i.e., they compute the activation level of each rule, the number of layers beingequal to the number of fuzzy rules. Each node of these layers calculates the weights which are normalized.Layer 4: This layer is called as the defuzzification layer and provides the output values y resulting from theinference of rules. Connections between the layers l3 and l4 are weighted by the fuzzy singletons that representanother set of parameters for the neuro fuzzy network.Layer 5: This layer is called as the output layer which sums up all the inputs coming from the layer 4 andtransforms the fuzzy classification results into a crisp (binary).

The ANFIS structure is tuned automatically by least-square-estimation and the back propagation algo-rithm. The algorithm shown above is used in the next section to develop the ANFIS controller to control thevarious parameters of the induction motor. Because of its flexibility, the ANFIS strategy can be used for awide range of control applications.

4 Controller design

A controller is a device which controls each and every operation in the system making decisions. From thecontrol system point of view, it is bringing stability to the system when there is a disturbance, thus safeguardingthe equipment from further damages. It may be hardware based controller or a software based controller or acombination of both. In this section, the development of the control strategy for control of various parametersof the induction machine such as the speed, flux, torque, and voltage, current is presented using the conceptsof ANFIS control scheme, the block diagram of which is shown in the Fig. 2. To start with, we design the



The ANFIS structure is tuned automatically by least-square-estimation & the back propagation algorithm. The algorithm shown above is used in the next section to develop the ANFIS controller to control the various parameters of the induction motor. Because of its flexibility, the ANFIS strategy can be used for a wide range of control applications.

4. Controller design A controller is a device which controls each & every operation in the system making decisions. From the control system point of view, it is bringing stability to the system when there is a disturbance, thus safeguarding the equipment from further damages. It may be hardware based controller or a software based controller or a combination of both. In this section, the development of the control strategy for control of various parameters of the induction machine such as the speed, flux, torque, and voltage, current is presented using the concepts of ANFIS control scheme, the block diagram of which is shown in the Fig. 2.

Fuzzification De-fuzzification

Con

trolle

d o

utpu

t

Reference

(set value)

IM(Plant)

A N F I Scontroller

Cris

pin

put

Crispoutput

Rule base

Data base

KNOWLEDGE BASE

ArtificialNeural

Network

Rule selectionBack-propagation algo

Fig. 2 : Block diagram of the ANFIS control scheme for the speed control of the IM

To start with, we design the controller using the ANFIS scheme. Fuzzy logic is one of the successful applications of fuzzy set in which the variables are linguistic rather than the numeric variables. Linguistic variables, defined as variables whose values are sentences in a natural language (such as large or small), may be represented by the fuzzy sets. Fuzzy set is an extension of a ‘crisp’ set where an element can only belong to a set (full membership) or not belong at all (no membership). Fuzzy sets allow partial membership, which means that an element may partially belong to more than one set. A fuzzy set A of a universe of discourse X is represented by a collection of ordered pairs of generic element and its membership function μXx∈ : X → [ 0 1], which associates a number μA(x) : X → [ 0 1], to each element x of X. A fuzzy logic controller is based on a set of control rules called as the fuzzy rules among the linguistic variables. These rules are expressed in the form of conditional statements. Our basic structure of the developed ANFIS coordination controller to control the speed of the IM consists of 4 important parts, viz., fuzzification, knowledge base, neural network and the de-fuzzification blocks, which are explained in brief in further paragraphs The inputs to the ANFIS controller, i.e., the error & the change in error is modeled using the Eq. (11) as

,)1()()(

,)(−−=Δ

−=

kekekeke rref ωω

(11)

where refω is the reference speed, rω is the actual rotor speed, is the e(k) error and Δe(k) is the change in error. The fuzzification unit converts the crisp data into linguistic variables, which is given as inputs to the rule based block. The set of 49 rules are written on the basis of previous knowledge / experiences in the rule based block.

8

Fig. 2. Power circuit connection diagram for the IM

controller using the ANFIS scheme. Fuzzy logic is one of the successful applications of fuzzy set in whichthe variables are linguistic rather than the numeric variables. Linguistic variables, defined as variables whosevalues are sentences in a natural language (such as large or small), may be represented by the fuzzy sets. Fuzzyset is an extension of a ’crisp’ set where an element can only belong to a set (full membership) or not belong atall (no membership). Fuzzy sets allow partial membership, which means that an element may partially belongto more than one set.

A fuzzy set A of a universe of discourse X is represented by a collection of ordered pairs of genericelement x ∈ X and its membership function µ : X → [01], which associates a number µA(x) : X → [0, 1], toeach element x of X . A fuzzy logic controller is based on a set of control rules called as the fuzzy rules amongthe linguistic variables. These rules are expressed in the form of conditional statements. Our basic structure ofthe developed ANFIS coordination controller to control the speed of the IM consists of 4 important parts, viz.,fuzzification, knowledge base, neural network and the de-fuzzification blocks, which are explained in brief infurther paragraphs

The inputs to the ANFIS controller, i.e., the error and the change in error is modeled using the Eq. (11)as

e(k) = ωref − ωr, (11)

∆e(k) = e(k)− e(k − 1), (12)

where ωref is the reference speed, ωr is the actual rotor speed, is the e(k) error and ∆e(k) is the change inerror.

The fuzzification unit converts the crisp data into linguistic variables, which is given as inputs to the rulebased block. The set of 49 rules are written on the basis of previous knowledge/experiences in the rule basedblock.

The rule base block is connected to the neural network block. Back propagation algorithm is used to trainthe neural network to select the proper set of rule base. For developing the control signal, the training is a veryimportant step in the selection of the proper rule base. Once the proper rules are selected and fired, the controlsignal required to obtain the optimal outputs is generated. The output of the NN unit is given as input to thede-fuzzification unit and the linguistic variables are converted back into the numeric form of data in the crispform.

In the fuzzification process, i.e., in the first stage, the crisp variables, the speed error and the change inerror are converted into fuzzy variables or the linguistics variables. The fuzzification maps the 2 input variablesto linguistic labels of the fuzzy sets. The fuzzy coordinated controller uses the linguistic labels. Each fuzzylabel has an associated membership function. The membership function of triangular type is used in our work.The inputs are fuzzified using the fuzzy sets and are given as input to ANFIS controller. The rule base forselection of proper rules using the back propagation algorithm is written as shown in the Tab. 1.

The developed fuzzy rules (7× 7) is included in the ANFIS controller and is not shown here for the sakeof convenience. The control decisions are made based on the fuzzified variables in the Tab. 1. The inferenceinvolves a set of rules for determining the output decisions. As there are 2 input variables and 7 fuzzifiedvariables, the controller has a set of 49 rules for the ANFIS controller. Out of these 49 rules, the proper rulesare selected by the training of the neural network with the help of back propagation algorithm and theseselected rules are fired. Further, it has to be converted into numerical output, i.e., they have to be de-fuzzified.



Table 1. Rule base for controlling the speed

E NB NM NS ZE PS PM PBNB NB NB NB NB NM NS ZENM NB NB NM NM NS ZE PSNS NB NM NS NS ZE PS PMZE NB NM NS ZE PS PM PBPS NM NS ZE PS PS PM PBPM NS ZE PS PM PM PB PBPB ZE PS PM PB PB PB PB

This process is what is called as de-fuzzification, which is the process of producing a quantifiable result infuzzy logic.

The defuzzifcation transforms fuzzy set information into numeric data information. There are so manymethods to perform the defuzzifcation, viz., centre of gravity method, centre of singleton method, maximummethods, the marginal properties of the centroid methods and so on. In our work, we use the centre of gravitymethod. The output of the defuzzification unit will generate the control commands which in turn is given asinput (called as the crisp input) to the plant through the inverter. If there is any deviation in the controlledoutput (crisp output), this is fed back and compared with the set value and the error signal is generated whichis given as input to the ANFIS controller which in turn brings back the output to the normal value, thusmaintaining stability in the system. Finally, the controlled output signal, i.e., y is given by Eq. (13) as

y =

R∑i=1

µiαi1x1 + Λ +

R∑i=1

µiαiqxq

R∑i=1

µi

, (13)

this controlled output y is nothing but the final output of the controller and is the weighted average of theproper rule based outputs, which are selected by the back propagation algorithm.

5 Development of simulink model

Simulink model for the control of various parameters of the induction motor was developed in Matlab7. This simulink model with the ANFIS controller was developed using the various toolboxes available inthe simulink library such as the power system, power electronics, control system, signal processing toolboxesand from its basic functions. The entire system modeled in Simulink is a closed loop feedback control systemconsisting of the plants, controllers, samplers, comparators, feedback systems, constants, buses, the mux,de-mux, summers, adders, gain blocks, multipliers, constant blocks, CT&DT blocks, ANFIS editor blocks,clocks, sub-systems, integrators, state-space models, the output sinks (scopes), the input sources, work-spaceblocks, etc. The developed simulink model for the control of various parameters of the SCIM is shown in theFig. 3. The specifications of the SCIM used for simulation purposes are given in the appendix.

6 Simulation results & discussions

Simulink model with the neuro-fuzzy controller for the speed control of IM was developed in Matlab. Inorder to start the simulations, the 49 fuzzy rule set has to be invoked first from the command window in theMatlab. Initially, the fuzzy file where the rules are written with the incorporation of the T-S control strategy isopened in the Matlab command window, after which the fuzzy editor (FIS) dialogue box opens in the fuzzyeditor window. The .fis file (sugenosevenrules2.fis) is then imported using the command window from thesource and then opened in the fuzzy editor dialog box using the file open command. Once the file is opened,the TS-fuzzy rules file gets activated. Further, the data is exported to the workspace and the simulations arerun for a specific amount of time. The fuzzy membership function editor is then obtained using the view



SIM

ULIN

K M

OD

EL FO

R C

ON

TRO

L OF S

PE

ED

OF IN

DU

CTIO

N M

OTO

R U

SIN

G A

NFIS

STR

ATE

GY

1/100

wref 3

100

wref 2

1800

wref 1

voltage_ab

torque

stator current

speed

f(u)

sliprt angle

Continuous

irdq

ir abc

Te*

Phir Iq*

iqs* Calculation

iq

Phir*

Id*

id* Calculation

idflux

Vdc

+−v

Vab

z 1

z 1

z 1

z 1irabc_anfis

iq_anfis

To Workspace8

id_anfis

To Workspace7

slip_anfis

To Workspace6

time

To Workspace5

torque_anfis

speed_anfis

y

load_anfis

stator_current_anfis

voltage_anfis

flux_anfis

To Workspace12

rtang_anfis

irdq_anfis

x2 x1

IqPhir

wm

Teta

Teta Calculation

In1O

ut1

Inut1 Inut1

Slip

Product1

Product

0.96

Phir*

signal1

signal2

2

Load_torque

Load

A

B

C

Tm

m

Induction Motor

50 HP

/ 460 V

+−pulses

ABC

IGB

T Inverter

IdP

hirFluxC

alc.

Flux Calculation

m ir_abc

ir_qd

is_abc

wmTe

thetam

Dem

ux

Id*

Iq*

Teta Iabc *

DQ

−AB

C

Iabc*

Iabc

Pulses

Current R

egulator

Clock

Teta

Iabc

IdIq

AB

C−D

Q

A N

F I SC

ontroller

Vab (V

)

Fig. 3 : The developed simulink model for the speed control of IM’s using neuro-fuzzy scheme (ANFIS)

10

Fig. 3. The developed simulink model for the speed control of IM’s using neuro-fuzzy scheme (ANFIS)

membership command from the menu bar. The written TS-fuzzy rules also can be viewed from the rule viewcommand. Further, the rule viewer for the 2 inputs and 1 output can also be observed.

Now, after performing all the preliminary operations, the simulations are run for a period of 3 seconds inMatlab 7 with a reference speed of 100 rads/sec

i.e.100× 60

2π= 955 rpm,

and with a load torque of 2 N-m. Once, the simulation is run, the various parameters such as speed, flux,torque, currents, slip, voltage, etc. gets stored in the workspace. After running the Takagi-Sugeno model, we



get the error (x1), change in error (x2) and an intermediate parameter (y). These 3 parameters, viz., x1, x2

and y are stored in a variable in the command window. The ’anfis’ editor is opened in the command window.These variables which are in the form of data in the workspace are loaded into the ’anfis’ editor. The .fis file isgenerated next in the ’anfis’ editor by loading the data from the workspace. Once the .fis file is generated, the’anfis’ has to be trained properly by selecting a proper algorithm with suitable number of epochs. In our work,we have used the back-propagation algorithm with a suitable number of epochs being used for training therules. This is done by selecting these 2 items in the ’train window’ of the ’anfis’ editor and training the neuralnetwork for proper selection of the rule base. The trained data is further exported to the workspace using thefile-export command. Also, the surface plot and the contour plots for the error speed and change in error withthe output can be observed.

number of epochs. In our work, we have used the back-propagation algorithm with a suitable number of epochs being used for training the rules. This is done by selecting these 2 items in the ‘train window’ of the ‘anfis’ editor & training the neural network for proper selection of the rule base. The trained data is further exported to the workspace using the file-export command. Also, the surface plot & the contour plots for the error speed & change in error with the output can be observed.

Fig. 4 : The developed adaptive neuro fuzzy controller architecture

The developed ANFIS model structure with 2 input neurons & 1 output neuron along with 4 hidden layers (input membership function, rule base, membership function, and aggregated output) can be observed from the view model icon in the editor tool box. The diagrammatic view of the developed adaptive neuro controller is shown in the Fig. 4. The training of the neural network by using the fuzzy rule base for the selection of the proper & optimal rule is taken care of by the designed ANFIS controller. Note that 7 by 7 rules are used in the hidden layers. The neuron 1 is connected to 7 fuzzy rules & the neuron 2 is also connected to the 7 fuzzy rules. The hidden layers contains 49-49 neurons to deal the problem (for selection of the proper rule base, because the rule base are written randomly in fuzzy, the neural network selects the right optimal rule base to fire). The 2 input neurons, viz., the error, change in error is given as input to the 1st hidden layer of the ANN. This 1st hidden layer deals with various input membership functions. In the 2nd & 3rd hidden layer, the set of 49 fuzzy rules are properly identified by training & the set of optimal rules are selected. These set of optimum rules are available at the 4th hidden layer. Out of the 49 rules, the optimal rules are fired here & the de-fuzzified output is obtained as the output neuron. The de-fuzzified output is further used to generate the firing pulse to be applied to the inverter bridge, which is further used to control the speed of the IM drive. After the simulation is run, the performance characteristics are observed on the respective scopes. The response curves of flux, load, torque, terminal voltage, speed, rotor angle, stator currents, slip, id, iq, rotor currents (3φ abc & d-q) v/s time, slip vs. speed for a reference speed of 100 rads / sec (955 rpm) & with a load torque of 2 N-m are observed & are shown in the Figs. 5 - 15 respectively. From the simulation results shown in the Figs. 5 to 15, it is observed that the stator current does not exhibit any overshoots nor undershoots. The response of the flux, slip, torque, terminal voltage, speed, currents, etc. takes lesser time to settle & reach the desired value compared to the results presented in [1], [2], [3].

12

Fig. 4. The developed adaptive neuro fuzzy controller architecture

The developed ANFIS model structure with 2 input neurons and 1 output neuron along with 4 hiddenlayers (input membership function, rule base, membership function, and aggregated output) can be observedfrom the view model icon in the editor tool box. The diagrammatic view of the developed adaptive neurocontroller is shown in the Fig. 4. The training of the neural network by using the fuzzy rule base for theselection of the proper and optimal rule is taken care of by the designed ANFIS controller. Note that 7 by7 rules are used in the hidden layers. The neuron 1 is connected to 7 fuzzy rules and the neuron 2 is alsoconnected to the 7 fuzzy rules. The hidden layers contains 49-49 neurons to deal the problem (for selectionof the proper rule base, because the rule base are written randomly in fuzzy, the neural network selects theright optimal rule base to fire). The 2 input neurons, viz., the error, change in error is given as input to the 1sthidden layer of the ANN. This 1st hidden layer deals with various input membership functions. In the 2nd and3rd hidden layer, the set of 49 fuzzy rules are properly identified by training and the set of optimal rules areselected. These set of optimum rules are available at the 4th hidden layer. Out of the 49 rules, the optimal rulesare fired here and the de-fuzzified output is obtained as the output neuron. The de-fuzzified output is furtherused to generate the firing pulse to be applied to the inverter bridge, which is further used to control the speedof the IM drive.

After the simulation is run, the performance characteristics are observed on the respective scopes. Theresponse curves of flux, load, torque, terminal voltage, speed, rotor angle, stator currents, slip, id, iq, rotorcurrents (3φabc&d − q) v/s time, slip VS speed for a reference speed of 100 rads/sec (955 rpm) and witha load torque of 2 N-m are observed and are shown in the Figs. 5 ∼ 15 respectively. From the simulationresults shown in the Figs. 5 ∼ 15, it is observed that the stator current does not exhibit any overshoots norundershoots. The response of the flux, slip, torque, terminal voltage, speed, currents, etc. takes lesser timeto settle and reach the desired value compared to the results presented in [7–9]. It was observed from thesimulation results that by using the neuro-fuzzy (ANFIS) control, for the set speed of 100 r/s and for the 49rules, the speed reaches its desired set value at 0.45 seconds. This shows the effectiveness of the designedneuro-fuzzy controller and the designed neuro-fuzzy controller tries to speed up the performance of the drive,thus showing faster dynamism. It is also observed that with the designed neuro-fuzzy controller, the responsecharacteristics curves take less time to settle and reach the final steady state value compared to that in [7–9].The motor speed increases like a linear curve upto the set speed of 955 rpm (100 r/s) in 0.45 secs as shown in



0 0.5 1 1.5 2 2.5 3-0.2

0

0.2

0.4

0.6

0.8

1

Time (s)

Flux

(wb)

0 0.5 1 1.5 2 2.5 3-200

-100

0

100

200

300

Time (s)

Tor

que

(N-m

)

Fig. 5 : Plot of flux vs. time Fig. 6 : Plot of torque vs. time

It was observed from the simulation results that by using the neuro-fuzzy (ANFIS) control, for the set speed of 100 r / s & for the 49 rules, the speed reaches its desired set value at 0.45 seconds. This shows the effectiveness of the designed neuro-fuzzy controller & the designed neuro-fuzzy controller tries to speed up the performance of the drive, thus showing faster dynamism. It is also observed that with the designed neuro-fuzzy controller, the response characteristics curves take less time to settle & reach the final steady state value compared to that in [1], [2], [3]. The motor speed increases like a linear curve upto the set speed of 955 rpm (100 r / s) in 0.45 secs as shown in Fig. 15. Further, it can also be observed that using the ANFIS control, the system stabilizes in a very less time compared to the other methods because of the training process of the ANN involved & the proper selection of the rule base. From the variation of flux with time as shown in the Fig. 5, it can be observed that when the motor speed is increasing (during the transient period), more stator current is required to develop the requisite flux in the air gap. Hence, the flux also starts increasing during the transient period (0 to 0.4 sec) exponentially. Once, the motor attains the set rated speed, the flux required to develop the torque almost remains constant after ≥ 0.4 secs. Once, the flux in the air gap remains constant, the variation of the load torque and speed will not disturb the flux curve. Hence, the IM will be operating at a constant flux.

Torque characteristics for a set reference speed of 100 r/s (955 rpm) is shown in the Fig. 6. From this figure, we arrive at a conclusion that when the motor is operating at lower speeds, the slip is more. Hence, the machine requires more torque to attain the set speed. Once the machine reaches the set speed of 955 rpm the average torque of the machine becomes nearly zero after 0.45 s, which is justified from the simulation result in Fig. 6. The terminal voltage of the IM is shown in Figs. 7 (a) & (b) respectively.

0 0.5 1 1.5 2 2.5 3

-500

0

500

1000

Time (s)

Vol

tage

(V)

0.42 0.425 0.43 0.435 0.44 0.445 0.45

-1000

-500

0

500

Time (s)

Vol

tage

(V)

(a) Plot of voltage vs. time (normal) (b) Plot of voltage vs. time (zoomed) between

t = 0.42 s to 0.45 s Fig. 7 : Plot of voltage vs. time (normal & zoomed)

13

Fig. 5. Plot of flux VS time

0 0.5 1 1.5 2 2.5 3-0.2

0

0.2

0.4

0.6

0.8

1

Time (s)

Flux

(wb)

0 0.5 1 1.5 2 2.5 3-200

-100

0

100

200

300

Time (s)

Tor

que

(N-m

)




0 0.5 1 1.5 2 2.5 3

-500

0

500

1000

Time (s)

Vol

tage

(V)

0.42 0.425 0.43 0.435 0.44 0.445 0.45

-1000

-500

0

500

Time (s)

Vol

tage

(V)

(a) Plot of voltage vs. time (normal) (b) Plot of voltage vs. time (zoomed) between

t = 0.42 s to 0.45 s Fig. 7 : Plot of voltage vs. time (normal & zoomed)

13

Fig. 6. Plot of torque VS time

0 0.5 1 1.5 2 2.5 3-0.2

0

0.2

0.4

0.6

0.8

1

Time (s)

Flux

(wb)

0 0.5 1 1.5 2 2.5 3-200

-100

0

100

200

300

Time (s)

Tor

que

(N-m

)




0 0.5 1 1.5 2 2.5 3

-500

0

500

1000

Time (s)

Vol

tage

(V)

0.42 0.425 0.43 0.435 0.44 0.445 0.45

-1000

-500

0

500

Time (s)V

olta

ge (V

)

(a) Plot of voltage vs. time (normal) (b) Plot of voltage vs. time (zoomed) between t = 0.42 s to 0.45 s

Fig. 7 : Plot of voltage vs. time (normal & zoomed)

13

Fig. 7. Plot of voltage VS time (normal & zoomed)

Fig. 15. Further, it can also be observed that using the ANFIS control, the system stabilizes in a very less timecompared to the other methods because of the training process of the ANN involved and the proper selectionof the rule base.

From the variation of flux with time as shown in the Fig. 5, it can be observed that when the motor speedis increasing (during the transient period), more stator current is required to develop the requisite flux in theair gap. Hence, the flux also starts increasing during the transient period (0 to 0.4 sec) exponentially. Once, themotor attains the set rated speed, the flux required to develop the torque almost remains constant after ≥ 0.4secs. Once, the flux in the air gap remains constant, the variation of the load torque and speed will not disturbthe flux curve. Hence, the IM will be operating at a constant flux.

Torque characteristics for a set reference speed of 100 r/s (955 rpm) is shown in the Fig. 6. From thisfigure, we arrive at a conclusion that when the motor is operating at lower speeds, the slip is more. Hence, themachine requires more torque to attain the set speed. Once the machine reaches the set speed of 955 rpm theaverage torque of the machine becomes nearly zero after 0.45 s, which is justified from the simulation resultin Fig. 6. The terminal voltage of the IM is shown in Figs. 7 (a) (b) respectively.

The variation of the 3φ stator currents (is) with time is shown in the Fig. 8. It can be clearly observedfrom this figure, that at lower speeds, the slip is more, the flux required to develop the suitable torque is alsomore. Also, the torque required to reach the set speed is also more. Hence, the magnitude of the stator currentswill also be more during the transient periods (starting periods) of the induction motor. When the speed isreaching the set value from zero, the 3φ stator currents decreases exponentially. Once, it attains the set speedat 0.45 secs, it requires a nominal stator current to drive the IM system.

The Fig. 9 shows the variation of slip VS time characteristics for a speed of 100 r/s (955 rpm). From thissimulation result, we infer that the IM attains the set reference speed of 955 rpm in 0.45 secs using the ANFIS(neuro-fuzzy) controller. At that instant, the slip being

Ns −N

Ns=

1800− 9551800

= 0.46,

can be verified from the result shown. Note that the slip decreases from 1.0 to 0.46 linearly in a time span ofjust 0.45 secs.



The variation of the φ3 stator currents (is) with time is shown in the Fig. 8. It can be clearly observed from this figure, that at lower speeds, the slip is more, the flux required to develop the suitable torque is also more. Also, the torque required to reach the set speed is also more. Hence, the magnitude of the stator currents will also be more during the transient periods (starting periods) of the induction motor. When the speed is reaching the set value from zero, the φ3 stator currents decreases exponentially. Once, it attains the set speed at 0.45 secs, it requires a nominal stator current to drive the IM system.

0 0.5 1 1.5 2 2.5 3-400

-200

0

200

400

Time (s)

Stat

or c

urre

nt (A

)

0 0.5 1 1.5 2 2.5 30.4

0.5

0.6

0.7

0.8

0.9

1

Time (s)

Slip

Fig. 8 : Plot of φ3 stator current vs. time Fig. 9 : Plot of slip vs. time

The Fig. 9 shows the variation of slip vs. time characteristics for a speed of 100 r/s (955 rpm). From this simulation result, we infer that the IM attains the set reference speed of 955 rpm in 0.45 secs using the ANFIS (neuro-fuzzy) controller. At that instant, the slip being

46.01800

9551800N

NN

s

s =−

=−

,

can be verified from the result shown. Note that the slip decreases from 1.0 to 0.46 linearly in a time span of just 0.45 secs.

The slip-speed characteristics is shown in the Fig. 10. It can be noted that when the speed is varied from 0 to the rated speed, the slip decreases, i.e., the slip is inversely proportional to the speed, which is the property of the IM. When the speed is zero, the slip is 100 %, while the IM is operating at near the rated speed (180 r/s), the slip is very very low. The plots of the direct axes (id) & quadrature axes currents (iq) versus time is shown in the Figs. 11 & 12 respectively. From these figures, it can be inferred that the machine reaches the set reference speed of 955 rpm in a time interval of 0.45 secs.

0 200 400 600 800 10000.4

0.5

0.6

0.7

0.8

0.9

1

Slip

Speed 0 0.5 1 1.5 2 2.5 3-50

0

50

100

150

200

250

300

Time (s)

i d

Fig. 10 : Plot of slip vs. speed Fig. 11 : Plot of id vs. time

14

Fig. 8. Plot of 3φ stator current VS time


0 0.5 1 1.5 2 2.5 3-400

-200

0

200

400

Time (s)

Stat

or c

urre

nt (A

)

0 0.5 1 1.5 2 2.5 30.4

0.5

0.6

0.7

0.8

0.9

1

Time (s)

Slip



46.01800

9551800N

NN

s

s =−

=−

,



0 200 400 600 800 10000.4

0.5

0.6

0.7

0.8

0.9

1

Slip

Speed 0 0.5 1 1.5 2 2.5 3-50

0

50

100

150

200

250

300

Time (s)

i d


14

Fig. 9. Plot of slip VS time


0 0.5 1 1.5 2 2.5 3-400

-200

0

200

400

Time (s)

Stat

or c

urre

nt (A

)

0 0.5 1 1.5 2 2.5 30.4

0.5

0.6

0.7

0.8

0.9

1

Time (s)

Slip



46.01800

9551800N

NN

s

s =−

=−

,



0 200 400 600 800 10000.4

0.5

0.6

0.7

0.8

0.9

1

Slip

Speed 0 0.5 1 1.5 2 2.5 3-50

0

50

100

150

200

250

300

Time (s)i d


14

Fig. 10. Plot of slip VS speed


0 0.5 1 1.5 2 2.5 3-400

-200

0

200

400

Time (s)

Stat

or c

urre

nt (A

)

0 0.5 1 1.5 2 2.5 30.4

0.5

0.6

0.7

0.8

0.9

1

Time (s)

Slip



46.01800

9551800N

NN

s

s =−

=−

,



0 200 400 600 800 10000.4

0.5

0.6

0.7

0.8

0.9

1

Slip

Speed 0 0.5 1 1.5 2 2.5 3-50

0

50

100

150

200

250

300

Time (s)i d


14

Fig. 11. Plot of id VS time

The slip-speed characteristics is shown in the Fig. 10. It can be noted that when the speed is varied from 0to the rated speed, the slip decreases, i.e., the slip is inversely proportional to the speed, which is the propertyof the IM. When the speed is zero, the slip is 100%, while the IM is operating at near the rated speed (180r/s), the slip is very very low. The plots of the direct axes (id) and quadrature axes currents (iq) versus time isshown in the Figs. 11 and 13 respectively. From these figures, it can be inferred that the machine reaches theset reference speed of 955 rpm in a time interval of 0.45 secs.

The variation of the 3φ rotor currents (ir-abc) with time is shown in the Fig. 13. It can be inferred that atlower speeds, the slip is more, the flux required to develop the suitable torque is also more. Also, the torquerequired to reach the set speed is also more. Hence, the magnitude of the rotor currents will also be moreduring the transient periods (starting periods) of the induction motor. When the speed is reaching the set valuefrom zero, the 3φ rotor currents decreases exponentially upto 0.45 secs, thereafter it is maintained constant.

0 0.5 1 1.5 2 2.5 3-400

-300

-200

-100

0

Time (s)

i q

0 0.5 1 1.5 2 2.5 3-400

-200

0

200

400

Time (s)

Rot

or c

urre

nt (A

BC

)

Fig. 12 : Plot of iq vs. time Fig. 13 : Plot of rotor current ir abc vs. time

The variation of the φ3 rotor currents (ir - abc) with time is shown in the Fig. 13. It can be inferred that at lower speeds, the slip is more, the flux required to develop the suitable torque is also more. Also, the torque required to reach the set speed is also more. Hence, the magnitude of the rotor currents will also be more during the transient periods (starting periods) of the induction motor. When the speed is reaching the set value from zero, the φ3 rotor currents decreases exponentially upto 0.45 secs, thereafter it is maintained constant.

0 0.5 1 1.5 2 2.5 3-400

-200

0

200

400

Time (s)

Rot

or c

urre

nt (d

-q)

0 0.5 1 1.5 2 2.5 30

200

400

600

800

1000

Time (s)

Spee

d (R

PM)

Fig. 14 : Plot of rotor current ir dq vs. time Fig. 15 : Plot of speed vs. time

Fig. 16 : Plot of speed vs. time

The φ3 rotor currents (ir - abc) is transformed to direct axes & quadrature axes currents using the d - q transformation techniques and the variation of the transformed currents with time is shown in the Fig. 14. Here, only two phases (d & q axes) of the currents can be observed in the characteristic curve. In this case, also, once the motor achieves the set speed at 0.45 secs, it requires a nominal current to drive the IM system. The comparison curves of the speed using 4 different types of controllers, viz., ANFIS, PI, Mamdani, TS is shown in the Fig. 16 [1], [2], [3].

15

Fig. 12. Plot of iq VS time

0 0.5 1 1.5 2 2.5 3-400

-300

-200

-100

0

Time (s)

i q

0 0.5 1 1.5 2 2.5 3-400

-200

0

200

400

Time (s)

Rot

or c

urre

nt (A

BC

)



0 0.5 1 1.5 2 2.5 3-400

-200

0

200

400

Time (s)

Rot

or c

urre

nt (d

-q)

0 0.5 1 1.5 2 2.5 30

200

400

600

800

1000

Time (s)

Spee

d (R

PM)




15

Fig. 13. Plot of rotor current ir abc VS time

The 3φ rotor currents (ir-abc) is transformed to direct axes and quadrature axes currents using the d− qtransformation techniques and the variation of the transformed currents with time is shown in the Fig. 14.Here, only two phases (d&q axes) of the currents can be observed in the characteristic curve. In this case, also,once the motor achieves the set speed at 0.45 secs, it requires a nominal current to drive the IM system. The



0 0.5 1 1.5 2 2.5 3-400

-300

-200

-100

0

Time (s)

i q

0 0.5 1 1.5 2 2.5 3-400

-200

0

200

400

Time (s)

Rot

or c

urre

nt (A

BC

)



0 0.5 1 1.5 2 2.5 3-400

-200

0

200

400

Time (s)

Rot

or c

urre

nt (d

-q)

0 0.5 1 1.5 2 2.5 30

200

400

600

800

1000

Time (s)

Spee

d (R

PM)




15

Fig. 14. Plot of rotor current irdq VS time

0 0.5 1 1.5 2 2.5 3-400

-300

-200

-100

0

Time (s)

i q

0 0.5 1 1.5 2 2.5 3-400

-200

0

200

400

Time (s)

Rot

or c

urre

nt (A

BC

)



0 0.5 1 1.5 2 2.5 3-400

-200

0

200

400

Time (s)

Rot

or c

urre

nt (d

-q)

0 0.5 1 1.5 2 2.5 30

200

400

600

800

1000

Time (s)

Spee

d (R

PM)




15

Fig. 15. Plot of speed VS time

Fig. 16. Plot of speed VS time

comparison curves of the speed using 4 different types of controllers, viz., ANFIS, PI, Mamdani, TS is shownin the Fig. 16[7–9].

7 Conclusions

A systematic method of achieving the speed control of an induction motor drive by means of adaptiveneuro fuzzy inference control strategy has been investigated in this research paper. Simulink model was de-veloped in Matlab 7 with the ANFIS controller put in closed loop with the plant. The control strategy wasdeveloped by writing a set of 49 adaptive fuzzy rules coupled with the back propagation algorithm. Simula-tions were run for a period of 3 secs and the characteristic curves of speed, torque, current, flux, slip, load, etc.VS time were observed on the corresponding scopes in the developed model. From the simulation results, itcan be observed that the characteristic curves of the IM take less time to stabilize and due to the incorporationof the ANFIS controller, it was observed that the motor reaches the rated speed very quickly compared to theother methods[7–9]. The main advantage of the developed ANFIS coordination scheme is to increase the dy-namic performance and to provide good stabilization. Also, the proposed ANFIS scheme is computationallyefficient, works well with linear techniques, optimization and adaptive techniques. This can also be combinedwith expert systems and rough sets for other applications. Another advantage of the ANFIS being, the task oftraining of membership functions is done in ANFIS, which is not taken care of in the fuzzy counterpart. Thedeveloped control strategy is not only simple, but also reliable and may be easy to implement in real time.

8 Appendix

Squirrel Cage Induction Motor (SCIM) specs: 50 HP, 1800 rpm, 460 V, 60 Hz., 3-Phase 2 pair of poles,Squirrel Cage type IM. Rs = 0.087Ω, Ls = 0.8 × 10−3H, Rr = 0.228Ω, Lr = 0.8mH, Lm = 34.7mH,J = 1.662kg·m2.



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modelling & simulation of an anfis controller for an ac … a. kusagur1 & s. kodad & b....

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