Fuzzy PID supervised online ANFIS based speedcontroller for brushless dc motor

K. Premkumar a,n, B.V. Manikandan b

a Department of Electrical and Electronics Engineering, Pandian Saraswathi Yadav Engineering College, Sivagangai-630561, Tamilnadu, Indiab Department of Electrical and Electronics Engineering, Mepco Schlenk Engineering College, Sivakasi-626005, Tamilnadu, India

a r t i c l e i n f o

Article history:Received 7 May 2014Received in revised form27 November 2014Accepted 16 January 2015Communicated by H.R. KarimiAvailable online 30 January 2015

Keywords:Brushless dc motorPID controllerAnti wind up PID controllerFuzzy PID controllerOffline ANFISOnline ANFIS

a b s t r a c t

In this paper, two different speed controllers i.e., fuzzy online gain tuned anti wind up ProportionalIntegral and Derivative (PID) controller and fuzzy PID supervised online ANFIS controller for the speedcontrol of brushless dc motor have been proposed. The control system parameters such as rise time,settling time, peak time, recovery time, peak overshoot and undershoot of speed response of thebrushless dc motor with the proposed controllers have been compared with already publishedcontrollers such as anti wind up PID controller, fuzzy PID controller, offline ANFIS controller, PIDsupervised online ANFIS controller and On-line Recursive least square—error back propagation algorithmbased ANFIS controller. In order to validate the effectiveness of the proposed controllers, the brushless dcmotor is operated under constant load condition, varying load conditions and varying set speedconditions. The simulation results under MATLAB environment have predicted better performance withfuzzy PID supervised online ANFIS controller under all operating conditions of the drive.

& 2015 Elsevier B.V. All rights reserved.

1. Introduction

Speed regulation is an important aspect in the field of brushlessdc motor drive for precise speed and position control applications.For the enhancement of brushless dc motor performance, differentcontrollers have been developed [1–4]. Proportional Integral (PI)based speed controller has been implemented for brushless dcmotor in [1] but, the controller has produced large settling time,rise time and more oscillations in the speed response. In [2], anoff-line least-squares approximation method has been developedfor identifying BLDC motor parameters and it has resulted inunacceptable level of tolerance which cannot be acceptable forprecise speed control applications. In [3], optimization of PIcoefficients of speed controller for a PMBLDC motor using GeneticAlgorithm (GA) has been developed. The speed response has largerovershoot in transient period and more fluctuation during thesteady state period. A brushless dc motor drive system incorpo-rated with proportional integral speed control loop has beenimplemented in [4], but it has resulted in larger steady state error.

An adaptive PID neural network controller has been developedand Particle Swarm Optimization (PSO) algorithm was used forinitializing the weight of the neural network and improvedgradient descent algorithm was used for adjusting the parameter

of the PID neural network [5]. The disadvantage of this method isthat PSO algorithm takes long time for initializing the weight ofthe PID neural network. A comparative analysis of PSO and BFOmethods for the tuning of PID controller for the speed control of aBLDC motor has been proposed in [6]. But, during sudden loaddisturbances, speed response has larger undershoot and largersteady state error. A comparative analysis of PI, Anti wind up PIand fuzzy Logic controllers have been developed for brushless dcmotor [7]. During load disturbance, the speed response has largerundershoot and steady state error with anti wind up PI control.

Adaptive fuzzy PID controller using multi objective PSO rein-forcement evolutionary algorithm has been developed for auto-mobile suspension system. The adaptive mechanism was formedby using parallel combination of PID controller and fuzzy logiccontroller. The controller effectively controls the system response,but it exhibits large steady state error [8]. Different types offractional order hybrid fuzzy PID structure have been developedfor the lag dominant, balanced lag and delay dominant system.Recommended structure for each system with specified operatingconditions was suggested. Conversely, the controller has reducedthe control system performance [9]. The Adaptive tuning methodfor the classical PID controller has been developed for nonlinearprocess system. The PID controller has been cascaded with a fuzzypredictor, where the controller gains are adjusted online based onthe predictions of a fuzzy predictor, but this controller producedlarger overshoot and noise in the output response [10].

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Neurocomputing

http://dx.doi.org/10.1016/j.neucom.2015.01.0320925-2312/& 2015 Elsevier B.V. All rights reserved.

n Corresponding author.E-mail address: prem.kamaraj@gmail.com (K. Premkumar).

Neurocomputing 157 (2015) 76–90

www.sciencedirect.com/science/journal/09252312www.elsevier.com/locate/neucomhttp://dx.doi.org/10.1016/j.neucom.2015.01.032http://dx.doi.org/10.1016/j.neucom.2015.01.032http://dx.doi.org/10.1016/j.neucom.2015.01.032http://crossmark.crossref.org/dialog/?doi=10.1016/j.neucom.2015.01.032&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1016/j.neucom.2015.01.032&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1016/j.neucom.2015.01.032&domain=pdfmailto:prem.kamaraj@gmail.comhttp://dx.doi.org/10.1016/j.neucom.2015.01.032

Fuzzy tuned PID controller was developed for brushless dcmotor. Simulations were carried out for sudden load disturbanceand step change in input. The effectiveness of controller wascompared with the conventional PID controller, the controllerproduced 750 percentage overshoot and large settling time inthe speed response [11]. In [12], particle swarm optimizationalgorithm has been applied for PID control of electrical dc drivesystem. From the simulated and experimental results, it wasobserved that speed response has large overshoot and moreoscillation in the steady state. Also, there were uncertaintyproblems due to load variations. In [13], comparative analysisbetween fuzzy logic and PID sliding mode fuzzy logic controllerhas been made for brushless dc motor. However, the controllerproduced indecision problem due to different loading conditions.In [14], GA and PSO optimized fractional order fuzzy PID controllerhas been developed for nonlinear process with time delay andunstable process with time delay. Effectiveness of this controllerwas compared with fuzzy PID controller. The controller hasimprecision due to load disturbances as outlined in [15]. Onlinetuning of fuzzy PID controllers via rule weighing based on normal-ized acceleration has been developed for the second order system.This method effectively controlled the system but, the systemoutput has larger overshoot and undershoots during sudden loaddisturbance [16]. Self tuning of PID type fuzzy logic controller hasbeen developed for dc motor system. The system output wascompared with conventional PI controller and this controlmechanism outperforms the PI controller, but the output has710 percentage of overshoot [17].

ANFIS based automatic generation control has been developed formulti area power system. The effectiveness of controller was com-pared with the integral controller. The ANFIS controller enhanced thesteady state response but degraded the transient response [18].Hybrid based controller with neuro fuzzy and PI controller has beendeveloped for brushless dc motor. The Hybrid controller has sluggishresponse during transient period and also, has uncertainty problemdue to load variations [19]. Comparative analysis between PI con-troller, fuzzy tuned PID controller, Fuzzy variable structure controllerand ANFIS controller based speed control of the brushless dc motorhas been explained in [20]. The main drawback with the developedANFIS controllers cited in [18–20] is that the controllers have beentrained in off line mode.

Fuzzy critic supervised neuro-fuzzy controller was developedfor brushless dc motor [21]. Fuzzy critic algorithms utilize thecontrol action of proportional derivative controller and it hasmodified the output layer of the neuro-fuzzy logic controller. Gaintuning of the PD controller has significant effect on the controlsystem performance. Online learning of neuro-fuzzy controllerusing sliding mode algorithm has been explained in [22]. Conven-tional PID and PD controller was paralleled with neuro-fuzzycontroller. This controller also has effect on control systemperformance with tuning of PID controller. In [23], online mixedlearning method of recursive least square and error back propaga-tion trained neuro fuzzy system with evolving clustering has beenapplied for the machinery condition monitoring applications.

Most of the research seldom concentrated on control systemperformance parameter such as rise time, settling time, recoverytime, steady state error, undershoot and overshoot. In this paper,all the above notified control system parameters are measured forthe proposed controllers namely, fuzzy online gain tuned antiwind up PID controller and fuzzy PID supervised learning of onlineANFIS controller and compared with the already published con-trollers namely anti wind up PID controller, fuzzy PID controller,offline ANFIS controller, PID supervised online ANFIS controllerand On-line Recursive least square—error back propagation basedANFIS controller notified in [7,14,20,22,23]. Organization of thepaper is as follows: State space model of the brushless dc motor

presented in Section 2. Structure of the speed control of brushlessdc motor is described in Section 3 and proposed controllers areexplained in Section 4. Section 5 discusses the simulation resultsand comments about the results discussion is summarized inSection 6. Concluding remarks are outlined in Section 7.

2. State space modeling of brushless dc motor

The BLDC motor has three stator windings and permanentmagnets on the rotor. The mathematical state space representationof variables of the BLDC motor can be described by the followingequation in (1),

ddt

iaibicωrθr

26666664

37777775¼

�RL�M 0 0 0 0

0 �RL�M 0 0 0

0 0 �RL�M 0 0

0 0 0 �BJ 0

0 0 0 P2 0

266666664

377777775

iaibicωrθr

26666664

37777775

þ

1L�M 0 0 0

0 1L�M0 0 0

0 0 1L�M0 0

0 0 0 �1J0 0 0 0

266666664

377777775

VaVbVcTL

26664

37775

þ

�1L�M 0 0

0 �1L�M 0

0 0 �1L�M0 0 00 0 0

26666664

37777775

eaebec

264

375 ð1Þ

where Va, Vb and Vc denotes stator phase voltages of the BLDCmotor in volts and R represents stator winding resistance in ohms.Phase currents of the motor are represented by ia, ib and ic in amps.The self inductance of the motor winding is represented by L andthe mutual inductances between stator windings are denoted byM in Henry. ea, eb and ec denotes the trapezoidal back-EMF of eachphase in volts. P is the number of poles in the rotor and θr is therotor position of the rotor in radians. J, B, ωr and TL denotes themoment of inertia, frictional coefficient, angular velocity and loadtorque of the motor, respectively. The electromechanical torque isexpressed in Eq. (2) as,

Te ¼ Jdωrdt þBωrþTL ð2Þ

The equation for instantaneous electrical Torque is given in Eq.(3) and also the relationship between angular velocity and rotorposition.

Te ¼eaia þ ebib þ ecicð Þ

ωrand ωr ¼

dθrdt

ð3Þ

3. Structure of speed control of brushless dc motor

The closed loop speed control system of brushless dc motor istaken from [20]. The overall speed control system is modeled byusing MATLAB/Simulink tool box. Fig. 1 shows the overall Simulinkmodel of speed control of brushless dc motor. The Simulink modelconsist of three phase voltage source PWM inverter, three phaseBLDC motor, speed controller, Switching logic and PWM generatorand motor measurement blocks.

K. Premkumar, B.V. Manikandan / Neurocomputing 157 (2015) 76–90 77

4. Proposed controllers for brushless dc motor

Two types of controllers are proposed for the speed control ofbrushless dc motor, i.e., fuzzy online gain tuned anti wind up PIDcontroller and fuzzy PID supervised online ANFIS controller.

4.1. Fuzzy online gain tuned anti wind up PID controller

The PID controller does not have output saturation limiters andhence potential conditions for the wind up phenomenon exist. Inorder to overcome this difficulty, a maximum integrator outputvalue will be kept within limit and a strategy is adapted for thiscondition, which is known as anti-windup phenomenon. The maingoal of anti windup PID control scheme is to avoid the over valuein the integrator thereby the integration output will be keptwithin a limited range.

The back calculation anti wind up PID controller is commonlyaccepted for speed control of brushless dc motor [7]. Unfortunately,many of the back calculation anti wind up PID loops that are inprocess are in need of continual monitoring and tuning of gains, i.e.,Kp, Ki, Kd and Kc, since they can easily become improperly tuned orbecome constant. Consequently, the control system parameters suchas rise time, settling time and steady state error of the speedresponse of the brushless dc motor will undergo drastic change withchange in operating conditions of the brushless dc drive. To over-come this drawback and for improving the control system para-meters, online tuning of gains in the anti wind up PID controller isproposed and this is considered to be vital. It is expected that therewill be considerable improvement in the controller performanceunder all operating conditions of the brushless dc drive due to onlinegains tuning.

The advantage of the fuzzy inference system has been provedin controlling nonlinear, complex, time-varying dynamic processesin real world problems. It can be used as an online gain tuner forthe back calculation anti wind up PID controller. The proposedcontrol scheme uses mamdani fuzzy inference system as a gaintuning-tool for the back calculation anti wind up PID controller.The structure of this controller is shown in Fig. 2 and in order toobtain the variable gain, fuzzy logic is employed for tuning thecontroller gain in online mode under all operating conditions.

Fuzzy online gain tuner is modeled by mamdani fuzzy inferencesystem. Fig. 3 shows the structure of fuzzy online gain tuner for antiwind up PID controller. It has two inputs i.e., speed error (e) and therate of change of error (Δe) and four outputs (Kp, Ki, Kd and Kc). Eachinput has five membership functions with bell shape norm andoutputs have five membership functions with Gaussian norm.

Distribution of input membership function is shown in Fig. 4.The universal bell shaped membership function is expressed byEq. (4) as,

f x; a; b; cð Þ ¼ 11þ x� ca

�� ��2b ð4Þ

The universal bell shaped function depends on three para-meters a, b and c where ‘a’ denotes the half width, ‘b’ controls theslopes at the intersecting points and ‘c’ determines the centre ofthe corresponding membership function. The input range for errorand rate of change error are from �1500 to 1500 and distributedwith five bell shaped membership functions denoted by NegativeBig (NB), Negative Small (NS), Zero (Z), Positive Small (PS) andPositive Big (PB).

Similarly each output is distributed with five Gaussian shapedmembership functions. Gaussian membership function has been

Fig. 1. Simulink model of speed control of brushless dc motor.

K. Premkumar, B.V. Manikandan / Neurocomputing 157 (2015) 76–9078

Fig. 2. Structure of fuzzy online gain tuned anti wind up PID controller.

Fig. 3. Proposed structure of fuzzy online gain tuner.

Fig. 4. Distribution of input membership functions for error (rpm) and rate of change of error (rev/s2).

K. Premkumar, B.V. Manikandan / Neurocomputing 157 (2015) 76–90 79

used to ease the design task. The Gaussian membership functionhas been widely used with mamdani fuzzy inference system andhas shown good performance in many applications. Besides, theuse of Gaussian membership function ensures that the wholeoutput space is covered by fuzzy rules and avoids the zero firingstrength problems. The generalized Gaussian function expressedby Eq. (5) as,

f x;σ; cð Þ ¼ e� ðx� cÞ2

2σ2 ð5Þ

where c and σ represents the center and width of the membershipfunction. Five Gaussian membership functions are denoted bySmall (S), Medium (M), Big (B), Very Big (VB), Very–Very Big (VVB).The range of proportional gain is from 0 to 5, integral gain rangesfrom �1 to 1, derivative gain ranges from �1 to 0 and backcalculation gain ranges from �1 to 1. Totally 25 rules are createdfor fuzzy online gain tuner and few rules are described in Eq. (6)as,

rule 1 : if e is NB andΔe is NB then Kp is VVBð Þ Ki is VVBð Þ Kd is Sð Þ Kc is VVBð Þ⋮rule 25 : if e is PB andΔe is PB then Kp is Sð Þ Ki is Sð Þ Kd is VBð ÞðKc is SÞ

ð6Þ

The overall rule base for fuzzy online gain tuner is shown inTable 1. The Fuzzy system utilizes the centroid defuzzification

method. Centroid defuzzification provides the center of area underthe curve. This is the most commonly used technique and it is veryaccurate. It is described by Eq. (7) as,

gainkp;ki;kd and kc ¼RμA xð Þx dxRμA xð Þdx ð7Þ

The output of the fuzzy online gain tuner is then multiplied withanti wind up PID controller and it provides the control signal (Uc) tothe system. The Simulink model of this controller is shown in Fig. 5.

4.2. Fuzzy PID supervised online ANFIS controller

Supervised learning techniques are more powerful in machinelearning than unsupervised techniques because the availability oflabeled training data provides clear criteria for model optimization[22]. Supervised learning of ANFIS structure can be formed usingoff line operation and online operation. Both operation have twotype of learning i.e., structure learning and parameter learning.Structure learning is primary to extract the fuzzy logic rules fromthe input data with tuning of fuzzy partitions for the input andoutput spaces. Then, the parameter learning adjusts the para-meters of each rule. These two phases are completed sequentiallyin off line operation. In the first phase, input data is partitionedand in second phase, premises and consequent parameter of the

Table 1Rule base of fuzzy online gain tuner.

Rate of change of error (Δe) Rate of change of error (Δe)Kp NB NS Z PS PB Ki NB NS Z PS PBNB VVB VVB VVB VB B NB VVB VB B B BNS VVB VVB VB VB B NS VVB VB VB B M

Speed error (e) Z VB VB B PS PS Speed error (e) Z B M S S SPS B M M M M PS B B M S SPB M M S S S PB M S S S SRate of change of error (Δe) Rate of change of error (Δe)Kd NB NS Z PS PB Kc NB NS Z PS PBNB S S M M VB NB VVB VB B B BNS S S S S M NS VVB VB VB B M

Speed error (e) Z S S S M VB Speed error (e) Z B M S S SPS M M M VB S PS B B M S SPB S S S M VB PB M S S B S

Fig. 5. Simulink model of fuzzy online gain tuned anti wind up PID controller.

K. Premkumar, B.V. Manikandan / Neurocomputing 157 (2015) 76–9080

network is updated using gradient descent method and recursiveleast square method, respectively.

Main drawback of this sequential learning scheme of off-lineoperation is that, it requires large quantity of representative datacollection in advance and also independent realization of thestructure and parameter learning usually takes lot of time. Toconquer these problems and for faster learning, online operationhas been introduced to perform the structure and parameterlearning phases concurrently. To enhance the performance stillfurther, fuzzy PID supervised online learning of ANFIS controller isproposed in this paper.

The proposed Fuzzy PID Supervised online Adaptive NeuroFuzzy Inference System combines the merits of fuzzy ART, neuralnetwork and fuzzy inference system. Moreover, it performs thestructure and parameter learning phases simultaneously. Thestructure learning is based on the partition of input space byusing different partitioning methods such as grid partitioning, treepartitioning and scatter partitioning. In grid partitioning, size offuzzy rules generated grows exponentially. Tree partitioningrelieves the above problem but it needs more membershipfunctions for each input to define fuzzy regions and thesemembership functions do not usually bear clear linguistic mean-ings. The scatter partitioning is usually dictated by the desiredinput–output data pairs and makes it hard to estimate the overallmapping directly from the consequent of each rule’s output. Inorder to overcome the drawbacks of partitioning methods, fuzzy

ART clustering method is proposed for structure learning of ANFISspeed controller. In addition, fuzzy ART has faster convergence ratei.e., it requires much less training iterations. Also it has high onlinelearning capability property i.e., fuzzy ART can learn a new patternwithout having to retain the network. The parameter learning isbased on the fuzzy PID adaptation control law.

The structure of fuzzy PID supervised learning of ANFIS con-troller is shown in Fig. 6 and its Simulink model is shown in Fig. 7.

Typical fuzzy PID controller is created with a fuzzy PD con-troller with an integrator and a summation unit at the output [14].It has two inputs that are error (e) and rate of change of error (Δe)and one output that is the supervised output (UF). The equation forfuzzy PID controller is expressed in Eq. (8) as,

UF ¼ αUþβZ

U ð8Þ

where α is the proportional gain, β is the integral gain and U is theoutput of the fuzzy PD controller. The Fuzzy PD controller has twoinputs that are error (e) and rate of change of error (Δe) and oneoutput (U) and it is shown in Fig. 8. The inputs are distributed withseven triangular membership functions and output is distributedwith forty-nine constant values.

Fuzzy inference system is modeled by zero order Takagi–Sugeno(T–S) fuzzy system. In realistic control applications, the triangularmembership function is generally selected for representing fuzzy setsin T–S fuzzy inference system. Because, in term of real-time require-ments by the inference engine, their parametric, functional descriptionof membership function can be easily obtained, stored with minimaluse of memory and can be manipulated efficiently. The triangularmembership function is described by Eq. (9) as,

f x; a; b; cð Þ ¼

0; xr0x�ajbj �aj; ajrxrbjcj � xcj �bj; bjrxrcj0; cjrx

8>>>>><>>>>>:

ð9Þ

where a and c locate the feet of the triangle and the parameter b locatesthe peak. The distribution of membership functions for the error andthe rate of change of error are shown in Fig. 9(a) and (b). The inputrange for the error is from �500 to 1500 and membership functiondenote by A,B,C,D,E,F and G. The range for the rate of change of error isfrom �1�108 to 3.824�104 andmembership function denoted by A1,B1, C1, D1, E1, F1 and G1. The range of output is from �1.584�104 to1.142�104. The distribution of output is shown in Fig. 10.

Totally 49 rules are created for fuzzy PD controller and fewrules are described in Eq. (10). The overall fuzzy rule is shown inFig. 6. Structure of fuzzy PID supervised online ANFIS controller.

Fig. 7. Simulink model of fuzzy PID supervised online ANFIS controller.

K. Premkumar, B.V. Manikandan / Neurocomputing 157 (2015) 76–90 81

Table 2. The set of rules can be separated into three clusters torealize the logic of incorporating the rule base as in Table 2. Cluster1: In this cluster of rules, error (e) and its rate of change of error(Δe) have very small positive or negative values or equal to zero.This implies that the process output has strayed off slightly fromthe set point but is still close to it. Thus small values of controlsignals (S) are required to correct these small deviations and theserules mainly relate to the steady state performance of the process.Cluster 2: For this group, error (e) is positive big and its rate of

change of error (Δe) is negative big or error (e) is negative big andrate of change of error (Δe) is positive big, suggesting that theprocess output is far below or far away from the set point. To bringthe process output towards the set point, the controller applies anappropriate positive control signal (P) to speed up or slow downthe approach towards the set point. Cluster 3: In this cluster theerror is negative large or medium, implying that the processoutput is significantly above the set point. Also the fractionalderivative of the error is negative implying that the process output

Fig. 8. Structure of fuzzy PD controller.

Fig. 9. (a) Distribution of membership function for error in rpm. (b) Distribution of membership function for rate of change of error in rev/s2.

K. Premkumar, B.V. Manikandan / Neurocomputing 157 (2015) 76–9082

is moving away from the set point. Hence the controller applies anegative control signal (N) to speed up or slow down the approachtowards the set point. Weighted average defuzzification method isused for converting fuzzy set into crisp set.

rule 1 : if e is A andΔe is A1 then U is P⋮

rule 14 : if e is B andΔe is G1 then U is N⋮

rule 28 : if e is D andΔe is G1 then U is P⋮

rule 35 : if e is E andΔe is D1 then U is S⋮

rule 49 : if e is G andΔe is G1 then U is P

ð10Þ

The output of fuzzy PD controller is processed by proportionalintegral controller and it will provide supervised output for theonline ANFIS controller. Error between supervised output andonline ANFIS controller output is expressed by Eq. (11) as,

EA ¼UF�UC ð11ÞNext, the process of applying online learning algorithm to

identify ANFIS parameters has been discussed. The ANFIS system,as the name suggests, is an adaptive neuro-fuzzy inferencemachine. It has two structures that are artificial neural networkand fuzzy inference system. The advantages of neural networksare: it has better learning capacity, generalization capacity androbustness in relation to disturbances. The disadvantages of theneural networks are: impossible interpretation of the functionality

and difficulty in determining the number of layers and number ofneurons. The advantages of the fuzzy systems are: capacity torepresent inherent uncertainties of the human knowledge withlinguistic variables, simple interaction of the expert of the domainwith the engineer designer of the system, easy interpretation ofthe results because of the natural rules representation, easyextension of the base of knowledge through the addition of newrules and robustness in relation of the possible disturbances in thesystem. The disadvantages fuzzy system are: incapable to general-ize, or either, it only answers to what is written in its rule base, it’snot robust in relation to the topological changes of the system,such changes would demand alterations in the rule base and itdepends on the existence of an expert to determine the inferencelogical rules. ANFIS combines the advantages of both artificialneural networks and classic fuzzy systems. It also eliminates theshortcomings of the neural network and fuzzy logic system and itworks as a universal approximator [20].

The Fuzzy ART-ANFIS controller consist of six layers and shown inFig. 11. They employ two algorithms for parameter learning (i.e.Recursive Least Square and error—back propagation) and one algo-rithm for automatic structure learning (i.e. fuzzy-ART). Fuzzy ARTimplements fuzzy logic into ART pattern recognition, thus enhancinggeneralizability. An optional feature of fuzzy ART is complementcoding, a means of incorporating the absence of features into patternclassifications, which goes a long way towards preventing inefficientand unnecessary category proliferation [24,25].

Layer 1 is known as the input normalization layer. In this layer,ANFIS-ART uses the technique of complement coding from fuzzy-ART to normalize the input training data. Complement codinghelps in avoiding the problem of category proliferation when usingfuzzy-ART for data clustering [24].

Layer 2 is known as input fuzzification layer. The nodes belongingto this layer are called input-term nodes and each represents a term ofan input-linguistic variable and functions as a 1-D membershipfunction. Fuzziness of the trapezoidal membership function is regular-ized. Premises parameters or non-linear parameters adjust the shapeand the location of the membership function. Those parameters areadjusted during the training mode of operation by the error back-propagation algorithm. These premises parameters or nonlinear para-meters are updated at each iteration i.e., after each input–output pairis received during training and the instantaneous error function isminimized. For each input–output training data pair, the ANFISoperates in the forward pass in order to calculate the current output.Afterwards, starting from the output layer, and moving backwards, theerror back-propagation executes to calculate the derivatives for eachnode at every layer of the network. At the end of each iteration, non-linear parameter of the input membership function is updated.

Fig. 10. Distribution of output of the fuzzy PD controller.

Table 2Rule base for fuzzy PD controller.

Rate of Change of Error (Δe)

Spee

d E

rror

(e)

U A1 B1 C1 D1 E1 F1 G1A P P S S S S S Cluster 1B P P S S S S S Cluster 2C P P S S S S S Cluster 3D N N S S S S SE N N S S S S SF N N N N P P PG N N N P P P P

K. Premkumar, B.V. Manikandan / Neurocomputing 157 (2015) 76–90 83

Layer 3 is known as fuzzy AND operation layer. Each node inthis layer performs a fuzzy-AND operation. T-norm operator of thealgebraic product is selected and it will results in each node’soutput being the product of all of its inputs. The output of eachnode in this layer represents the firing strength or the activationvalue of the corresponding fuzzy rule and the number of fuzzyrules will be equal to the number of input term nodes. The latter iscommon for all the input variables. Therefore, each fuzzy rule maybe assigned an index equal to the corresponding index of the inputterm node, which is common for each input linguistic variable.

Layer 4 is known as the normalization of each rule firingstrength layer. The output of the kth node is the firing strengthof each rule divided by the total sum of the activation values of allthe fuzzy rules. This results in the normalization of the activationvalue for each fuzzy rule.

Layer 5 is known as a linear rule consequence parameter layer.Each node k in this layer is accompanied by a set of adjustableparameters and implements the linear function. Adjustable para-meters are called consequent parameters or linear parameters ofthe ANFIS system and they are adjusted by the Recursive LeastSquare algorithm. For the Online supervised ANFIS controller, theinputs and output parameters are considered to be e, Δe and UC.The output is expressed in Eq. (12) as,

f e mð Þ;Δe mð Þ� � dðmÞ ¼ UCðmÞ ð12Þwhere e(m) and Δe(m) are controller input vectors, f is the knownfunction of the inputs and d(m) is the unknown parameter to beestimated. In order to identify the unknown parameter d(m),input–output training data is required for the target system andit is obtained from the fuzzy PID supervised control algorithm andexpressed in set of ‘t’ linear equation given in (13) as,

f t e mð Þ;Δe mð Þ� �

dðmÞ ¼ UF ðmÞ ð13Þ

By the application of recursive least square algorithm, theconsequent or linear parameter of the online ANFIS controller isupdated in the layer 5.

Layer 6 is known as output layer. This layer consists of one andonly node that creates the network’s output as the algebraic sumof the node’s inputs.

5. Simulation results and discussions

Speed response for constant load condition, varying loadconditions and varying set speed conditions are analyzed for theconsidered brushless dc motor. Control system performance para-meters such as rise time, settling time, recovery time, steady stateerror, overshoot and undershoot are obtained for the proposedcontrollers and compared with anti wind up PID controller, fuzzyPID controller, offline ANFIS controller, PID supervised ANFIScontroller and On-line Recursive least square—error back propaga-tion algorithm based ANFIS controller. The specifications of theBLDC motor are taken from [20] and it is shown in Table 3.

5.1. Result for constant load condition

In this section, simulation results of the speed response ofbrushless dc motor under no load and full load conditions arepresented. Fig. 12(a) shows the speed response curve for no loadcondition with a set speed of 1500 rpm and the control systemparameters are presented in Table 4. The speed response isseparated into two periods i.e., transient period and steady stateperiod. During transient period, the peak overshoot of speedresponse is 2.5008% and 2.1150% for anti wind up PID controllerand fuzzy PID controller, respectively. For offline ANFIS controller,the peak overshoot is 1.5789%, it is 1.2457% for PID supervised

Fig. 11. Architecture of Fuzzy ART- ANFIS Network.

Table 3Specifications of BLDC motor drive.

Specifications Value

Rated voltage (Volts) 470Rated current (Amps) 50Rated speed (rpm) 1500Stator phase resistance, R (ohm) 3Stator phase inductance, L (H) 0.001Flux linkage established by magnets, λ (V-s) 0.175Voltage constant, Kb (V/rpm) 0.1466Torque constant, Kt (N-m/A) 1.4Moment of inertia, J (kg-m2/rad) 0.0008Friction factor, B (N-m/(rad/s)) 0.001Pole pairs, P 4

K. Premkumar, B.V. Manikandan / Neurocomputing 157 (2015) 76–9084

ANFIS controller and 0.7460% overshoot for online recursive leastsquare—error back propagation based ANFIS controller. For fuzzyonline gain tuned anti wind up PID controller, it is 0.2133% andtherefore it is better than the controllers notified above. But withfuzzy PID supervised online ANFIS controller, the peak overshoot is0.1103% only and it is the best controller.

During steady state period, the set speed is attained in shorttime of 0.036 s for fuzzy PID supervised online ANFIS controllerand it is comparatively higher for other controllers. Steady state

error is comparatively lower (0.133%) for fuzzy online gain tunedanti wind up PID controller and it gets almost eliminated (0.15 rpmor 0.01%) for fuzzy PID supervised online ANFIS controller. Fromthe comparison results, it evident that, fuzzy online gain tunedanti wind up PID controller is the better controller and fuzzy PIDsupervised online ANFIS controller is the best controller.

Fig. 12(b) shows the speed response curve for full load conditions(25 Nm). Control system parameters are provided in Table 5. Fromthis plot and Table 5, rise time for the proposed controllers i.e., fuzzy

Fig. 12. (a) Speed response of brushless dc motor under no load condition (0 N m) with set speed of 1500 rpm. (b) Speed response of brushless dc motor under full loadcondition (25 N m) with set speed of 1500 rpm.

Table 4Control system parameters for no load condition.

Controllers Control system parameters

Rise time (s) Peak time (s) Peak value (rpm) Peak overshoot (%) Settling time (s) Steady state error (rpm) Steady state error (%)

AW PID 0.0314 0.0436 1537.5 2.5008 0.0446 17 1.133Fuzzy PID 0.0300 0.0415 1531.7 2.1150 0.0420 10.5 0.7Offline ANFIS 0.0300 0.0411 1523.7 1.5789 0.0384 4 0.266PIDþANFIS 0.0300 0.0410 1518.7 1.2457 0.0384 3.5 0.233Online RLS-BP-ANFIS 0.0300 0.403 1511.2 0.746 0.045 2.5 0.166Fuzzy AW PID 0.0300 0.0420 1503.2 0.2133 0.043 2 0.133Fuzzy PIDþANFIS 0.0300 0.0403 1501.7 0.1103 0.036 0.15 0.01

K. Premkumar, B.V. Manikandan / Neurocomputing 157 (2015) 76–90 85

online gain tuned anti wind up PID controller and fuzzy PIDsupervised online ANFIS controller, it is only 0.03 s but other con-trollers has larger rise time i.e., greater than 0.04 s. Also, set speed of1500 rpm is attained quickly with fuzzy PID supervised online ANFIScontroller. The steady state error is also in favor of the proposed

controllers, i.e., 0.166% for fuzzy online gain tuned anti wind up PIDcontroller and 0.066% for fuzzy PID supervised online ANFIS controller.It is clear that, the proposed controllers outperform the othercontrollers in all aspects. Fuzzy PID supervised online ANFIS controlleris the best of all considered controllers.

Table 5Control system parameters for full load condition.

Controllers Control system parameters

Rise time (s) Peak time (s) Peak value (rpm) Peak overshoot (%) Settling time (s) Steady state error (rpm) Steady state error (%)

AW PID 0.0449 0.4343 1527.9 1.8633 0.0578 16 1.066Fuzzy PID 0.0418 0.0573 1518.7 1.2490 0.0538 10.8 0.72Offline ANFIS 0.0418 0.0569 1509.5 0.6351 0.0538 3 0.2PIDþANFIS 0.0453 0.7662 1500 0 0.0584 5.5 0.36Online RLS-BP-ANFIS 0.044 – – – 0.05 8.5 0.566Fuzzy AW PID 0.0300 0.0405 1500 0 0.042 2.5 0.166Fuzzy PIDþANFIS 0.0300 0.0403 1501.7 0.1103 0.036 1 0.066

Fig. 13. (a) Speed response of brushless dc motor with load variation from no load (0 N m) to full load (25 N m). (b) Speed response of brushless dc motor with load variationfrom full load (25 N m) to no load (0 N m).

K. Premkumar, B.V. Manikandan / Neurocomputing 157 (2015) 76–9086

5.2. Result for varying load condition

In most of the industrial applications, the drive is alwayssubjected to varying load conditions. In order to ascertain thesuperiority of the proposed controller, the closed loop system ofthe brushless dc motor is operated with sudden change in loadconditions. The speed responses for varying load conditions aredescribed in this section for two cases. For case A, speed is set at1500 rpm and load is varied from no load (0 N m) to full load(25 N m) at 0.4 s. In case B, speed is set at 1500 rpm and load isvaried from full load (25 N m) to no load (0 N m) at 0.4 s. Fig. 13(a) shows the speed response curves for case A.

At the time of load change, very low speed drop is witnessed forfuzzy online gain tuned anti wind up PID controller and lowest speeddrop for fuzzy PID supervised online ANFIS controller. Also, with thesecontrollers, the overshoot is zero. When any sudden disturbance inoperating condition occurs, the system will take time to return to theset speed and this is termed as recovery time. Recovery time ismeasured for all controllers and it is 0.42 s for fuzzy online gain tunedanti wind up PID controller and 0.41 s for fuzzy PID supervised onlineANFIS controller. For the other controllers the recovery time is larger.

Fig. 13(b) shows the speed response of brushless dc motor withload change from full load to no load and control system parameter forboth cases are provided in Table 6. When sudden load rejection occurs,speed will get increased and rise in speed is witnessed for allcontrollers except proposed controllers. For realistic load variationconditions, fuzzy online gain tuned anti wind up PID controller isperforming better and clearly fuzzy PID supervised online ANFIScontroller is the best controller than the other considered controllers.

5.3. Result for varying set speed condition

In process industries, the set speed of the drive will be changed asper the requirement of processes. In order to validate the effectivenessof the proposed controllers under varying set speed conditions, twovarying set speed operating conditions are assumed and simulated. Incase A, set speed is varied from 1500 rpm to 1000 rpm and in case B,set speed is varied from 1000 rpm to 1500 rpm. For both cases, theload is set at no load. Fig. 14(a) shows the speed response for case Aand Fig. 14(b) shows the speed response for case B.

The control system parameters for both cases are presented inTable 7. The system exhibits oscillatory response for all othercontrollers except the proposed fuzzy online gain tuned anti windup PID controller and fuzzy PID supervised online ANFIS controller.

Also, these controllers have produced less steady state errorthan the other controllers. Steady state error is 0.25% for case Aand 0.1% for case B of fuzzy online gain tuned anti wind up PID

controller and it is 0.1% for case A and 0.013% for case B of fuzzyPID supervised online ANFIS controller. The proposed controllershave outperformed the other considered controllers. In the con-trollers proposed for brushless dc motor, fuzzy PID supervisedonline ANFIS controller has shown superior performance under alloperating conditions. Fuzzy online gain tuned anti wind up PIDcontroller is the second best controller in all aspects.

6. Comments on results and discussion

All considered controllers are able to track the set speed correctly.Performance under sudden load variations is not satisfactory for antiwind up PID, fuzzy PID and offline ANFIS controllers. Again, anti windup PID, fuzzy PID and offline ANFIS controllers are not able to providecomplete damping as oscillations are witnessed in the speed responsecurves. Remaining controllers are able to damp out the oscillation inspeed response. Overall performance attributes are provided in Table 8for comparing the performance of all controllers at ease. From thesummary of results it can be concluded that, wind up phenomenonelimination and complete reduction of steady state error are thespecial features of the two proposed controllers. Almost all controllershave shown improvement in settling time. Reduction of peak over-shoot and undershoot is the additional advantage claimed by fuzzyPID supervised online ANFIS controller. Considering the controlcapabilities, it is very easy to single out the proposed fuzzy PIDsupervised online ANFIS controller as the most versatile controller. Theother proposed controller, i.e., fuzzy online gain tuned anti wind upPID controller is the next best controller.

Considering the two proposed controllers alone for comparison, forconstant and varying load conditions, fuzzy PID supervised onlineANFIS controller performs better than the fuzzy online gain tuned antiwind up PID controller. It is evident from the values obtained andshown in Tables 4–6 for vital parameters such as overshoot, settlingtime and steady state error. The control system parameters undervarying speed conditions which are shown in Table 7 are also in favorof fuzzy supervised online ANFIS controller. The important positivepoint about the two proposed controllers is that the wind upphenomenon is effectively rejected by them.

7. Conclusion

Two effective controllers have been presented for the speedcontrol of brushless dc motor. The control system parameters areobtained for the proposed controllers and compared with alreadypublished modern controllers such as anti wind up PID controller,

Table 6Control system parameters for varying load condition.

Controllers Load conditions Control system parameters

Peak time (s) Peak value (rpm) Peak overshoot (%) Recovery time (s) Steady state error (rpm) Steady state error (%)

AW PID Case A 0.4417 1519.5 1.3025 0.46 10 0.666Case B 0.5313 1533.5 2.2304 0.6 21.5 1.433

Fuzzy PID Case A 0.4010 1516.5 1.1255 0.44 10.5 0.7Case B 0.4517 1521.9 1.4587 0.445 9.5 0.633

Offline ANFIS Case A 0.4002 1501.8 0.120 0.46 2.8 0.186Case B 0.4028 1507.2 0.4821 0.45 3.5 0.233

PIDþANFIS Case A 0.7948 1500 0 0.44 5.5 0.366Case B 0.7752 1503.5 0.2363 0.48 2 0.133

Online RLS-BP-ANFIS Case A – – – 0.43 6.5 0.433Case B 0.430 1503 0.2 0.45 2.5 0.166

Fuzzy AW PID Case A – – – 0.42 1.5 0.1Case B 0.404 1502 0.1333 0.42 1 0.066

Fuzzy PIDþANFIS Case A 0.4001 1500 0 0.41 1 0.066Case B 0.7939 1500.2 0.0144 0.405 0.16 0.0106

K. Premkumar, B.V. Manikandan / Neurocomputing 157 (2015) 76–90 87

fuzzy PID controller, offline ANFIS controller, PID supervised ANFIScontroller and On-line Recursive least square—error back propaga-tion algorithm based ANFIS controller. In order to test the

effectiveness of the proposed controllers under realistic operatingenvironment, various operating conditions such as constant load,varying load and varying set speed conditions are considered and

Table 7Control system parameters for varying set speed condition.

Controllers Set speed conditions Control system parameters

Peak undershoot (%) Peak overshoot (%) Recovery time (s) Steady state error (rpm) Steady state error (%)

AW PID Case A 0.1 – 0.495 15.5 1.55Case B – 2.133 0.48 9.5 0.633

Fuzzy PID Case A 0.35 – 0.47 10.3 1.03Case B – 2.033 0.475 10.8 0.72

Offline ANFIS Case A 0.6 – 0.47 6 0.6Case B – 1.58 0.465 4.5 0.3

PIDþANFIS Case A 1.6 – 0.48 20 2Case B – 1.23 0.46 1.5 0.1

Online RLS-BP-ANFIS Case A 0 – 0.43 4 0.4Case B – 1.58 0.45 3 0.133

Fuzzy AW PID Case A 0.1 – 0.44 2.5 0.25Case B – 0.33 0.425 3 0.100

Fuzzy PIDþANFIS Case A 0 – 0.415 1 0.1Case B – 0.32 0.421 0.2 0.013

Fig. 14. (a) Speed response of brushless dc motor with set speed variation from 1500 rpm to 1000 rpm. (b) Speed response of brushless dc motor with set speed variationfrom 1000 rpm to 1500 rpm.

K. Premkumar, B.V. Manikandan / Neurocomputing 157 (2015) 76–9088

the performances are observed. From the parameters consideredfor comparison, it has been ascertained that, the fuzzy PIDsupervised online ANFIS controller clearly outperforms the othercontrollers under all considered operating conditions of thebrushless dc motor and it is the best of all. The other proposedcontroller, Fuzzy online gain tuned anti wind up PID controller isconsidered to be second best controller. Since the two controllershave been rigorously tested under varying operating conditions, itcan be readily implemented for speed control of brushless motor.

The efficiency of proposed controllers relies on fuzzy membershipfunction selection, fuzzy rules and input and output scaling factor ofthe controller. This might be the limitation of the proposed controllers.Certain optimization algorithms may be applied for fuzzy membershipfunction selection, tuning of fuzzy rule and input–output scaling factortuning to achieve effective results under different circumstances andthis may be reserved as scope for future work.

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K.Premkumar received the B.E. degree from AnnaUniversity Chennai, Tamilnadu, India, in 2005, and M.E. Degree from Anna University Chennai, Tamilnadu,India, in 2007, all in faculty of electrical and electronicsengineering. At present, he is doing Ph.D. in AnnaUniversity Chennai, Tamilnadu, India. Also he is work-ing as Assistant Professor in the Department of Elec-trical and Electronics Engineering of PandianSaraswathi Yadav Engineering College, Sivagangai,Tamilnadu, India. His current research interests includedesign of speed and current controller is based on PIDcontroller, fuzzy logic controller, ANFIS controller andCANFIS controller for the special electrical machines.

Table 8Comparative performance analysis of considered controllers.

Sl. no Control objectives Controllers

AWPID

FuzzyPID

OfflineANFIS

PIDþANFIS Online RLS-BPANFIS

Fuzzy AW PID(proposed)

Fuzzy PIDþANFIS(proposed)

1 Set speed tracking ability ● ● ● ● ● ● ●2 Sudden load disturbance

rejection● ● ● ●

3 Damping of oscillations ● ● ● ●4 Wind up phenomenon

elimination● ●

5 Steady state error minimization ● ●6 Reduction of overshoot/

undershoot●

7 Improved settling time ● ● ● ● ● ● ●Comments on overall performance Better Best

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B.V.Manikandan obtained his B.E. degree in Electricaland Electronics Engineering during 1990 and M.E.degree in Power Systems Engineering during 1992 fromMadurai Kamaraj University. He obtained his Ph.D.degree from Anna University, Chennai in the year2010. His special fields of interest include powersystem restructuring issues, FACTS controllers, Specialmachines and Drives & Controls. Presently, he is work-ing as Professor in the Electrical and Electronics Engi-neering department of Mepco Schlenk EngineeringCollege, Sivakasi, and Tamilnadu, India.

K. Premkumar, B.V. Manikandan / Neurocomputing 157 (2015) 76–9090

Fuzzy PID supervised online ANFIS based speed controller for brushless dc motorIntroductionState space modeling of brushless dc motorStructure of speed control of brushless dc motorProposed controllers for brushless dc motorFuzzy online gain tuned anti wind up PID controllerFuzzy PID supervised online ANFIS controller

Simulation results and discussionsResult for constant load conditionResult for varying load conditionResult for varying set speed condition

Comments on results and discussionConclusionReferences