Speed control of Brushless DC motor using bat algorithm optimized Adaptive Neuro-Fuzzy Inference System

Applied Soft Computing 32 (2015) 403–419

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Applied Soft Computing journal homepage: www.elsevier.com/locate/asoc

Speed control of Brushless DC motor using bat algorithm optimized Adaptive Neuro-Fuzzy Inference System K. Premkumar a,∗ , B.V. Manikandan b a b

Department of Electrical and Electronics Engineering, Pandian Saraswathi Yadav Engineering College, Sivagangai 630561, Tamil Nadu, India Department of Electrical and Electronics Engineering, Mepco Schlenk Engineering College, Sivakasi 626005, Tamil Nadu, India

a r t i c l e

i n f o

Article history: Received 21 June 2014 Received in revised form 31 January 2015 Accepted 2 April 2015 Available online 13 April 2015 Keywords: ANFIS controller Bat algorithm Brushless DC motor Fuzzy PID controller PID controller

a b s t r a c t In this paper, speed control of Brushless DC motor using Bat algorithm optimized online Adaptive NeuroFuzzy Inference System is presented. Learning parameters of the online ANFIS controller, i.e., Learning Rate (), Forgetting Factor () and Steepest Descent Momentum Constant (˛) are optimized for different operating conditions of Brushless DC motor using Genetic Algorithm, Particle Swarm Optimization, and Bat algorithm. In addition, tuning of the gains of the Proportional Integral Derivative (PID), Fuzzy PID, and Adaptive Fuzzy Logic Controller is optimized using Genetic Algorithm, Particle Swarm Optimization and Bat Algorithm. Time domain specification of the speed response such as rise time, peak overshoot, undershoot, recovery time, settling time and steady state error is obtained and compared for the considered controllers. Also, performance indices such as Root Mean Squared Error, Integral of Absolute Error, Integral of Time Multiplied Absolute Error and Integral of Squared Error are evaluated and compared for the above controllers. In order to validate the effectiveness of the proposed controller, simulation is performed under constant load condition, varying load condition and varying set speed conditions of the Brushless DC motor. The real time experimental verification of the proposed controller is verified using an advanced DSP processor. The simulation and experimental results confirm that bat algorithm optimized online ANFIS controller outperforms the other controllers under all considered operating conditions. © 2015 Elsevier B.V. All rights reserved.

1. Introduction Most of the problems associated with brushed DC motor have been overcome by Brushless DC motor. Brushless DC motor has high efficiency and lower susceptibility to mechanical wear, high torque per weight ratio, increased reliability, reduced noise, longer lifetime and overall reduction of electromagnetic interference. The speed control of the Brushless DC motor is an important aspect in many industrial processes [1–4]. Various control schemes have been developed for improving the speed control performance of Brushless DC motor drives. As a result, interests in emerging intelligent control systems for Brushless DC motor drive has increased significantly and numerous intelligent control schemes for Brushless DC motor were designed based on linear and non-linear models [5–15]. The Proportional Integral Derivative (PID) controller based speed controller has been developed for three phase Brushless DC motor in [5]. However, PID controller degrades the system

∗ Corresponding author. Tel.: +91 9786992345. E-mail address: [email protected] (K. Premkumar). http://dx.doi.org/10.1016/j.asoc.2015.04.014 1568-4946/© 2015 Elsevier B.V. All rights reserved.

performance by constant gain parameter of the controller and also this controller suffered from improper tuning of constant parameters of the controller. In [6], hybrid fuzzy PID controller has been presented for Brushless DC motor. Genetic Algorithm is used to tune the input and output scaling factor of the fuzzy PID controller. But fuzzy PID controller also has uncertainty problem due to sudden load disturbance and set speed variations. Fuzzy sliding mode controller has been designed for Brushless DC motor in [7] and the effectiveness of the fuzzy sliding mode controller was compared with Proportional Integral Derivative controller. The design of fuzzy controller relies very much on human expertise based on the proposed objective and the sliding mode controller design is also very complex. In [8], parallel fuzzy PID algorithm has been adopted to realize the speed regulator for Brushless DC motor, but fuzzy PID controller has experienced uncertainty problem due to sudden load disturbance. Adaptive Fuzzy Logic Controller has been developed for Brushless DC motor in [9] and the speed response of the Brushless DC motor has a larger steady state error and settling time. Adaptive Fuzzy Logic speed controller for Brushless DC motor drive has been discussed in [10] and effectiveness of the controller has been compared with PI controller. However, controller degrades the

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performance of the speed of the Brushless DC motor during transient period. In [11], hybrid PI fuzzy logic controller has been developed for Brushless DC motor. The performance of the hybrid PI Fuzzy controller was better than conventional PI controller. But, the controller exhibits uncertainty problem due to set speed variations. In [12], the speed of the Brushless DC motor has been controlled using a fuzzy PD controller. This controller has produced larger overshoot and undershoots in the speed response due to load variations. In [13], fuzzy neural network based PI/PD controller with extended Kalman filter online learning has been outlined for Brushless DC motor. This control design increases the complexity of the controller. In [14], ANFIS controller based on a supervised critic algorithm has been presented, but tuning of the critic proportional and derivative gains has significant effect on the control system performance such as large overshoot, larger settling time and high steady state error in the speed response of the motor. In [15], gain tuning of dead beat proportional integral based speed controller for Brushless DC motor has been designed by particle swarm with ANFIS. If the operating condition changes, the response of the speed has also changed and hence, the controller was designed only for particular operating conditions. Also, online ANFIS controller has suffered from learning parameters that are Learning Rate (), Forgetting Factor () and Steepest Descent Momentum Constant (˛) with change in operating points of the Brushless DC motor. These parameters have significant effect on time domain specifications. Since the operating point of Brushless DC motor changes regularly, it has become essential to vary the ,  and ˛ based on operating point of the motor. For an optimization objective, numerous algorithms have been formulated and every algorithm has its own advantages and disadvantages. Genetic Algorithm (GA) is developed in [16] for optimal design of fuzzy logic controller. However, this optimization technique requires very long run time depending on the size of the system under study. Also, it suffered from settings of algorithm parameters which have given rise to repeat of the similar suboptimal solutions. Particle Swarm Optimization (PSO) based design of membership parameters has been demonstrated in [17]. PSO has some advantages over other related optimization techniques such as GA. However, PSO suffers from the biased optimism, which causes the less exact at the regulation of its velocity and the track. Furthermore, the algorithm suffers from sluggish convergence in advanced search stage, weak local search capability and algorithm may lead to possible trap in local optimum solutions. In order to overcome these drawbacks and for better clarity, recently researchers started to use bat algorithm [18,19]. Bat algorithm is categorized under the group of meta-heuristic algorithms. Bat algorithm is a novel search algorithm which stands on the echolocation behavior of micro bats. Preliminary studies indicated that the Bat algorithm is better to GA and PSO for solving unconstrained optimization problems because these methods fail to deal with the multimodal optimization problems [19]. Since, the operating condition of the Brushless DC motor tends to vary much, design of robust controller to work under wide range of operating conditions and also to enhance the control system performance parameters has given ample research scope. In this paper, online Adaptive Neuro-Fuzzy Inference System based speed controller is presented for Brushless DC motor. GA, PSO, and Bat algorithm are applied for optimizing the learning parameter of the ANFIS controller under different operating condition of Brushless DC motor. The performance of the BAT-online ANFIS is compared with GA-ANFIS and PSO-ANFIS. Moreover, the gain of the PID, fuzzy PID and adaptive Fuzzy Logic is optimized using GA, PSO and Bat algorithm and the effectiveness of the Bat algorithm is compared with GA and PSO. The performance of the proposed BAT-online ANFIS controller is compared with

BAT-Proportional Integral Derivative controller, BAT-Fuzzy PID controller, BAT-Adaptive Fuzzy Logic, GA-ANFIS, and PSO-ANFIS controller for the constant load conditions, varying load conditions and varying set speed conditions of the Brushless DC motor. Finally, the proposed controller has been tested with hardware set up under real time operating conditions using an advantaged DSP processor. 2. Modeling of the Brushless DC motor drive Brushless DC motor has three stator windings and a permanent magnet on the rotor. The mathematical state space representation of variables of the Brushless DC motor can be characterized by the following equation,

⎡ −R ⎡ i ⎤ ⎢ L−M ⎢ a ⎢ ⎢i ⎥ ⎢ 0 ⎢ b⎥ ⎢ ⎥ ⎢ d ⎢ ⎢ ic ⎥ = ⎢ 0 ⎥ ⎢ dt ⎢ ⎢ ⎥ ⎢ ⎣ ωr ⎦ ⎢ ⎢ 0 ⎢ r ⎣ 0

⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ +⎢ ⎢ ⎢ ⎢ ⎢ ⎣

0

0

−R L−M

0

0

−R L−M

0

0

0

0

1 L−M

0

0

1 0 L−M

0

0

0

0

0

0

⎡ −1 ⎢ L−M ⎢ ⎢ 0 ⎢ ⎢ +⎢ ⎢ 0 ⎢ ⎢ ⎣ 0 0

0 −1 L−M 0 0 0

0

0

P 2

0

⎤

⎥⎡ ⎤ ⎥ ia 0 0⎥ ⎥⎢ i ⎥ ⎥⎢ b ⎥ ⎥⎢ ⎥ ⎢ ⎥ 0⎥ 0 ⎥ ⎢ ic ⎥ ⎥⎢ ⎥ ⎥ ⎣ ωr ⎦ −B 0⎥ ⎥ J ⎦ r

0

0

0

0

⎤

⎥⎡ ⎤ ⎥ V a 0 0 ⎥ ⎥⎢ ⎥ ⎥ ⎢ Vb ⎥ ⎥⎢ ⎥ 1 ⎥ 0 ⎥ 0 ⎥⎢ L−M ⎥ ⎣ Vc ⎦ ⎥ −1 ⎥ TL 0 J ⎦

0

⎤

⎥ ⎥⎡ ⎤ e 0 ⎥ ⎥ a ⎥⎢ ⎥ ⎣ eb ⎦ −1 ⎥ ⎥ ⎥ L − M ⎥ ec ⎦ 0

(1)

0

where Va , Vb and Vc denotes stator phase voltages of the Brushless DC motor in Volts. 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 and the mutual inductances between stator windings are denoted by M in Henry. ea , eb and ec denotes the trapezoidal back-EMF of the each phase in Volts. P is the number of poles of the rotor.  r is the rotor position of the rotor in radian. J, B, ωr and TL denotes the moment of inertia, frictional coefficient, angular velocity and load torque of the motor respectively. The electromechanical torque is expressed in the following equation as, Te = J

dωr + Bωr + TL dt

(2)

The equation for the instantaneous electrical torque is given in Eq. (3) and also the relationship between angular velocity and rotor position. Te =

(ea ia + eb ib + ec ic ) dr and ωr = ωr dt

(3)

K. Premkumar, B.V. Manikandan / Applied Soft Computing 32 (2015) 403–419

405

Fig. 1. Bat algorithm optimized ANFIS based Speed controller for Brushless DC motor.

3. Bat algorithm optimized ANFIS based speed controller for Brushless DC motor The block diagram of the proposed system is shown in Fig. 1. In the proposed system, rotor position of the Brushless DC motor is sensed by rotor position encoder. The speed (Na ) of the motor is obtained by differentiating the rotor position of the motor, and then the actual speed of the motor is compared with the reference speed (Nr ) to produce a speed error (e). The rate of change of speed error (e) is obtained by differentiating the speed error. The ANFIS controller receives the six inputs that are e, e, , , ˛ and learning error (es ) and produce a control signal (Ua ) to the switching Logic and PWM Inverter. The learning error is obtained by comparing the outputs of the PID control training data with the output of the ANFIS controller. The Lookup table for PID control training data consists of input–output data of the PID controller. The inputs to the block are e and e and output is the PID supervised data (Uc ). The Lookup table for bat algorithm optimized values of ,  and ˛ consists of input–output data of the learning parameter as obtained from Bat algorithm optimization for different operating conditions of the motor. The inputs for the blocks are reference speed and load torque (TL ) and output is the learning parameter (,  and ˛). The switching logic circuit provides necessary PWM signals for the inverter gate with respect to rotor position of the motor and the control signals obtained from proposed controller. The PWM inverter controls the speed of the motor by controlling the DC bus voltage of the inverter.

3.2. Online Adaptive Neuro-Fuzzy Inference System Adaptive Neuro-Fuzzy Inference System combines the structures of the neural network and fuzzy inference system. Normally, ANFIS structure is formed using two methods namely offline method and online method. Each method consists of two learning, one is structure learning and another one is parameter learning. In offline method, structure and parameter learning are done in

3.1. Proportional Integral Derivative control training data PID control training data is depicted in Fig. 2(a). It consists of a 2D lookup table. The 2D lookup table has two inputs that are speed error (e) and rate of change of error (e) and single output (U). Totally 6561 data is stored in the lookup table and it is shown in Fig. 2(b). The lookup table arrangement is established based on the principles of proportional derivative controller. The yield of the lookup table is processed via proportional integral controller and it provides the supervised input for the online ANFIS controller.

Fig. 2. (a) The structure of PID control training data. (b) 2D lookup table for the PD control action.

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the error back-propagation executes to calculate the derivatives ∂E(n)/∂w for each node at every Layer of the network. At the end of every iteration, the non-linear parameter aij , bij and cij of the input membership function is updated by the following equation as,

 (1) aij (n + 1)

=

(1) ˛(aij (n)) + 



−

 (1) bij (n + 1)

=

(1) ˛(bij (n)) + 

=

(1) ˛(cij (n)) + 

−

 (1) cij (n + 1)

Fig. 3. Architecture of Scatter Partition type ANFIS network.

a sequential manner. In the beginning phase of the offline mode, initial membership function and fuzzy rules is produced based on partition algorithm. In the second phase of the offline mode, parameter of the ANFIS network, i.e., linear and nonlinear parameters are updated using gradient descent and recursive least square algorithms. But offline mode has some disadvantages, it requires a large amount of input and output data for the training and also a sequential process of the offline mode takes more time to train the ANFIS network. In order to overcome the shortcomings of the offline mode of ANFIS, online mode of the ANFIS network is developed. In online mode, structure and parameter learning are treated concurrently. In this paper, Scatter Partition type structure learning is employed in the ANFIS network. The Scatter Partition type ANFIS consists of five layers as shown in Fig. 3. The scatter partition reduces the number rules to reasonable quantities. Layer 1 is known as the input layer. In this layer input fuzzification takes place. Each input is assigned a membership value to each fuzzy subset that comprises that input’s universe of discourse. Mathematically, this function can be expressed by the following equation, (1) oij

=

(1) j (Ii )

where

o1ij

linguistic term of the ith input variable Ii1 . A generalized Gaussian function memberships functions used for input variables and expressed in the following equation as, j (xi ) =

1 1 + |xi − cij /aij |bij

(5)

where i = 1. . .q and j = 1. . .y. Number of input variables are equal to q and y is equal to number of fuzzy subsets for each input variable. While the triplet of parameters aij , bij and cij is referred to as premise parameters or non-linear parameters and they adapt the conditions and the position of the membership function role. Those parameters are corrected during the training mode of procedure by the error back-propagation algorithm. Those premise parameters or nonlinear parameters are updated at each iteration, i.e., after each input–output pair is received during training and to minimize the instantaneous error function as given in the following equation, E(n) =

1 (Uc (n) − Ua (n))2 2

(6)

where Uc (n) is the desired output or supervised output and Ua (n) is the output of the online ANFIS controller at each step time (n). For each input–output training data pair, the ANFIS operates in the forward pass in order to calculate the current output Ua (n). Subsequently, going from the output layer, and moving backwards,

∂a(1) ij



∂E(n) ∂b(1) ij

(7)



∂E(n) ∂cij(1)

where  is the learning rate of the network parameters and ˛ is the steepest descent momentum constant. Layer 2 is known as fuzzy AND operation layer. Each node in this layer performs a fuzzy-AND operation. Here, T-norm operator of the algebraic product was chosen. This will result to each node’s output. It is the product of all of its inputs and expressed in Eq. (8). Every input node is connected to that rule node. (2)

ok = wk =

q

(1)

oij

(8)

i=1

where k = 1 . . . y2 . The output of each node in this layer represents the firing strength or the activation value of the corresponding fuzzy rule. Layer 3 is known as normalization layer. The output of the kth node is the firing strength of each rule divided by the total sum of the activation values of all the fuzzy rules. This will result in the standardization of the activation value for each fuzzy rule and it is presented in the following equation as, (2)

(3)

ok = w¯ k =

(4)

is the layer 1 node’s output, which matches to the jth

−

∂E(n)

ok

y2

(9)

(2) o m=1 m

Layer 4 is known as a linear parameter layer. Each node k in this layer is accompanied by a set of adjustable parameters d1k , d2k . . . dyk , d0 and implements the linear function as expressed in the following equation, (4)

(1)

(1)

(1)

ok = w¯ k fk = w¯ k (d1k I1 + d2k I2 + · · · + dyk Iy + d0 )

(10)

The weight w¯ k is the normalized activation value of the kth rule, calculated with the aid of Eq. (9). Adjustable parameters are called consequent parameters or linear parameters of the ANFIS system and they are set by a Recursive Least Square algorithm. For online supervised ANFIS controller, inputs and output parameters are considered to be e, e and Ua . The output is expressed in the following equation as, f (e(m), e(m))d(m) = Ua (m)

(11)

where e(m) and e(m) are controller input vectors, f is the known function of the inputs and d(m) is the unknown parameter to be estimated. In order to identify the unknown parameter d(m), we need input–output training data on the target system and it is obtained from the PID control algorithm and expressed in a set of ‘t’ linear equation given in the following equation as, ft (e(m), e(m))d(m) = Uc (m)

(12)

K. Premkumar, B.V. Manikandan / Applied Soft Computing 32 (2015) 403–419

By the application of recursive least square algorithm, the consequence or linear parameter of the online ANFIS controller is updated in the layer 4. It is given in the following equation as, djkn+1 = djkn +

1 



Pn −

Pn ff T Pn  + f T Pn f

f (U − f T djkn ) and d0n+1 = d0n (13)

T

−1

where Pn = (ft ft ) and  is the forgetting factor of the online ANFIS controller. Layer 5 is known as output layer. This layer consists of one and only node that produces the network’s output as the algebraic sum of the node’s inputs. It is presented in the following equation as, y  2

Ua = o5 =

k=1

y 

k=1

2

(4)

ok =

k=1

w¯ k fk =

y2

wk fk

k=1 y2

(14)

wk

3.3. Learning parameter update law for the online ANFIS controller In this section, learning parameter (, ˛ and ) update law for the online ANFIS controller with different operating conditions of the Brushless DC motor has been described. Fig. 4(a) shows the lookup table for the learning parameter. It consists of three lookup tables. Each lookup table has two inputs, i.e., set speed and load torque of the Brushless DC motor and it provides the learning parameter to the online ANFIS controller based operating conditions of the Brushless DC motor. Fig. 4(b) shows the flowchart for the learning parameters update law for the online ANFIS controller. Initially read the values of the set speed and load torque of the motor. Flowchart consists of two loops, i.e., loop1 is used to update the learning parameter if set speed is between 1000 and 1500 rpm else if set speed is between 0 and 1000 rpm then loop2 is used. If set speed is between 1000 and 1500 rpm, then check the load torque of the motor. If torque is between 0 and 0.5 N m then update the learning parameter of the online ANFIS controller for set speed of 1500 rpm and torque of 0 N m conditions, else if torque is between 0.5 N m to 1.2 N m then update the learning parameter of the online ANFIS controller for the set speed of 1500 rpm and torque of 1.1 N m condition, else if torque is between 1.2 N m to 2 N m then update the learning parameter of the online ANFIS controller for set speed of 1500 rpm and torque of 2.2 N m condition, else go to read the value of the set speed and load torque of the motor, the same process is followed for the loop2. 4. Tuning of learning parameter of the online ANFIS Controller using Bat algorithm In this section, optimization of parameter (, ˛ and ) of the ANFIS controller under different operating conditions of Brushless DC motor by Bat algorithm is explained. Also, the learning parameter is optimized using GA and PSO algorithm. The bat algorithm uses the echolocation behavior of bats. These bats emit a very loud sound pulse (echolocation) and takes heed of the echo that bounces back from the surrounding objects. Their signal bandwidth varies depending on the species. Each sound pulse includes frequency, loudness, and pulse emission rate. Most bats use signals with tuning frequencies while the rest use fixed-frequency signals. The frequency range used by these creatures is between 25 kHz and 150 kHz. Bat algorithm is based on following aspects; all bats use echolocation and distinguish the difference between victim and obstruction. Bats are flying with a random velocity, in a random location, with a variable frequency, loudness and the pulse emission rate [18,19]. The flowchart for the bat algorithm is shown in Fig. 5. Application of Bat algorithm for optimization of learning parameter of ANFIS controller as follows:

407

Step 1 Formulation of Objective function J1 (S) for optimization with S = (S1 . . . Sd ),where d is the number of tuning parameters. The value of d = 3, S1 = , S2 = ˛ and S3 = . The fitness function can be defined as a particular type of objective function that is used to summarize, as a single figure of merit; In general, the fitness function should be a measure of how closely the model prediction matches the observed or expected data for a given set of model parameters. The notion of fitness is fundamental to the application of evolutionary algorithms; the degree of success in their application may depend critically on the definition of a fitness that changes neither too rapidly nor too slowly with the design parameters of the optimization problem. The fitness function must guarantee that individuals can be differentiated according to their suitability for solving the optimization problem. In evolutionary algorithms, the performance of the individual run is measured by a fitness function. After each iteration, the members are given a performance measure derived from the fitness function, and the “fittest” members of the population will propagate for the next iteration. In this paper, to assure stability and attain superior damping to sudden load disturbance and set speed variations, the parameters of the controllers may be chosen to minimize the following objective function described by Eq. (15) is considered as a fitness function for the optimization, J1 (S) = H1 + H2

(15)



m (ωref i=1

H1 =

 H2 =

− ωacti )2

m ωmax − ωref

if ωmax > ωref

0

otherwise

where ωref is the reference speed in rpm, ωacti actual speed of the motor in rpm at each sample. “m” is the number samples, in this paper, 20,000 samples has been taken for investigation. ωmax is the maximum speed of the motor in rpm. The range of tuning parameter of the ANFIS controller is given in Eqs. (16)–(18) as, 0≤≤2

(16)

0≤˛≤2

(17)

0≤≤5

(18)

Sep 2 Initialize the bat population Si and initial velocity Li for (i = 1, 2 . . . n), where n is the number of bat populations. Step 3 Define pulse frequency fi at Si . Initialize pulse rates Pi , maximum number of iterations and the loudness factor Ri Step 4 Loop: Start; t = 0; While (t < Maximum number of iterations) t = t + 1; iteration count. Generate new solutions by adjusting frequency and updating velocities and locations/solutions by Eqs. (19)–(21) fi = fmin + (fmax − fmin ) Lit

=

Lit−1

+ (Sit−1

Sit = Sit−1 + Lit

− Sb )fi

(19) (20) (21)

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Fig. 4. (a). Lookup table for the learning parameter (, ˛ and ). (b). Flowchart for the learning parameters update law.

where is a random vector drawn from a uniform distribution and frequency range fmin = 0 and fmax = 100. Sb is a global best for every iteration or generation. If (random number (0 to 1) > Pi ) Select a solution among the best solutions and generate a local solution around the selected best solution using the following equation,

where ε is a random number. While Rt = Rti  is the average loudness of all the bats at this time step (t). End if Generate a new solution by flying randomly If (random number (0 to 1) < Ri & J(Si ) < J(Sb )) Accept the new solutions, Increase Pi and reduce Ri using Eqs. (23) and (24).

Sit = Sb + εRt

Rit+1 = ˇRit , Pit+1 = Pi0 (1 − e(−t) )

(22)

(23)

K. Premkumar, B.V. Manikandan / Applied Soft Computing 32 (2015) 403–419

409

Fig. 5. Flowchart for the Bat algorithm.

where ˇ and  are constants. For any 0 < ˇ < 1 and  > 0, we have Rit → 0,

Pit = Pi0 , as t → ∞

(24)

For simplicity, ˇ =  can be used and for this work, ˇ =  = 0.9 is considered. End if Rank the bats and find the current best (Sb ) End while Loop end

The objective function is minimization function as given in the equation (15), Different operating conditions are considered for Brushless DC motor as given in Table 2. For each operating conditions leaning parameter is optimized. The convergence curves for the considered operating conditions are depicted in Fig. 7. From the convergence graphs shown in Fig. 7, it is clear that, the bat algorithm minimizes the fitness value to global optimum at

Step 5 Display the optimum solutions. This paper focuses on optimal tuning of learning parameter of the online ANFIS speed controller using GA, PSO, and Bat algorithm. The intention of this optimization is to minimize the target function, in order to amend the time domain specification and performance indices such as rise time, overshoot, undershoot, recovery time, settling time, steady state error, root mean squared error (RMSE), integral of absolute error (IAE), integral of time multiplied absolute error (ITAE) and integral of squared error (ISE) under different operating conditions. Block diagram of the tuning parameters of the online ANFIS controller using GA, PSO and BAT algorithm is shown in Fig. 6. The Parameters used for the GA, PSO and BAT algorithm are presented in Table 1.

Fig. 6. Tuning of learning parameters of the online ANFIS Controller using GA, PSO and BAT algorithm.

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Table 1 Parameter of the GA, PSO and Bat algorithm. Genetic Algorithm Population size Generations Crossover rate

Mutation rate

Stopping criteria

Trial

Particle Swarm Optimization 10 10 0.5

0.2

Maximum number of generation 50

Bat optimization

Population size Generations Minimum inertia weight (Wmin )

10 10 0.1

Maximum inertia weight (Wmax )

0.9

Cognitive coefficient (c1)

1.2

Social coefficient (c2)

1.2

Stopping criteria

Maximum number of generation 50

Trial

Population size Generations Initial loudness factor (R0 ) Initial pulse rate (P0 ) Minimum frequency (fmin ) Maximum frequency (fmax ) Stopping criteria

10 10 0.9

Trial

50

0.9 0 100 Maximum number of generation

Fig. 7. Convergence curve for all operating conditions with objective function J1.

second iteration for all operating conditions. But, GA and PSO minimize the fitness value to global optimum at second iteration for some operating conditions and it take more than two iterations for the some operating conditions. And finally, average computation time and optimal value of , ˛ and  of the online ANFIS controller for the different operating conditions of the Brushless DC motor using GA, PSO and bat algorithm are presented in Table 3. From

Table 2 Operating conditions considered for Brushless DC motor. Operating conditions

Speed (rpm)

Load torque (N m)

Condition 1 Condition 2 Condition 3 Condition 4 Condition 5 Condition 6

1500 1500 1500 1000 1000 1000

0 1.1 2.2 0 1.1 2.2

these results, it is evident that, BAT algorithm has minimum fitness value than GA and PSO for all operating conditions. Moreover, average computation time also favors only for the BAT algorithm. The Minimal value of fitness function and average computation time is not only the decisive parameter for judging the BAT algorithm to be better than GA and PSO. In order to evaluate the superiority of the BAT algorithm, time domain specification (rise time, overshoot, undershoot, settling time and steady state error) and performance indices (RMSE, IAE, ITAE, and ISE) are measured and analyzed for different operating conditions of the Brushless DC motor and also compared with GA and PSO. Table 4 shows the performance parameter of the Brushless DC motor for the all operating conditions with GA, PSO and BAT. From these results, BAT algorithm has small value total indices for the different operating conditions of the Brushless DC motor than GA and PSO. Considering all vital parameters such fitness value, average computation time and total indices, it is evident that BAT algorithm is performing better than GA and PSO.

K. Premkumar, B.V. Manikandan / Applied Soft Computing 32 (2015) 403–419

411

Table 3 Optimal value of , ˛ and  for all operating conditions with GA, PSO and BAT algorithms. Objective function (J1) Operating condition

Algorithm



˛



Best

Standard deviation

Mean

Worst

1

GA PSO BAT

0.7180 0.1000 0.2155

0.4935 0.1000 0.1890

4.9186 4.9664 4.8313

0.343749 0.343742 0.343742

0.033555 0.032491 0.009347

0.356582 0.360828 0.347352

0.453749 0.437431 0.374290

909.86 827.21 821.87

2

GA PSO BAT

0.1080 0.9070 0.3789

0.4918 0.9978 0.6406

1.3356 2.5770 3.7557

0.35153 0.351528 0.351522

0.038672 0.017288 0.006355

0.36932 0.360435 0.354153

0.471565 0.401557 0.371536

1097.10 1093.60 858.24

3

GA PSO BAT

0.6711 0.2302 0.2880

0.5665 0.1000 0.3085

3.0160 3.9218 1.9047

0.359892 0.359870 0.359858

0.010661 0.018724 0.006467

0.363108 0.370482 0.362586

0.395251 0.408859 0.379859

1042.90 1016.10 1001.00

4

GA PSO BAT

0.1000 0.1000 0.8446

1.0000 0.8588 0.2579

1.0000 3.8047 4.2153

0.281831 0.281529 0.281529

0.038685 0.014834 0.010183

0.300440 0.287774 0.285887

0.398183 0.328178 0.312878

1207.30 962.99 950.49

5

GA PSO BAT

0.1042 0.1392 0.3487

0.8356 0.8236 0.5075

1.3377 1.3893 4.7703

0.287151 0.287134 0.287134

0.033094 0.012948 0.009244

0.305606 0.292358 0.290771

0.387151 0.328715 0.317134

1395.70 1179.90 865.96

6

GA PSO BAT

0.3914 0.6259 0.4560

0.4517 0.1301 0.4988

1.0000 2.5550 2.6980

0.293375 0.293113 0.293109

0.031712 0.005757 0.011016

0.306473 0.295431 0.297662

0.393375 0.311592 0.329633

1057.20 970.46 836.68

5. Tuning of gain parameters of the PID, Fuzzy PID and Adaptive Fuzzy Logic controller using GA, PSO and Bat algorithm In this section, optimization of the gain of the PID (Kp , Ki , Kd and Td ), Fuzzy PID (Ke , Kce , Gp , Gi , and Gd ), and Adaptive Fuzzy Logic Controller (Ke , Kce , Ku , and Kb ) using GA, PSO and BAT algorithm is presented. Fig. 8 shows the structure of the PID, fuzzy PID and Adaptive Fuzzy Logic controller. Same objective function in Eq. (15) is used for optimization of gains of the above controller using GA, PSO and BAT algorithm.

Average computation Time (sec)

Convergence curve of the optimization is shown in Fig. 9. From this curve (Fig. 9), it is clear that, BAT algorithm converges to the fitness value of the global optima within second iteration but GA and PSO takes more than two iterations to converge. The optimal values of the gain of the PID, Fuzzy PID, and Adaptive Fuzzy Logic controller and average computation time are presented in Table 5. From these analyses, BAT algorithm has best fitness value and average computation time than GA and PSO. Minimum fitness function value and average computation time are not only the vital parameter to judge the superiority of bat algorithm over GA and PSO. Time domain specification and performance indices are also

Table 4 Performance analysis for all operating conditions with GA, PSO and BAT algorithms. Algorithm

Time Domain Specification Rise time

Overshoot

Performance indices Undershoot

Settling time

RMSE

IAE

ITAE

ISE

2.13300 2.97448 0.80506

0.17188 0.24309 0.24219

0.01773 0.01713 0.01713

0.00025 0.00021 0.00021

0.01156 0.01130 0.01129

2.57284 5.36370 1.21858

0.05841 0.04213 0.04375

0.88224 0.23262 0.20289

0.17683 0.24858 0.24821

0.01975 0.01784 0.01791

0.00031 0.00023 0.00023

0.01221 0.01179 0.01179

1.18551 0.61634 0.57986

Performance analysis for operating condition 3 GA 0.04208 0.00000 0.00012 0.07265 0.00000 0.00012 PSO 0.03284 0.03123 0.00012 BAT

0.08158 0.11542 0.04221

0.71528 3.38149 0.21879

0.18059 0.19322 0.17782

0.02174 0.02815 0.01890

0.00041 0.00083 0.00025

0.01270 0.01437 0.01235

1.05450 3.80624 0.53451

Performance analysis for operating condition 4 GA 0.01761 5.09696 0.00000 PSO 0.01761 4.07423 0.00000 0.01742 3.84528 0.00001 BAT

0.02899 0.02818 0.02814

10.67048 10.63514 10.69096

0.19926 0.19922 0.20077

0.01210 0.01206 0.01201

0.00015 0.00015 0.00015

0.00771 0.00771 0.00729

16.03327 14.97429 14.80203

Performance analysis for operating condition 5 GA 0.01850 3.52518 0.00007 0.01850 3.52518 0.00007 PSO 0.01850 3.52518 0.00007 BAT

0.02864 0.02864 0.02864

9.74510 9.68983 9.63420

0.20316 0.20315 0.20315

0.01240 0.01240 0.01239

0.00015 0.00015 0.00015

0.00801 0.00801 0.00801

13.54121 13.48593 13.43029

Performance analysis for operating condition 6 0.01908 3.28878 0.00021 GA 0.01908 3.28878 0.00021 PSO 0.019049 3.09098 0.00020 BAT

0.02907 0.02907 0.02903

7.39810 7.12802 6.35121

0.20562 0.20561 0.2052

0.01253 0.01252 0.01208

0.00014 0.00014 0.00014

0.00820 0.00820 0.00821

10.96173 10.69165 9.716099

Performance analysis for operating condition 1 0.02998 0.17007 0.00000 GA 0.02998 2.04564 0.00000 PSO 0.02067 0.08333 0.00001 BAT

0.03838 0.04187 0.03869

Performance analysis for operating condition 2 0.03572 0.00000 0.00004 GA 0.03183 0.03129 0.00004 PSO 0.03183 0.02321 0.00004 BAT

Steady state error

Total Indices

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Table 5 Optimal value of gains for PID, Fuzzy PID and Adaptive Fuzzy Logic controller using GA, PSO and BAT algorithm. Algorithm

Kp

Ki

Kd

Td

Best

Worst

Mean

Standard deviation

Average computation time (s)

PID controller GA PSO BAT

0.494888 1.000000 0.935863

0.966719 1.000000 0.491688

0.357278 1.221969 1.065582

0.357357 2.000000 1.609595

0.318887 0.317825 0.317517

0.418897 0.417835 0.417952

0.349075 0.337435 0.330145

0.038649 0.033275 0.030870

119.200000 119.033600 117.016000

Kce

Gp

Gi

Gd

Best

Worst

Mean

Standard deviation

Average computation time (s)

Fuzzy PID controller 0.100391 GA PSO 0.294738 BAT 0.524221

0.100391 1.000000 0.258287

1.999541 1.333162 0.526137

1.999541 1.396398 0.407012

1.999541 1.059168 0.272571

0.359880 0.359855 0.359855

0.399988 0.399857 0.398577

0.367544 0.368215 0.365731

0.013744 0.013914 0.013383

762.174000 767.288000 746.597000

Algorithm

Kce

Worst

Mean

Standard deviation

Average computation time (s)

0.509865 0.528760 0.459860

0.400280 0.384311 0.372471

0.056791 0.056528 0.031227

176.386000 183.793000 183.780000

Algorithm

Ke

Ke

Adaptive Fuzzy Logic Controller 0.883970 0.180258 GA 1.000000 0.391188 PSO 0.933682 0.655566 BAT

Ku

Kb

Best

0.550855 0.746619 0.336133

0.500000 0.100000 0.432323

0.359865 0.359858 0.359850

Table 6 Performance analysis of PID, Fuzzy PID, and Adaptive Fuzzy Logic controller with GA, PSO and BAT algorithm. Algorithm

Time domain specification Rise Time

Performance indices

Total indices

Overshoot

Undershoot

Settling time

Steady state error

RMSE

IAE

ITAE

ISE

PID controller 0.061493 GA PSO 0.061493 BAT 0.061493

0.000000 0.961959 0.000000

0.000118 0.000118 0.000118

0.262453 0.081050 0.081001

16.351200 12.783300 2.887600

0.221200 0.220300 0.220200

0.033600 0.031300 0.030600

0.001300 0.000899 0.000765

0.018700 0.018600 0.018600

16.950064 14.159019 3.300377

Fuzzy PID controller 0.032841 GA 0.032841 PSO 0.032841 BAT

0.707466 1.015746 0.193296

0.000118 0.000118 0.000118

0.042030 0.042030 0.042021

1.353500 1.241700 1.339000

0.177800 0.177800 0.177800

0.019000 0.019000 0.019000

0.000271 0.000272 0.000271

0.012300 0.012300 0.012300

2.345326 2.541808 1.816647

Adaptive Fuzzy Logic controller GA 0.032841 1.227126 0.032841 1.054959 PSO BAT 0.032841 0.562003

0.000118 0.000118 0.000118

0.042038 0.042060 0.042002

9.191700 7.301300 6.667600

0.177917 0.177900 0.177900

0.019832 0.019600 0.019600

0.000407 0.000374 0.000364

0.012354 0.012400 0.012400

10.704333 8.641553 7.514828

Fig. 8. Structure of the controller: (a) PID controller, (b) Fuzzy PID controller, and (c) Adaptive Fuzzy Logic controller.

evaluated and tested for the motor with set speed of 1500 rpm and load torque of 1 N m condition. Table 6 shows the performance analysis parameters for the PID, fuzzy PID, and Adaptive Fuzzy Logic controller with GA, PSO, and BAT algorithm. From these analysis results presented in Table 6, it is proved that, BAT algorithm has good quality of fitness value, average computation time and total indices than GA and PSO.

Fig. 9. Convergence curve for the PID controller, Fuzzy PID controller, and Adaptive Fuzzy Logic controller with objective function J1.

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6. Simulink model and simulation results In this section, Simulink model and simulation results are presented to validate the effectiveness of the proposed bat algorithm optimized ANFIS controller (BAT-ANFIS). Speed response characteristics for constant load condition, varying load conditions and varying set speed conditions of Brushless DC motor are obtained for the proposed controller and compared with BAT-PID controller (BAT-PID), BAT-fuzzy PID controller (BAT-FPID), BAT-Adaptive Fuzzy Logic controller (BAT-AFLC), GA-Online ANFIS (GA-ANFIS), and PSO-Online ANFIS (PSO-ANFIS) acting separately. The specifications of the Brushless DC motor drive system are: Rated power – 1.1 HP, rated current – 4.52 Amps, rated voltage – 310 V DC, rated speed – 2000 rpm and rated Torque – 2.2 N m. 6.1. Simulink model of ANFIS based speed controller for Brushless DC motor The overall Simulink model of bat algorithm optimized ANFIS based speed controller for Brushless DC motor is shown in Fig. 10. The Simulink model consist of three phase voltage source PWM inverter, three phase Brushless DC motor, Online ANFIS controller, switching logic, PWM generator and motor measurement blocks. The Simulink model of switching logic and PWM generator model consists of a triangular wave generator, three AND gates, comparator and three NOT gates. Another simulink model is invoked consisting of an online ANFIS controller and two lookup tables. One lookup table used to provide the PID controller training data. Another lookup table is used to provide the learning parameter such as Learning Rate (), Forgetting Factor () and Steepest Descent Momentum Constant (˛) to the ANFIS controller. Another Simulink model is created for measuring rotor speed, rotor position, electromagnetic torque, back EMF and stator current. 6.2. Simulation result for constant load condition In this section, speed response characteristics of Brushless DC motor under no load and full load conditions are explained. Fig. 11

413

(a) shows the speed response for no load condition with set speed of 1500 rpm. The performance parameter of the speed response is shown in Table 7. The proposed BAT-online ANFIS has a better time domain specification and performance indices than the other considered controllers. The vital parameters such as overshoot and steady state error are in favor of the proposed controller only. Fig. 11(b) shows the speed response characteristics for full load condition with set speed of 1500 rpm. The performance parameter of the speed response is shown in Table 8. From the results, it is clear that the proposed controller has better time domain specifications in speed response and performance indices. All considered parameters such as rise time, overshoot, undershoot, settling time, steady state error, RMSE, ITAE are favoring only the proposed controller. The transient state region, speed response is under damped for BATPID controller, BAT-FPID controller and BAT-AFLC controllers. The speed response is over damped nature for the proposed controller and the proposed BAT-ANFIS controller outperforms the other considered controllers. 6.3. Simulation result for varying load condition In order to validate the effectiveness of the proposed controller, the motor is subjected to sudden load changes also and the response is observed. The speed response characteristics for varying load conditions are analyzed for two cases. Case A, speed is set at 1500 rpm and load is varied from no load to full load at 0.1 sec. Case B, speed is set at 1500 rpm and load is varied from full load to no load at 0.1 sec. Fig. 12(a) shows the speed response for case A condition and performance parameters are shown in Table 9. The total performance indices are less for the proposed controller than other considered controllers. Moreover, the very important parameter such as recovery time, overshoot, and steady state error are also in support of the proposed controller. Fig. 12(b) shows the speed response for case B condition. The performance parameter of the speed response is shown in Table 10. From these outcomes, it is ascertained that the proposed controller is able to perform better under sudden change in load conditions also. The uncertainty problem due load variations is completely

Fig. 10. Simulink model of bat algorithm optimized ANFIS based speed controller for Brushless DC motor.

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Fig. 11. (a) Speed response for no load condition at 1500 rpm. (b) Speed response for full load condition at 1500 rpm.

Table 7 Result of performance parameters for No load condition. Controller

BAT-PID BAT-FPID BAT-AFLC GA-ANFIS PSO-ANFIS BAT-ANFIS

Time domain specification

Performance indices

Total indices

Rise time

Overshoot

Settling time

Steady state error

RMSE

IAE

ITAE

ISE

0.052208 0.029980 0.029980 0.029980 0.029980 0.020667

1.022778 1.457941 1.721486 0.165518 2.045638 0.083329

0.067886 0.038680 0.038575 0.038379 0.041872 0.03688

10.831344 11.397349 16.188594 2.074968 2.974476 0.805063

0.294961 0.243169 0.243269 0.243067 0.243088 0.245192

0.025653 0.017465 0.017678 0.017042 0.017132 0.017024

0.000521 0.000247 0.000267 0.000209 0.000215 0.000201

0.016184 0.011302 0.011306 0.011298 0.011299 0.011185

12.311534 13.196133 18.251154 2.580462 5.363700 1.219541

Table 8 Result of performance parameters for Full load condition. Controller

BAT-PID BAT-FPID BAT-AFLC GA-ANFIS PSO-ANFIS BAT-ANFIS

Time domain specification

Performance indices

Total indices

Rise time

Overshoot

Undershoot

Settling time

Steady state error

RMSE

IAE

ITAE

ISE

0.06261 0.03302 0.03302 0.04476 0.03302 0.03284

0.00000 0.20366 0.57277 0.00000 0.00954 0.00000

0.00014 0.00014 0.00014 0.00014 0.00014 0.00012

0.08331 0.04287 0.04268 0.08189 0.04395 0.04221

4.37532 1.15298 6.36660 0.80587 0.30539 0.21879

0.31279 0.25206 0.25209 0.25743 0.25208 0.17782

0.02876 0.01834 0.01854 0.02105 0.01838 0.01801

0.00066 0.00024 0.00026 0.00038 0.00024 0.00024

0.01799 0.01210 0.01210 0.01254 0.01210 0.01205

4.88158 1.71542 7.29820 1.22406 0.67483 0.50208

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Fig. 12. (a) Speed response characteristics for Case A. (b) Speed response characteristics for Case B.

Table 9 Result of performance parameters for Case A condition. Controller

BAT-PID BAT-FPID BAT-AFLC GA-ANFIS PSO-ANFIS BAT-ANFIS

Time domain specification

Performance indices

Total indices

Overshoot

Undershoot

Recovery time

Steady state error

RMSE

IAE

ITAE

ISE

0.00000 0.10000 0.45000 0.00000 1.00000 0.00000

0.40000 0.04667 0.00000 0.06667 0.00000 0.00333

0.15000 0.13000 0.13000 0.10500 0.10500 0.10300

4.95388 0.83038 6.30484 0.61877 2.72706 0.37454

0.29493 0.24311 0.24317 0.24307 0.24309 0.24190

0.02556 0.01730 0.01752 0.01702 0.01711 0.01702

0.00051 0.00023 0.00025 0.00021 0.00021 0.00021

0.01618 0.01130 0.01130 0.01130 0.01130 0.01129

5.84106 1.37898 7.15708 1.06202 4.10376 0.75129

Table 10 Result of performance parameters for Case B condition. Controller

BAT-PID BAT-FPID BAT-AFLC GA-ANFIS PSO-ANFIS BAT-ANFIS

Time domain specification

Performance indices

Total indices

Overshoot

Recovery time

Steady state error

RMSE

IAE

ITAE

ISE

0.73333 0.86667 1.33333 0.05333 0.10000 0.10033

0.15000 0.13000 0.13000 0.10800 0.10900 0.10100

11.30718 11.86537 16.08494 2.25229 1.91382 1.72878

0.31282 0.25212 0.25218 0.25743 0.25206 0.25201

0.02885 0.01851 0.01869 0.02106 0.01836 0.01803

0.00067 0.00026 0.00028 0.00038 0.00024 0.00024

0.01799 0.01210 0.01210 0.01254 0.01210 0.01210

12.55084 13.14503 17.83153 2.70503 2.40559 2.21249

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Fig. 13. (a) Speed response characteristics for Case C. (b). Speed response characteristics for Case D.

tackled and tracked by the proposed controller and this makes it ideal controller for Brushless DC motor foe use in industrial environment.

6.4. Simulation result for varying set speed condition In order to judge the superiority of the proposed controller, the motor is subjected to varying set speed conditions also. Two important cases are considered. In Case C, speed is varied from 1500 rpm to 1000 rpm at 0.1 s. In Case D, speed is varied from 1000 rpm to 1500 rpm at 0.1 s. Fig. 13(a) shows the speed response characteristics for case C. The corresponding performance parameters are shown in Table 11. The response is over damped nature with proposed controller whereas it is under damped nature for the other considered controllers. Fig. 13(b) shows the speed response characteristics for the case D condition. And the corresponding time domain and performance indices are shown in Table 12. Important parameters such as overshoot, recovery time, steady state error, RMSE, IAE, ITAE, and ISE are favoring the proposed controller for the varying set speed conditions also like the other results discussed above. The system response is also well damped for the proposed controller under different operating conditions considered.

7. Experimental verification of the Bat algorithm optimized online ANFIS based speed controller for Brushless DC motor In order to validate the performance of the proposed controller under extreme working conditions such as varying load and set speed conditions, simulation results alone could not be taken for consideration. Verification of the performance through experimental set up supplements the justification in favor of the proposed controller.

7.1. Experimental setup Block diagram of the DSP-based computer control system for a Brushless DC motor drive using the voltage-controlled technique is shown in Fig. 14(a). Real time hardware setup is provided in Fig. 14(b). The setup consists of Micro-2407 trainer, personal computer, rectifier, Inverter module, Brushless DC motor, torque sensor and Hall sensor signal conditioner. The Micro-2407 a 16-bit fixed point DSP trainer based on TMS320LF2407A DSP Processor is used as a controller unit. This trainer has digital control along with basic DSP functions such as filtering, PWM generation and calculation of spectral characteristics of input analog signals. The TMS320LF2407A contains a C2xx DSP core along with useful peripherals such as ADC, DAC, Timer,

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Table 11 Result of performance parameters for Case C condition. Controller

BAT-PID BAT-FPID BAT-AFLC GA-ANFIS PSO-ANFIS BAT-ANFIS

Time domain specification

Performance indices

Recovery time

Steady state error

RMSE

IAE

ITAE

ISE

0.35000 0.35000 0.35000 0.25000 0.25000 0.12623

29.87367 55.83189 51.19851 9.68253 8.89290 4.73784

0.32914 0.26688 0.26662 0.26360 0.27155 0.26289

0.03097 0.02088 0.02100 0.01987 0.02124 0.01980

0.00114 0.00064 0.00065 0.00052 0.00055 0.00048

0.01804 0.01238 0.01238 0.01228 0.01306 0.01234

and PWM Generation integrated onto a single piece of silicon. The Micro-2407 trainer can be operated in two modes. In mode 1(serial mode) the trainer is configured to communicate with PC through serial port. In mode 2 (stand alone mode), the trainer can be interacted with the IBM PC keyboard and 16 × 2 LCD display [20,21]. The Personal computer is used for displaying the actual speed of the motor and giving reference set speed to the DSP processor. The

Total indices

30.60297 56.48266 51.84914 10.22880 9.44931 5.15958

input AC voltage is rectified by the Diode Bridge Rectifier circuit. The rectified DC voltage is fed to the power circuit through a filter capacitor. The Power circuit consists of three leg IGBT-diode pair switches. The PWM signal from the driver IC is fed to the gate of the switch. The output of the power circuit is given to the Brushless DC motor. The PWM signals to the IGBT switches are generated by the DSP controller unit. The PWM signal from the controller is fed to the

Fig. 14. (a) DSP based Bat algorithm optimized online ANFIS controlled Brushless DC motor. (b) Snapshot of real time hardware setup for the proposed system.

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Table 12 Result of performance parameters for Case D condition. Controller

BAT-PID BAT-FPID BAT-AFLC GA-ANFIS PSO-ANFIS BAT-ANFIS

Time domain specification

Performance indices

Total indices

Overshoot

Recovery time

Steady state error

RMSE

IAE

ITAE

ISE

0.85773 1.25390 1.45414 1.45252 1.38579 0.94196

0.35000 0.19974 0.35000 0.12132 0.15201 0.12504

9.09684 7.42763 16.11490 0.95643 2.15685 0.75820

0.24664 0.20903 0.20815 0.20736 0.22102 0.20763

0.02091 0.01516 0.01526 0.01325 0.01532 0.01325

0.00061 0.00039 0.00040 0.00027 0.00053 0.00027

0.01117 0.00813 0.00809 0.00803 0.00850 0.00804

10.58390 9.11398 18.15095 2.75918 3.94003 2.05439

IGBT PWM inverter module through the connector provided on the front panel. In this implementation, controller is used for PWM generation and switching logic generation for the IGBT module. Torque sensor, Hall sensor and speed sensor units are used for sensing the load torque, position and speed of the rotor of the Brushless DC motor. It is fed to the DSP processor via A/D converter. The DSP controller program for the proposed control process was written in C language. Controlling and compiling process was performed by a compiler program. 7.2. Experimental verification Some experimental results are provided to demonstrate the control performance of the proposed Bat algorithm optimized online ANFIS controller for the Brushless DC motor. Two test conditions are provided in the experimentation, which are the sudden load variation case and the set speed variation case. Fig. 15(a) and (b) depicts the speed response characteristics of the Brushless DC motor for sudden increases in load from 0 N m to 2 N m and from 2 N m to 0 N m respectively. During load variation, speed of the motor decrease lightly for load increasing conditions

Fig. 16. (a) Speed response for set speed command decreased from 1500 rpm to 1000 rpm. (b) Speed response for set speed command increased from 1000 rpm to 1500 rpm.

and speed increases lightly for load decreasing conditions and then track the set speed quickly. Fig. 16(a) and (b) depicts the speed response characteristics for set speed variations from 1500 rpm to 1000 rpm and from 1000 rpm to 1500 rpm respectively. During set speed variations, speed response of the Brushless DC motor is able to track the set speed command for both increasing and decreasing conditions of the reference speed. From the experimental studies, it is proved that the proposed controller has excellent tracking performance. 8. Conclusion

Fig. 15. (a) Speed response for sudden load increase from 0 N m to 2 N m. (b) Speed response for sudden load decrease from 2 N m to 0 N m.

A bat algorithm optimized online Adaptive Neuro-Fuzzy Inference System based speed controller for Brushless DC motor has been presented. Also, performance the proposed controller is compared with GA and PSO optimized online ANFIS, Bat algorithm optimized PID, Fuzzy PID, and Adaptive Fuzzy Logic controller. The proposed controller has superior performance than other considered controllers in terms of minimum fitness value, less average computation time, improved time domain specifications and improved performance indices under all operating conditions.

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The real time implementation of the proposed controller has been verified experimentally using DSP processor. From the results of the simulation and experimental set up, it is made clear that, the proposed controller is able to eliminate the uncertainty problem occurring due to load variations and set speed variations. Since the controller exhibits unmatched performance, it is ideal for application in process industries. Application and performance study of the proposed Bat algorithm to the structure learning and parameter learning of the ANFIS structure is reserved for future scope of work. References [1] H.-B. Wang, H.-P. Liu, A novel sensorless control method for brushless DC motor, IET Electr. Power Appl. 3 (3) (2009) 240–246. [2] B. Singh, S. Singh, Single-phase power factor controller topologies for permanent magnet brushless DC motor drives, IET Power Electr. 3 (2) (2010) 147–175. [3] D. Gambetta, A. Ahfock, New sensorless commutation technique for brushless DC motors, IET Electr. Power Appl. 3 (1) (2009) 40–49. [4] S.S. Bharatkar, R. Yanamshetti, D. Chatterjee, A.K. Ganguli, Dual-mode switching technique for reduction of commutation torque ripple of brushless dc motor, IET Electr. Power Appl. 5 (1) (2011) 193–202. [5] C. Sheeba Joice, S.R. Paranjothi, V. Jawahar, Senthil Kumar, Digital control strategy for four quadrant operation of three phase BLDC motor with load variations, IEEE Trans. Ind. Inform. 9 (2) (2013) 974–981. [6] A. Rubaai, M.J. Castro-Sitiriche, A.R. Ofoli, DSP-based laboratory implementation of hybrid Fuzzy-PID controller using genetic optimization for high-performance motor drives, IEEE Trans. Ind. Appl. 44 (6) (2008) 1977–1986. [7] J.-B. Cao, B.-G. Cao, Fuzzy-logic-based sliding-mode controller design for position-sensorless electric vehicle, IEEE Trans. Power Electr. 24 (10) (2009) 2368–2378. [8] A. Rubaai, M.J. Castro-Sitiriche, A.R. Ofoli, Design and implementation of parallel fuzzy PID controller for high-performance brushless motor drives: an integrated environment for rapid control prototyping, IEEE Trans. Ind. Appl. 44 (4) (2008) 1090–1098.

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