Technology, Coimbatore , Tamilnadu, India.

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1 Research Paper PERFORMANCE ANALYSIS OF PERMANENT MAGNET SYNCHRONOUS MOTOR USING HYBRID OPTIMIZATION ALGORITHM Dr. S. Viayabaskar 1, Dr.T.Manigandan 2 Address for Correspondence 1 Professor, Department of Electrical and Electronics Engineering, P.A. College of Engineering and Technology, Coimbatore , Tamilnadu, India. 2 Principal, P.A. College of Engineering and Technology, Coimbatore , Tamilnadu, India. ABSTRACT This work deals with the detailed analysis of a Permanent Magnet Synchronous Motor (PMSM) drive system in Simulink. Field oriented control technique is used for the operation of the drive. In Closed Loop operation, Speed control of PMSM is achieved through Artificial Bee Colony (ABC) and Evolutionary Algorithm (EA) optimization technique with PID Speed Controller. The ABC and EA techniques are acts as hybrid optimization algorithms. The transient performance also improved by the proposed hybrid optimization PID controller. First, ABC PID control design is developed based on common control Engineering Knowledge. Better transient performance is achieved by increasing the P and I gains and decreasing the D gains. Then the Evolutionary Algorithm technique is applied for autotuning the control parameters of the ABC and PID controller. EA based ABC PID controller provides better speed control and guarantees the closed loop stability. The Evolutionary ABC PID controller can be executed in real time applications without any concern about instabilities that leads to system failure or damage. The simulation includes all realistic components of the system. This enables the calculation of currents and voltages in various parts of the inverter and motor under transient and steady conditions. The losses in various parts are calculated, facilitating the design of the inverter. A closed loop control system with a Proportional Integral (PI) controllers in the speed loop has been designed to operate in constant torque and flux weakening regions. Implementation has been done using Simulink. KEYWORDS Artificial Bee Colony (ABC), Evolutionary Algorithm (EA), Genetic Algorithm (GA), Permanent Magnet Synchronous Motor (PMSM). I. INTRODUCTION Recent studies had shown that with the progression of control theories, power electronics and microelectronics in connection with new concept motor design and magnetic materials since 1980s, electrical (AC) drives are making tremendous impact in the area of different high-performance variable speed control systems [1]-[3]. Among AC drives PMSM with high energy permanent magnetic materials. Although many possible solutions like nonlinear, adaptive control are available [4], the business sector of electrical drives doesn t ustify the cost needed to implement such sophisticated solution in industrial drives and (PI) Proportional Integral based control system scheme still remains the most widely adopted solution. Such a penchant is supported by a fact that, though it is simple, a PI control achieves high performance when optimally designed [5]. PI controllers have been broadly utilized for decades in industries for process control applications and their reason for their wide prevalence lies in the effortlessness of design and performances including low percentage overshoot and low maintenance cost [6]. The evolutionary optimization algorithms executed by representing the optimization parameters via a gene like structure and in this manner using the basic mechanisms of Darwinian natural selection to find a population of superior parameters. There are different approaches to evolutionary optimization algorithms including evolution strategies, genetic algorithms, evolutionary programming and genetic programming. These various algorithms are similar in their basic concepts of evolution and differ mainly in their way to deal with parameter representation. Genetic algorithms (GA), in particular, is an evolutionary technique which has shown to perform well in noisy, nonlinear and uncertain optimization landscapes typical of Artificial Bee Colony(ABC) systems. PID control is a feedback mechanism which is used in control system. This type of control is likewise termed as three term control. By controlling the three parameters - proportional, integral and derivative we can accomplish distinctive control actions for specific work. PID is considered to be the best controller in the control system. In PID controller, two parameters can work while keeping the third one to zero. So PID Controller becomes sometimes PI (Proportional Integral), PD (Proportional Derivative) or even P or I. The derivative term D is responsible for noise measurement while integral term is implied for reaching the targeted value of the system. The optimization model developed includes minimizing the error which is the difference of reference speed and obtained speed. Numerically, the obective function has a multimodal error surface which limits the application of conventional gradient based methods. Therefore consideration is given to global optimization techniques like Genetic Algorithm (GA) [7], Bacterial Foraging Optimization [8], and Particle Swarm Optimization [9]-[10]. In the present study we have Proected a hybrid of Differential Evolution (DE) [11] and Artificial Bee Colony Algorithm (ABC) [12]-[15] to deal with this optimization model, fuzzy speed regulator method [16], adaptive control [17]-[19], fuzzy PI current control [20], adaptive fuzzy controller [21], [22], nonlinear optimal control [23], neuro adaptive control [24], novel fuzzy control [25]. This paper gives an evolutionary Artificial Bee Colony (ABC) PID controller design method for a PMSM. First, we develop a Artificial Bee Colony(ABC) PID control design method based on the common control engineering knowledge that transient performance can be improved if the P and I gains are increased and the D gain is decreased when the transient error is large. We derive an inequality condition which the PID parameter should satisfy for asymptotic stability. Second, we give an Evolutionary Algorithm (EA) to optimize and auto tune the Artificial Bee Colony (ABC) PID control parameters. Unlike the most previous methods, it is shown in our paper that any Artificial Bee Colony (ABC) control parameter vector generated by the

2 proposed evolutionary auto tuning algorithm guarantees the closed-loop stability. II.PERMANENT MAGNET SYNCHRONOUS MOTOR In general, PMSM with ust about sinusoidal back electromotive force (i.e., back EMF) can be broadly categorized into two types (1) Interior Permanent Magnet Synchronous Motors (IPMSM) (2) Surface mounted Permanent Magnet Synchronous Motors (SPMSM). In this method, we have considered the SPMSM. The cross-sectional layout of SPMSM is shown in Figure1. Here the magnets are mounted on the surface of the motor. Because the incremental permeability of these magnets is between 1.02 and 1.20 relations to external fields, the magnets have high reluctance and accordingly the SPMSM can be measured to have large and effective uniform air-gap. This property makes the saliency effect negligible. Thus quadrature axis of synchronous inductance of SPMSM is equal to its direct axis inductance. As a result magnetic torque can only be created by SPMSM, which arises from the communication of magnet flux and quadrature axis current. The stator carries a three-phase winding which creates a close sinusoidal distribution of magneto motive force based on the value of stator current. They have the same part as the field winding in a synchronous machine except that their magnetic field is constant and there is no control on it [13]. Figure 1: Structure of permanent magnet synchronous motor By considering all the parameters, equivalent circuit of PMSM can be represented in direct-quadrature (dq axis) reference frame. III.PROBLEM FORMULATION The PMSM drive model consists of a Pulse Width Modulation (PWM) inverter, a PWM generator and a current controller followed by speed controller and it is also embedded with speed/position estimator. The PMSM drive receives power from three-phase AC supply and runs mechanical load at required speed. The developed model of the drive system is used for design in current and speed controllers. The mathematical design model of PMSM in d-q synchronously rotating frame of reference can be obtained from synchronous machine model. The parameters used in PMSM are represented in Equations (1), (2), (3) and (4). V sd = R s I sd + P sd - ɷ e sq (1) V sq = R s I sq + P sq + ɷ e sd (2) sd= L d I sd + m (3) sq= L q I sq (4) A field oriented vector controlled isotropic PMSM dynamic equation is shown in Equation (5):. ( t) i ( t) ( t) T ( t) (5) 1 qs 2 3 L where ω= is the electrical rotor angular speed, is the electrical rotor angle, represents the load torque disturbance input, and, i 3 are the parameter values that are represented in equation (6) p 1 m 2 J 4 (6) B 2 J P 3 2 J where ρ is the number of poles,,, and are the rotor inertia, the viscous friction coefficient, and the magnetic flux, respectively. Field oriented PMSM control system is shown in Figure 2. In a field oriented PMSM controller, the three phase current commands are computed by converting the controller current commands i qsd and i dsd. The d axis reference current is usually set as zero. Thus our problem can be formulated as proposing an EA based fuzzy PID speed control algorithm to generate the q- axis reference current command i qsd for the system model. Parameter values are represented in Equation (6). Figure 2: Block diagram of field oriented PMSM control system IV. PID CONTROLLER The PID term refers, P for the proportional term, I for the integral term and D for the derivative term in the controller. Appropriately varying of these parameters will improve the performance of the plant, reduce the overshoot, eliminate steady state error and improve the stability of the system. The main problem of that simple controller is the correct selection of the PID gains. Using the fixed gains, the controller may not provide the required control performance, when there is a variation in the plant parameters and operating conditions. Therefore, the tuning process must be performed to insure that the controller can compact with the variations in the plant. Because most PID controllers are adusted on-site, different types of tuning rules have been proposed in the literature. Using these tuning rules, delicate and fine tuning of PID controllers can be made perfectly. Also, automatic tuning methods have been developed and some of the PID controllers possess on-line automatic tuning capabilities. The PID controller is by far the most common control algorithm. The PID controller is represented in equation (7). Most practical feedback loops are based on PID control or some slight variations of it. Many controllers do not even use derivative action. The PID controllers appear in many different forms, as standalone controllers, they can also be part of a DDC (Direct Digital Control) package or a hierarchical distributed process control system or they are built into embedded systems. The PID controller is, u(t)= k e (t) + k d de/dt (7) where u is the control signal and e is the control error (e = r y). The reference value is also called the set point. The control signal is thus a sum of three terms: the P-term (which is proportional to the error), the I-term ( proportional to the integral of the error),

3 and the D-term (proportional to the derivative of the error). The controller parameters are proportional gain k, integral gain ki and derivative gain kd. The controller can also be parameterized as represented in equation (8). u(t)= k(e(t) + T d ) (8) where Ti is called integral time and Td derivative time. The proportional part acts on the present value of the error, the integral represent an average of past errors and the derivative can be interpreted as a prediction of future error. An effect of coefficients is shown in Table I. Table 1: EFFECTS OF COEFFICIENTS Speed of Parameter Stability Accuracy Response increasing K p increases deteriorate improves increasing K i decreases deteriorate improves increasing K d increases improves no impact V. P CONTROLLER P controller is widely used in first order processes with single energy storage to stabilize the unstable process. The purpose of the P controller is to decrease the steady state error of the system. As the proportional gain factor K p increases, the steady state error of the system decreases. However, despite the reduction, P control can never manage to wipe out the steady state error of the system. By increasing the proportional gain, it provides smaller amplitude and phase margin, fast dynamics satisfying wider frequency band and larger sensitivity to the noise. The output never reaches the steady state error. Where the process and the controller have transfer functions C(s) and P(s). The transfer function from reference to output is represented in equation (9). (9) The steady state gain with proportional control C(s) = k is given in equation (10). (10) The steady state error for a unit step is 1/(1+kP(0). The error decreases with increasing gain, but the system also becomes more oscillatory. To avoid a steady state error, the proportional controller can be change to u(t) = Ke(t) + ub. P controller is used only when system is acceptable to a constant steady state error. In addition, it can be easily found that applying P controller decreases the rise time and after a certain value of reduction on the steady state error, increasing Kp only leads to overshoot of the system response. P control also causes oscillation if suitably aggressive in the presence of lags or dead time. The more lags (higher order), the more problem it leads. Plus, it directly amplifies process noise. VI. I CONTROLLER Integral action guarantees that the output process agrees with the reference in steady state. This can be shown in equation (11). Assume that the system is in steady state with a constant control signal (u0) and a constant error 0. U 0 = ke 0 + kie 0 t. (11) The left hand side is constant but the right hand side is a function of t. We thus have a contradiction and e0 must be zero. Notice that in this argument the only assumption made is that there exists a steady state. Nothing specific is said about the process, it can for example be nonlinear. The following equation (12) and (13) gives nonlinear examples. u = u (12) Solving for u gives, u = k + (13) which is transfer function of a PI controller. The proportional gain is constant, k = 1, and the integral gain is changed. The case ki = 0 corresponds to pure proportional control; with a steady state error is 50%. The steady state error is removed when integral gain k i is increased. The response creeps slowly towards the reference for small values of k i. The approach is faster for larger integral gains and the system also becomes more oscillatory. VII. D CONTROLLER The need of using a derivative gain component in addition to the PI controller is to eliminate the overshoot and the oscillations taking place in the output response of the system. One of the main advantages of the PID controller is that it may be used with higher order processes including more than single energy storage. derivative action can improve the closed-loop system stability. The input-output relation of a controller with proportional and derivative action is represented in equation (14). u(t)= k e (t) + k d )= ke p (t) (14) where T d = k d /d is the derivative time. The PID controller transfer function with a filtered derivative is represented in equation (15). C(s) = K(1+ ) (15) VIII. EVOLUTIONARY ALGORITHM (EA) The Evolutionary (Genetic) Algorithm is an optimization algorithm is used to search for optimal solutions to a problem. This algorithm executes on a population of potential solutions applying the principle of survival of the fittest to produce best approximations to a solution. Evolutionary algorithms provide a universal optimization technique that emulates the type of genetic adaptation occurs in natural evolution. Unlike specialized methods designed for particular types of optimization goals, they need no particular knowledge about the problem structure other than the obective function itself. In each iteration step, a new set of approximations is assumed by the process of selecting individuals according to their stage of fitness in the problem domain and breeding them together using operators, such as mutation, crossover and selection, getting from natural genetics in order to generate the new generations. EA s are used to autotune the Artificial Bee Colony(ABC) PID Parameters. The EA based Fuzzy PID controller provides better transient performances and the instability and steady state errors are overcome by using this method. The above steps imply that the maximum generation number, the population size, crossover rate, mutation rate are the essential parameters of an Evolutionary algorithm. Evolutionary algorithm is used to autotune the Artificial Bee Colony (ABC) PID parameters which is represented in following steps. A. Encoding/Decoding of Chromosome B. Initialization C. Fitness Function and Selection

4 D. Crossover E. Mutation F. Stopping Criteria XI.ARTIFICIAL BEE COLONY ALGORITHM (ABC) The ABC algorithm like swarm based, meta-heuristic algorithm based on foraging character of honey bee colonies. The method is consisting of three important elements: employed and unemployed foragers, and food sources. The employed and unemployed foragers are the first two elements and the third element is the rich food sources close to their hive. The two leading modes of characters are also described by the model. These characters are necessary for self organization and collective intelligence and recruitment of forager bees to rich food sources, resulting into positive feedback and simultaneously, the reection of poor sources by foragers, which causes the negative feedback. The ABC basically of three groups of artificial bees: employed foragers, onlookers and scouts. The employed bees comprise the first half of the colony though the second half comprises of the onlookers. The employed bees are linked to particular food sources or the number of employed bees is equal to the number of food sources for the hive. The onlookers watch the dance of the employed bees inside the hive, to select a food source, whereas randomly scouts search for new food sources. Analogously in the optimization context, the number of food sources in ABC algorithm, is equivalent to the number of solutions in the population. Further, the position of a food source connotes the position of a promising solution to the optimization problem, whereas the quality of nectar of a food source gives the fitness cost (quality) of the associated solution. The search cycle of ABC consists of three rules: (i) sending the employed bees to a food source and finding the nectar quality; (ii) onlookers selecting the food sources after obtaining information from employed bees and finding the nectar quality; (iii) calculating the scout bees and sending them into correct possible food sources. Randomly the positions of the food sources are selected by the bees at the stating stage and their nectar qualities are measured. Then the employed bees discuss the nectar information of the sources with the bees waiting at the dance area within the hive. After discussing this information, each employed bee returns to the food source visited during the previous cycle, since the position of the food source had been retained and then selects another food source using its visual information in the neighborhood area of the present one. At the last stage, an onlooker uses the information obtained from the employed bees at the dance range to choose a food source. The probability for the food sources to be selected increases with increase in its nectar quality. Thusly, the employed bee with information of a food source with the highest nectar quality initiates the onlookers to that source. It in this way chooses another food source in the neighborhood of the one currently in her memory based on visual information. A new food source is randomly produced by a scout bee to supplant the one abandoned by the onlooker bees. X. PROCEDURE OF ABC ALGORITHM A. Initialization Optimization problem could be formulated as, represented in equation in (16). min f ( x) { x x X} subected to g( x) 0, h( x) 0 (16) f(x)= obective function to be minimized x=set of decision variable X= is the possible range for each decision variable, where X = {X 1, X 2,..., X N } N represents the number of decision variables and, g(x) and h(x) are the inequality and equality constraints, respectively. B. Initialization of the Food Source Memory (FSM): The Food Source Memory (FSM) is an augmented matrix of size SN*N comprised in each row, a vector representing a food source is given in following matrix (17). Each vector is generated as follows (18): x1 (1) x1 (2) x1 ( N) f ( x1 ) x2 (1) x2 (2) x2 ( N) f ( x2) FSM (17) xsn (1) xsn (2) xsn ( N) f ( xsn ) r= random number between 0 and 1, SN=population size, LB i and UB i are the lower and upper bound values for the variable x i. x ( i) LBi ( UBi LBi ) * r (18) (1, 2..., SN ), (1, 2..., SN ) C. Assigning employed Bees to the food sources In this step, each employee bee is assigned to its food source and in turn, a new one is generated from its neighbouring solution, using following equation (19). x ' ( i) x ( i) r( x ( i) xk ( i)) (19) k (1,2..., SN), k and r (0,1) D. Sending the onlooker bees The fittest food source is selected by the onlooker, using Roulette Wheel selection mechanism. For each employed bee a selection probability p as follows (20): p SN k1 f ( x ) f ( x ) k (20) E. Sending the Scout to search for possible new food sources. XI. SIMULATION RESULTS Figure 3 illuminates the block diagram of the proposed EA based ABC PID controller. The DC supply is given to the inverter. The output from the inverter (i.e. three phase AC supply) is connected with Permanent Magnet Synchronous Motor (PMSM). The current feedback from the motor is given to the dq transformation block. The speed feedback is given to the Proposed EA based ABC PID controller. The output from, both dq transformation block and Proposed EA based ABC PID controller is given to the PI current controller. The SVPWM block which generates PWM pulses for inverter. The simulation result for both conventional method and ABC based evolutionary PID controller shown in following waveforms.

5 The torque is varied from +20 NM to -20 NM which is shown in Figure 8. The fluctuations in torque is also reduced by using the EA based ABC PID controller. Figure 3: Block Diagram of EA Based Artificial Bee Colony (ABC) PID Controller Figure 9: Back EMF Waveform The Back EMF waveform for PMSM is varied from +200V to -200V which is obtained by using the EA based ABC method is shown in Figure 9. Figure 4: Pulse Width Waveform Pulse width for each phase is shown in Figure 4. It shows the changes in width of the pulses with respect to amplitude and time of the pulses. Figure 5: Speed Waveform for PMSM EA based Fuzzy PID controller is used for controlling the speed of PMSM. The set speed is 1500 rpm. By using the EA based Fuzzy PID controller the speed is obtained as 1488 rpm which is depicted in Figure 5. Figure 6: Speed Waveform for PMSM EA based ABC PID controller is used for controlling the speed of PMSM. The set speed is 1500 rpm. By using the EA based ABC PID controller the speed is obtained as 1500 rpm which is depicted in Figure 6. Figure 7: Torque Waveform for PMSM The torque is varied from +20 N-M to -20 N-M which is shown in Figure 7. The fluctuations in torque is also reduced by using the EA based Fuzzy PID controller. Figure 8: Torque Waveform for PMSM Figure 10: Waveform for Stator Current Figure 10 shows the Stator current characteristics of PMSM with respect to time. The stator current is varied from +4A to -4A with respect to time. XII. CONCLUSION In this work, a new Evolutionary Algorithm based ABC PID controller for PMSM drives is proposed. Based on the common control engineering knowledge that the transient responses can be improved if the P and I gains are increased and the D gain is decreased at the beginning, an ABC PID controller design method was developed. An EA to autotune the ABC PID control parameters were also presented. Simulink models were developed in MATLAB 2013a with the EA based ABC PID controller and the speed control of PMSM motor. The main advantage is control the speed of the PMSM motor is to increase the dynamic performance and gives good stabilization. The results shows that, the proposed control technique gives better performance as the motor torque and speed control is better than that of the conventional type the feedback based modulation technique was rearranged by carrier based space vector modulation at the expense of simplicity lost and partially of inferior quality dynamics. The proposed EA based ABC PID Controller can be implemented in real time without any concern about instability problems that leads to system damage (or) failure. EA based ABC PID speed controller has been designed effectively for closed loop operation of the PMSM drive system so that the motor runs at the commanded or reference speed. The simulated system has a quick response with practically zero steady state error thus validating the design method of the speed controller. REFERENCES 1. Bose BK (1993), Power electronics and motion controltechnology status and recent trends, IEEE Trans Ind. Appl. 29(5): Vas P (1998), Sensor less Vector and Direct Torque Control, 1stedn, Oxford University Press, Oxford. 3. Leonhard W (1986), Microcomputer control of high dynamic performance ac drives - a survey, Automatic 22(1): Slotine JJ & Li W (1991), Applied nonlinear control, Pearson Education, Englewood Cliffs. 5. Astrom KJ, Hugglund T (2001), The future of PID Control, Eng. Pract. 9:

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