Comperative Performance Analysis of PMSM Drive Using MPSO and ACO Techniques

ABSTRACT


INTRODUCTION
During last two decades, a gradual and noteworthy advancement on Permanent Magnet Synchronous Motor (PMSM) drive front has motivated researchers for Artificial Intelligence (AI) based speed controller designs. PMSM drives have been increasingly applied in a wide variety of industrial and automotive applications. These drives are also used in hybrid electrical vehicles and washing machines due to high power density, improved efficiency, larger torque to inertia ratio and high reliability. The controlling of PMSM drive has undergone remarkable improvements over the passage of time, however, numerouschallenges are yet to be resolved in order to improve the performance of this drive to be practically viable in the current scenario and future commercial applications. As per literature survey, it is found that DC and induction motor drives face various constraints, hence, researchers and manufacturers prefer the PMSM drive over these, Therefore, lot of scope to take initiative is prevalent in this area to design and develop enhanced and compact intelligent PID Speed Controller for PMSM drives [1], [2].
A very effective control system is needed to obtain optimal performance of a PMSM in industry. The Proportional Integral Derivitive (PID) controller is one of the traditional controllers which are widely used in many drive system. But it has sluggish response due to sudden change in load torque and the sensitivity to controller gains (K p , K i and K d ) [3]- [5]. The control effect of PID depends solely on tuning of PID controller. However, finding optimal gain coefficients is cumbersome because of dynamics involved in motor performance and variation of system parameters with time [5]. Traditionally, "trial and error" approach was employed to find appropriate gain values but it is complex, time consuming and does not guarantee optimal solution. Another traditional method is Ziegler-Nichols (Z-N) method which is the most standard method and widely used. But this method is tedious for systems with non-linearities such as PMSM. It provides high overshoot in system response and not suitable to achieve fast dynamic response [6]- [8]. In recent times artificial intelligence (AI) techniques are being adopted for efficient and optimum tuning of PID speed controllers [9]. In this paper, speed of PMSM is controlled with the help of a PID speed controller using AI techniques. The designing of the PID speed controller is treated as an optimization problem, employing MPSO [10]- [17] and Ant Colony Optimization (ACO) [18]- [23] for its solution. In this work tuning of PID controller by using MPSO and ACO technique is implemented to control speed of PMSM. This chapter is arranged in six sections including the current introductory Section 1. The tuning of PID speed controller using MPSO method is discussed in Section 2. Problem formulation of PID controller that has been used in PMSM drive is discussed in Section 3. The tuning of PID speed controller using ACO method is discussed in Section 4. PMSM simulation model and analytical results are validated in Section 5. Finally, a summary of the paper is concluded in Section 6.

METHODOLOGY OF PROPOSED MODIFIED PSO
The Modified PSO technique overcome the demerits of PSO technique [24], it improve the convergence rate and prevent the prematurely condition. When each group is divided, the group which has maximum population at the center is preferred. It shows a particle subgroup as a central subgroup, and the other subgroups are neighborhoods to the central subgroups, it can communicate with other subgroup near to it and other subgroups cannot share the information with each other. By using MPSO technique the information can transmit faster and improving efficiency of the algorithm. Accordingly, the distance of two vectors was obtained by the space posi-tion of each particle. The L max denoted as the maximum distance of any two particles. Meanwhile ||X i (k)-X j (k)||/L max was also calculated. If the ratio is smaller than a certain value then two particles merge into one group, if the ratio is greater than a certain value then they should be divided from the group. Each particle updates its status according to equation (1),(2) as follows [25]: Fitness function is used to evaluate every new position. In MPSO technique, the value of weight w adjust the properly, which prevent algorithm from getting into a local optimization. In the further stage, small one is propitious to accelerate algorithm converge. This way used is illustrated as follows: k denotes current iterate time; K denotes max iterate time.
The optimized values of PID controller gains are shown in Table 1. Implemented MPSO-PID controller is described in flowchart as shown in Figure 1.

PROBLEM FORMULATION
In this section, the basic concept of the PID controller is explained. The block diagram of the PID speed controller employed in the work is illustrated in Figure 2. The transfer function of the PID speed controller for a continuous system is described by the equation (6) ( ) where K p , K i , K d are proportional, integral and derivative gains respectively of the PID speed controller and N is constant filter coefficient. The gains K p , K i , and K d are generated by ACO algorithm. The schematic block diagram of PMSM drive with PID speed control system used in transient response analysis and parameter extraction is shown in Figure 3. As shown in the Figure 3, the reference speed ω ref is compared with the measured speed ω r and the error signal is fed to the PID speed controller. This compares the actual and reference speed. The output of the controller is transformed dq to abc transformation. Then, that reference current is fed to the PWM inverter to generate the inverter"s command signals. Here the phase current I abc and I ref are given as input. These are compared by using the comparators. The output of the comparators is fed to the motor.
To achieve desired response through control system a cost function is implemented that describes the performance of the system quantitatively. The transient response specifications and performance indices taken into consideration are as follows.

Maximum Overshoot (Mp)
It is the normalized difference between the maximum speed (ω max ) attained by the PMSM and the desired reference speed (ω ref ) of the motor i.e.

Peak Time (t p )
It is the time taken by PMSM to reach the maximum speed (ω max ).

Rise Time (t r )
It is the time taken by the PMSM to raise its speed from 10% to 90% of the desired reference speed.

Settling Time (t s )
It is the time required by PMSM speed to reach and stay within a permissible tolerance band (selected as 0.02%) of the reference speed. (10)

Integral Absolute Error
It is the integral of the absolute magnitude of the error which is given as: Thus summarizing, the cost function (f) is given as: The objective is to minimize this function f, to achieve fast and effective speed control of PMSM.

ANT COLONY OPTIMIZATION ALGORITHM
ACO is defined as a meta-heuristic algorithm derived from the co-operative foraging behaviour of  [18]. The optimization problem to be solved using ACO algorithm is modeled as a graphical problem. Virtual ants traverse the nodes of this graph in search of a minimum cost path. Each ant individually chooses a rather poor-quality path. Better paths are found by co-operation among the entire ant population [19], [20]. The problem of finding optimized values of K p , K i , K d of the PID speed controller is represented as a graphical problem as shown in Figure 4. In this graph K p , K i , K d are represented as three different vectors in which each value of the vector acts as a node of the graph. An ant while traversing the graph must choose three nodes, one from each vector. The choice for a node is made by the ant based on a probabilistic function [17], [18] given in equation (13): h ij : heuristic factor dependent on problem parameters p ij : pheromone factor determining the amount of pheromone deposited at a node α : constant determining relative importance of pheromone value at a node β : constant determining relative importance of heuristic factor at a node S : set of nodes not yet visited by the ant One iteration or tour is completed when all the ants have chosen three nodes, one from each vector. An ant while travelling marks its presence on a node by depositing pheromones. Pheromone deposition is a way of communication between the ants. The pheromone levels at a node are updated after each tour so as to differentiate between good and bad paths i.e. paths with low and high cost respectively. In the proposed algorithm, two fold updating of pheromone is implemented. These are called local and global pheromone updating rule. Local pheromone updating is carried after each ant has completed one tour according to equation (14): p(k) ij : pheromone deposited on path connecting the nodes i and j at the k th tour p : constant pheromone value p pos : positive pheromone updating coefficient C : cost function of the tour traversed by the ant Global pheromone updating is implemented after completion of a tour by all the ants of the colony. According to this rule the pheromone of the best and worst tours paths are updated as follows: Global pheromone updating is carried out to avoid early convergence due to ants being trapped in local minima, and allowing ants to continue searching in new directions. The ACO algorithm applied to design an optimal PID speed controller for PMSM is as follows ( Figure 5): Step 1: Initialization Number of ants k in the colony are initialized at the start node. Number of tours m and values of p, p pos , p neg and λ are also set. A gain matrix with three columns one for each of the gain parameter K p , K i and K d is also constructed. For: number of tours = 1 to m For: number of ants = 1 to k Step 2: Choice of nodes Ants traverse the gain matrix and choose the values of K p , K i and K d with maximum pheromone level according to equation (13).
Step 3: Calculation of cost of tour Cost of the tour traversed by an ant is calculated according to the cost function given in equation (12).
Step 4: Local pheromone updating Local pheromone updating is carried out according to equation (14) until maximum ant count has been reached. Steps 2 to 4 are repeated out until maximum ant count is reached.
Step 5: Global pheromone updating Once maximum ant count is reached, best tour having lowest cost and worst tour having highest cost is chosen. Pheromone of best tour nodes is increased while that of worst tour nodes is decreased according to equations (15)- (17). Steps 2 to 5 are repeated until maximum tour count is reached.

MODEL OF PMSM AND RESULTS
The reference speed of the PMSM is chosen as 1000 rpm and step function applied for load torque with simulation time of 0.5 seconds. The values of gain parameters obtained from classical Z-N method, MPSO and ACO method are tabulated in Table 1 and 2. The model for speed control of PMSM is as shown in Figure 6. Matlab R2013a is used for simulation of the model.  Figure 6. Model of PMSM The motor speed is compared with reference speed by the comparator and the output is fed to the PID controller. These controllers improve the transient response. The output of controller is fed to the dq to abc transformation by using inverse park"s transformation. The inverter circuit is fed by the dq to abc transformation. The output of inverter circuit is fed to PMSM. The output of PMSM is taken with the help of bus-selector. The Rotor speed is fed back to the comparator to achieve the desired speed which is required. The simulation is carried out under the different operating conditions such as starting, braking and load application and removal.

Starting Characteristics
The motor is started at no load with 1000 rpm reference speed. The motor try to attain the reference speed of 1000 rpm. At this instant, the torque reaches it"s no load value (zero Nm) and the stator winding currents settle down to their normal values. The PMSM drive using AI techniques minimized the overshoot and rise time, peak time and settling time is lower when compared to existing Z-N tuned PID speed controller.

Speed Reversal Characteristics
The reference speed is reversed at t = 0.08s to -1000rpm. The rotor speed follows it and tries to attain the reference value. The torque T em also reduces, the speed settles down to its new reference value of -1000 rpm and the torque reverts to the no load value of zero Nm. The current waveforms show a sharp increase in the magnitude with low frequency.

Load Application and Load Removal
When the load is applied at t=0.15s. The rotor speed ω m decreases but with the increased stator winding current and torque. When the load is removed at t=0.35s, the AI techniques responds immediately by decreasing the stator winding current and torque. The speed of the motor changes accordingly by settling down to its reference value.
The results presented above that MPSO and ACO algorithm are much more efficient in speed control of PMSM as compared to the classical Z-N method. MPSO and ACO algorithm has sufficiently suppressed the peak overshoot in speed response of PMSM during starting and speed reversal conditions which was dominant in Z-N tuning method. The sudden drop in electromagnetic torque at the time of application of load has also improved considerably.
The summary of extracted parameters from the sets of inset graphs from Figures 7-15, respectively under starting of the motor, speed reversal, load application and load removal conditions are summarized in Table 3. These parameters are analyzed during the various operating conditions of the Z-N method tuned PID speed controller for PMSM drive.

CONCLUSION
The aim of the work was to design a speed controller for PMSM which has been achieved successfully. The PID speed controller designed provides efficient load disturbance and transient response to the motor as is evident from Table 3. The result obtained from MPSO and ACO techniques has been compared with that derived from classical Z-N technique and have proven to be better than it. The most important feature of this work is that online tuning of PID speed controller has been conducted using MPSO and ACO techniques so that any dynamic conditions of the plant can be reflected immediately in the PID gain parameters. PMSM"s have found wide application in servo robotics industry. PMSM control strategy employing MPSO and ACO can be of immense help in precision control of robots. Moreover, this analysis has also helped in development of new speed controller under various load conditions and techniques for industry applications.  Initial inertial-weight 0.9 w2 Final inertial-weight 0.2 c1 Initial cognitive-parameter 0.5 c2 Final cognitive-parameter 2.5 r1 Initial social-parameter 0.5 r2 Final social-parameter 2.5