Application of Adaptive PSO and Adaptive Fuzzy Logic Controllers to Speed Control PMSM Motor Servo Systems

Three phases Permanent Magnet Synchronous Motors (PMSM) are non-linear resistors, resistance of stator winding, air gap flux, cross-coupling, saturation variable times and cogging torque in operation. Due to the nonlinear nature of PMSM, it is a challenge to control exactly the speed, torque and position. This paper presents two methods for speed control stabilization of the PMSM using the Adaptive Fuzzy Logic Proportional Integral Derivative controller (AFL-PID) and Adaptive Particle Swarm Optimization Proportional Integral Derivative controller (APSO-PID). The response results of the speed control PMSM Servo Systems use AFLC-PID and APSO-PID methods are compared and the conclusions are given.


Introduction
The Permanent magnet synchronous motors (PMSM) advantages high power factor, high efficiency [1] and large starting torque that it has been widely used in electric vehicles and industrial applications [2].However, PMSM disadvantages are non-linear objects, strong coupling, increasing the difficulty of control.Recent years, there are many researchers to improving ensure the static and dynamic performance of this servo systems motor driver.
Proportional + Integral + Derivative (PID) controllers are widely used in industrial applications to provide optimal and robust performance for stable, unstable, and nonlinear processes [3].In addition, the dynamic performance of the PMSM, especially the response speed, but optimal PID controller is limited by the fixed PID controller parameters [4].The fuzzy control method complementarily has strong robustness and can shorten the response time of system [4].Therefore, Adaptive Fuzzy Logic Controller -PID is applied to speed control systems of PMSM.
The design process of an AFL-PID controller relies on expert experience.The AFL-PID controller is nonlinear and it is scarcely possible to establish accurate mathematical model.So it gets hard to analysis the stability of the system with an AFL-PID controllers [5].But still there are several ways for solving the problem, such as Lyapunov stability theory and circle stability criterion method, etc... PSO algorithm is appropriate for parameter optimization in continuous search space in many dimensions.This method is intended to produce high quality of the solution by shorter time [6].
The drawbacks of these approaches are that they are obscure to understand or complicated implement.The main objectives of this paper are to design an improved AFL-PID and APSO-PID controllers for speed regulation of a PMSM and to validate the controller by simulation.Besides, a novel but simple way to analyse the stability of a system based on both AFL-PID and APSO-PID controllers is proposed and it is used for the PMSM control system.
In this paper, the first it is introduced in Section I.Then, Section II based on the mathematic model of PMSM.After, that the APSO-PID and AFL-PID speed controllers for PMSM motor are develop in Section III and Section IV.Next section V presents simulations compare two methods for speed control of PMSM servo systems driver.Finally, Section VI presented the conclusions of the paper.

Model mathematic of PMSM motor
The PMSM has ability to operate in both motor mode and generation mode depending upon the sign of the mechanical torque.Positive for motor and negative for generator.A second order state space model is used to represent the electrical and mechanical parts of the machine.The model of PMSM has been developed on rotor reference frame using the following assumptions:  Neglecting the saturation. Assuming the induced EMF is sinusoidal in nature  Eddy currents and hysteresis losses are negligible  Field current dynamics are not present.
The equations of PMSM are given [7]: where: Li   and q q q q Li   are the total flux linkages along the d and q axes, respectively, d  and q  are the PM flux linkages along the d and q axes, respectively, and e  is the electrical angular speed.Further, d u and q u are the stator voltages along the d and q axes, respectively, d i and q i are the stator currents along the d and q axes, respectively, R is the stator resistance, d L and q L are the stator inductances along the d and q axes, respectively.It has been further assumed that, since the surface mounted PMSM is nonsalient, d where m  is the mechanical angular speed, J is the inertia, m T is the electromagnetic torque, L T is the load torque and B is the friction coefficient.p is the number of pole pairs.

PSO optimal the parameters PID
PSO algorithm is based upon animal social systems such as birds flocking or fish schooling which is commonly used as an optimization technique.There are several particles donating a set of optimization particles which search for the best solution in a multi-dimensional search space.This algorithm finds the best optimized value for each particle by convergence [8].The optimized value is estimated using some cost function which defines the best value for that fitness function.Each particle has two main parameters: the first is particle position x i and the second is particle velocity v i where i denotes the iteration index.Afterwards the best values, attained from all the particles, combine to get the best value for the whole swarm.For a swarm of N particles traversing a D-dimensional space.After finding the two best values: best known velocity and best known positions, the particles update their velocity and positions based on the following equations [9,10]: where max  and min  are respectively the lower and upper boundaries of the inertia weight  .The argument max iter is the maximum number of iteration and the variable iter is the current iteration.

Adaptive PSO-PID speed controller
This paper proposes the improved Particle Swarm Optimization (PSO) by a careful combination of the original PSO algorithm and the response characteristics.More specifically, the improvements mainly concern three aspects: the first is the constitution of solution components, the second parameter setting based on prior, and the third is evaluation function definition.
Firstly, three controller parameters are defined to compose an individual ( , , ) there are only three members in an individual.Each member is assigned as a real value.If there are n individuals in a population, then a population X can be expressed as the following matrix form.
where the j Secondly, some parameter settings are associated with the prior knowledge extracted: The proportional gain p K can be used for decreasing the rise time and the derivative gain d K can regulate the overshoot and settling time and the integral gain i K contributes to eliminating the steadystate error.The key parameter  in ( 2) is extended from a scalar to a vector, expressed as ( , , )  is fined as a nonlinear piece-wise function: where  and  are thresholds of overshoot and steadystate error, respectively.According to general definitions,  can be defined as 0.25 and  is 0.01.
The inertia weight p  according to the overshoot and steady-state error, where the  = 0.01 and  = 0.25.The argument p  increases non-linearly with ( 1) The position update equation ( 3) is made to minor modifier to meet the requirements of the special cases.

Adaptive fuzzy-PID speed controller PMSM
The block diagram of PMSM speed control system based on an AFL-PID controller is shown in Figure .4.The controller for speed regulation is an AFL-PID controller cascade whose parameters change with the system status, so it can improve the dynamic performance.It contains a conventional PID and a Fuzzy Logic inference system.The design work includes the following aspects: 1) The initial parameters  In addition to the experimental method, the initial parameters of conventional PID can be calculated by the process in literature [11,12].Practically, the results can be directly applied to the control system if a conventional PID is adopted, but they are just initial value for the fuzzy PID.In this paper, the information about PMSM is shown in Table I, p K = 79.0,i K = 3.0, d K = 0.0014.

Design of membership functions
The membership functions of Mamdani Fuzzy controller for input map the normalized speed error ( E ) and error change rate ( C E ) to the membership degree [-3,3], while the membership functions for output play an opposite role.
There are seven linguistic variables, namely Positive Large (PL), Positive Medium (PM), Positive Small (PS), Zero (ZO), Negative Small (NS), Negative Medium (NM), Negative Large (NL).The input membership functions are characterized by that the fuzzy controller becomes less sensitive when the input value is relatively small.In other words, when the speed motor is close to the reference value, the conventional PID parameters remain stable, so that the fluctuation of limited motor speed and the steady-state performance is ensured.
As for the output membership functions, when E and c E keep small, the initial correction value ( ,, Compared with the membership functions adopted in [6], the ones proposed focus on not only the dynamic performance but also the steady-state performance of the system.

Design of fuzzy control rules
Fuzzy control rules, the link between inputs and outputs, which depend on the fundamental knowledge and expert experience are undoubtedly important to a fuzzy controller.
Only by making reasonable fuzzy control rules can good.  3; 3]; The number laws are 49 laws (7x7 = 49 laws).
Performance of the system be guaranteed.According to a large number of experimental results, the fuzzy control rules suited to the system are shown in Table II

Simulation results
The compared adaptive controller by AFL-PID and APSO-PID speed rotor controller are always in the working process of the PMSM servo systems from results Simulation.From "Fig.10" to "Fig.22" and Table III show compared between the AFL-PID and APSO-PID speed controllers.And the results simulation given quality of speed control PMSM servo systems when they were start-up, charge load and discharge load.
The "Fig.10" shows the simulation result of proposed AFL-PID and APSO-PID and PID controllers to speed control of PMSM servo systems.The figure shows the desired speed ( m  ) (set point speed) and the respond speed motor of PID and AFL-PID and APSO-PID controllers in overall: start-up, step increate speed, step discreate speed, charge load, discharge load and reverse rotation motor.The evaluations are given in Table III by the numbers and images in "Fig.11" to "Fig.22" The error speeds of PID and AFL-PID and APSO-PID controllers in "Fig.11" illustrated the APSO-PID controller smaller than AFL-PID, PID controller and AFL-PID smaller than PID controller.And the "Fig.

Simulation results
This paper, the AFL-PID and the APSO-PID algorithms are proposed based on the analysis of the relationships between optimal p K , i K and d K of the PID parameters and response characteristics.The dynamic response information is fully utilized for the search in progress, including the monitoring of the stability for generating the new solution to replace the slow stable ones.The design new update rules of inertia weight with respect to the values; and integrating the new time-domain performance criterion.Through the simulation speed control of the PMSM motor systems driver.The results show that the proposed controller can nearly perform an efficient search for the optimal PID controller parameters in comparison with PID controller and APSO-PID controller and AFL-PID controller.It is clear from the good results that the proposed methods can solve the searching and adaptive control with tuning problems of PID controller parameters more easily and quickly by the improved Fuzzy Logics and PSO methods.The best quality results were APSO-PID speed controller.

Figure 1 .
Figure 1.Block diagram of an Adaptive PSO-PID controller.

Figure 2 .
Figure 2. The Folowchart of the PSO Algorithm optimal Parameters PID.

2 )
Membership functions of fuzzy inference system; 3) Fuzzy control rules; 4) The input scaling factors E, Ec.

EFigure 6 .Figure 9 .
Figure 6.The final correction value p K  , i K  and d K  .In this case, Figure.5 shows illustrative p K  =1, i K  = 1 and d K  = 0.005.
12" shows operator of change and dischange of Torque Load on Rotor PMSM systems Driver from 0 to 30(N.m) to test speed rotor Systems diver.The a I , b I and c I currents stator of PMSM in operated change/dischange Load and increase/descreate speed control servo systems drive when they used PID, AFL-PID and APSO-PID controllers show in the "Fig.14" to "Fig.16".The frequencys and amplitudes, phase angles of a I , b I and c I always change with a values difference in testing systems.

Figure 12 .Figure 13 .
Figure 12.Change and dischange of Torque Load on Rotor PMSM systems Driver.

Figure
Figure 14.,, a b c I I I stator of PMSM use speed control PID.

Figure
Figure 15.,, a b c I I I stator of PMSM use speed control AFL-

Figure
Figure 16.,, a b c I I I stator of PMSM use speed control APSO-

Table 2 .
Fuzzy control rules for

Table 3 .
PID controllers in operation PMSM servo systems shown in the "Fig.21" to "Fig.23".They always change increate or descreate when the system have any change parameters know or unknow of PMSM servo systems driver.The p K , i K and d K of two adaptive controlles show clearly the adaptive with operated systems drive.The quality of AFL-PID and APSO-PID speed controllers for PMSM servo Systems in the cases: start-up, charge load and discharge load.