Mathematical Problems in Engineering

Volume 2016, Article ID 9724917, 9 pages

http://dx.doi.org/10.1155/2016/9724917

## A Hybrid Wavelet Fuzzy Neural Network and Switching Particle Swarm Optimization Algorithm for AC Servo System

Department of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing 210094, China

Received 6 May 2016; Revised 4 October 2016; Accepted 3 November 2016

Academic Editor: Andrea L. Facci

Copyright © 2016 Run-min Hou et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

A hybrid computational intelligent approach which combines wavelet fuzzy neural network (WFNN) with switching particle swarm optimization (SPSO) algorithm is proposed to control the nonlinearity, wide variation in loads, time variation, and uncertain disturbance of the high-power AC servo system. The WFNN method integrated wavelet transforms with fuzzy rules and is proposed to achieve precise positioning control of the AC servo system. As the WFNN controller, the back-propagation method is used for the online learning algorithm. Moreover, the SPSO is proposed to adapt the learning rates of the WFNN online, where the velocity updating equation is according to a Markov chain, which makes it easy to jump the local minimum, and acceleration coefficients are dependent on mode switching. Furthermore, the stability of the closed loop system is guaranteed by using the Lyapunov method. The results of the simulation and the prototype test prove that the proposed approach can improve the steady-state performance and possess strong robustness to both parameter perturbation and load disturbance.

#### 1. Introduction

In the recent years, with the advancement of technology, AC servo system has been widely used. As a servo drive system, it needs not only a good steady-state performance, but also a high dynamic performance. As a controlled object, the dynamic mathematical model of a high-power AC motor is a complex system, which is characterized by heavy varying load, slow time variation, nonlinearity, and uncertain disturbance. Traditional control algorithm adopts PID control, easily influenced by the model of nonlinear characteristics and the parameters such as the uncertainty of dynamic response and the unbalance of antidisturbance ability, which may deteriorate the system control performance. Thus, the practical intelligent control strategy has become a focus in the field of servo system control [1].

As neural networks may approach any nonlinear function, they have already been widely utilized in the modeling of nonlinear systems and have advantages of easy realization and learning capability [2, 3]. Some scholars [4, 5] construct the motor servo system model by using neural network and obtain the conclusion that the application accuracy of the neural network in the identification of nonlinear systems is higher than that of the linear system. However, in the neural network, the sigmoid function is used as the activation function of BP neural network, which leads to the result that the BP neural network is easy to get into local minimum, slow convergence speed, and difficult to understand the mapping rules which make it impossible to be used in real-time tasks. Fuzzy logic uses human-like reasoning and expert knowledge to model complex and uncertain systems [6, 7]. Some researchers have proposed various structures for modeling and controlling of nonlinear systems [8, 9]. Reference [10] uses fuzzy control and has the ability to deal with the uncertainty of self-learning ability of the neural network by combining fuzzy neural network and its application in the controller of a servo motor, which effectively improves the robustness of the system and does not require accurate mathematical model of the controlled object. The main features are as follows: (1) the use of fuzzy neural network tuning fuzzy membership functions; (2) the inference rules of logic systems; (3) the use of construction in the form of inference rules propagation network structure to realize the benefits of functional complementarily. However, in the common conditions, these parameters learning algorithm require presetting fuzzy system topology.

As an alternative, wavelet neural network is a feed-forward network based on wavelet analysis, effectively combining the structural model of neural network, and the determination of the entire network structure has a reliable theoretical basis and thereby avoids the blindness of the structural design. Many researchers have proposed wavelet fuzzy neural network (WFNN) combining wavelet theory with fuzzy neural network (FNN) [11–14]. In WFNN, each fuzzy rule corresponds to sub-WNN, and the approximation accuracy of the WFNN can be improved greatly by learning the setting parameters of wavelet and fuzzy [15]. Although the WNN has been successfully applied in nonlinear system, some challenging issues still exist, such as how to optimize the structure of WNN.

Particle swarm optimization (PSO) algorithm is a global optimization algorithm, through collaboration and competition between individuals to find the optimal solution, and particle swarm optimization search process is started from the entire group, with the implicit parallel search features to improve the performance of the algorithm [16]. However, the PSO algorithm has some disadvantages such as easily falling into local minima and slow convergence speed. In order to overcome these drawbacks, a new SPSO algorithm is proposed to train the FWNN in this paper. The SPSO algorithm [17, 18] has been using velocity updating equation with Markovian switching parameters to overcome the contradiction between the local search and the global search. The proposed SPSO algorithm can not only avoid the local search stagnating in a local area but also lead the swarm to move to a more potential area quickly. Therefore, the SPSO algorithm can greatly improve the ability of WNN and global search.

In this study, in order to achieve control over the high-power AC servo system, a WFNN is applied to build the intelligent model and control for this system, which is trained by means of learning rate with using SPSO algorithm. The convergence rate is greatly accelerated, and the local optimum is avoided. Finally, simulation results illustrating the validity and advantages of the proposed WFNN for the AC servo control system are discussed.

This paper is organized as follows. In Section 2, the servo system is being analyzed. The structure of the fuzzy wavelet neural network (FWNN) and the structure learning and parameter learning algorithms are introduced in Sections 3 and 4. In addition, the design procedures, adaptive learning algorithms, and the stability analysis of the proposed FWNN controller are also described in detail in Section 4. Simulation results are discussed in Sections 5 and 6; last part gives the conclusion of this paper.

#### 2. Modeling AC Servo System

The control structure chart of an AC servo system is presented in Figure 1. Due to the nonlinearity of the motor itself, the nonlinear phase comparison brought by the system load changes is very small, so the derivation of the model makes some assumptions [19]: (a) no saturation effect; (b) motor evenly distributed air gap and magnetic induction EMF sinusoidal shape; (c) excluding the hysteresis and eddy current loss; (d) no rotor excitation winding.