An Optimal PID Controller for Linear Servo-System Using RBF Neural Networks

Abstract

An optimal PID controller using radical basis function (RBF) for the so-called direct-drive permanent magnet linear synchronous motor (PMSM) is proposed in this paper. The control system is designed using two neural networks. One neural network with single neuron is used for the realization of the PID controller; the other three-layered RBF neural network is used to identify PMSM system to provide the sensitivity information to the neural controller. Also, to guarantee the stability and tracking performance of the control system, a modified gradient descendent (MGD) method for the weights tuning of the neural controller is derived with the introduction of a modified optimal quadric performance index. Thus, the proposed control scheme is capable of reconciling the conflict between the tracking performance and anti-disturbance ability of controller for the linear servo system. Finally, the simulation validation results have shown that the proposed method presents a good tracking performance and satisfactory robustness against the parametric variation and ambient disturbances. use of the neural networks for the control of the permanent magnet linear synchronous motor (PMSM) servo system. Ref. (4) proposed a RBF neural network controller in parallel with a fixed parameter PID controller to compensate the drastic changes of the system function. Ref. (7) studied the application of the neural networks for the control of the PWSM speed and position with the introduced estimation algorithm. In this paper, two neural networks have been implemented for the identification of the servo-motor and the adaptive controller respectively. The neural controller with single neuron acts as an adaptive PID controller to combat the insufficiency of the traditional PID controller in controlling the system when subject to the environmental uncertainties. Subsequently, a modified optimal quadratic performance index is introduced for the stability analysis to derive the update laws for the parameters of the controller. The paper is organized as follows. Section II states the control scheme for the direct-drive PMSM servo system. Section III gives the structure of the concerned neural identification model for the serve system. Then in section IV, the optimal PID controller using the RBF neural networks is proposed and the stability is analyzed. Then section V gives the simulation validation results of applying the proposed approach to a PMSM. Finally, the concluding remark is summarized in section VI.