IEEE TRANSACTIONS ON FUZZY SYSTEMS, VOL. 7, NO. 1, FEBRUARY 1999 41 A Supervisory Fuzzy Neural Network Control System for Tracking Periodic Inputs Faa-Jeng Lin, Member, IEEE, Wen-Jyi Hwang, Member, IEEE, and Rong-Jong Wai Abstract—A supervisory fuzzy neural network (FNN) control system is designed to track periodic reference inputs in this study. The control system is composed of a permanent magnet (PM) synchronous servo motor drive with a supervisory FNN position controller. The supervisory FNN controller comprises a supervisory controller, which is designed to stabilize the system states around a defined bound region and an FNN sliding-mode controller, which combines the advantages of the sliding-mode control with robust characteristics and the FNN with on-line learning ability. The theoretical and stability analyses of the supervisory FNN controller are discussed in detail. Simulation and experimental results show that the proposed control system is robust with regard to plant parameter variations and external load disturbance. Moreover, the advantages of the proposed control system are indicated in comparison with the sliding-mode control system. Index Terms—Fuzzy neural network, periodic inputs, PM syn- chronous servo motor, supervisory control. I. INTRODUCTION T HERE are many control system applications where the tracking of periodic reference inputs are required, e.g., radar tracking and repetitive trajectories tracking of robots. Repetitive control systems with the application of internal model principle [1]–[3] have been shown to function well to track periodic reference inputs. However, a tradeoff between stability and accuracy is necessary for the performance of repetitive control systems [3]. The variable structure control strategy using the sliding mode can offer a number of attractive properties for the tracking of periodic reference inputs, such as insensitivity to parameter variations, external disturbance rejection, and fast dynamic responses [4], [5]. The motion of the sliding-mode control system can be described as two modes: reaching and sliding modes. The reaching mode is the control mode before the states of the system reaching the designed sliding surface and during which there is a control action toward the sliding surface. Once the states of the controlled system enter the sliding mode, the dynamics of the system are determined by the choice of sliding hyperplanes and are independent of uncertainties and external disturbances. On the other hand, the chattering phenomena in the sliding mode due to switching operation will influence the accuracy of tracking performance. Recently, many research results have been accomplished by applying the fuzzy neural network (FNN) systems, which com- Manuscript received September 1, 1997; revised September 14, 1998. The authors are with the Department of Electrical Engineering, Chung Yuan Christian University, Chung Li, 32023 Taiwan. Publisher Item Identifier S 1063-6706(99)01362-4. bine the capability of fuzzy reasoning in handling uncertain information [6]–[8] and the capability of neural networks in learning from processes [9]–[13], in the control fields to deal with nonlinearities and uncertainties of the control systems [8], [14]–[19]. For instance, in Wang [8, ch. 3], the adaptive fuzzy systems (or the FNN’s) are introduced as identifiers for nonlinear dynamic systems based on backpropagation algorithm; Chen and Teng [15] proposed a model reference control structure using an FNN controller, which is trained on-line using an FNN identifier with adaptive learning rates; Zhang and Morris [16] described a technique for the modeling of nonlinear systems using an FNN topology; Jang and Sun [17] reviewed the fundamental and advanced developments in neuro-fuzzy synergisms for modeling and control based on adaptive network; in Lin et al. [19] a PM synchronous servo motor drive with integral-proportional (IP) position controller and an on-line trained FNN controller is introduced. Furthermore, to overcome the mentioned disadvantage of the sliding-mode controller, some techniques have used fuzzy or neural network control techniques [8], [20], [21] to alleviate the chattering phenomena and guarantee the system stability. In this study, a field-oriented control [22], [23] permanent magnet (PM) synchronous servo motor drive [24] with a super- visory FNN controller is designed to track periodic reference inputs of rotor position with robust and accuracy tracking performance. The supervisory FNN controller comprises a supervisory controller [8], [25] and a FNN sliding-mode controller. The supervisory controller is designed so that the system states are stabilized around a defined bound region. The FNN sliding-mode controller combines the advantages of the sliding-mode control with robust characteristics and the FNN with on-line learning ability. The on-line learning algorithm for the FNN is derived according to the sliding condition, i.e., the parameters of the FNN are adjusted in the direction that minimizes the value of where is the switching function. The main advantages of the specific FNN sliding- mode controller are: 1) the ability of on-line training according to sliding condition; (2) the alleviation of the chattering phenomena while maintaining sliding behavior with accurate tracking performance; 3) a structure fuzzy concepts that is easy to understand; and 4) a high degree of robustness and fault tolerance. The FNN sliding-mode controller is chosen to perform the main control action in the supervisory FNN control system. Moreover, the key in the proposed approach is to design the appended supervisory controller [8] to guarantee stability. Therefore, the supervisory controller is chosen to operate in the following supervisory fashion: if the FNN 1063–6706/99$10.00  1999 IEEE