Design and Application of Discrete Sliding Mode Control with RBF Network-based Switching Law

This article proposes a novel approach combining exponential-reaching-law-based equivalent control law with radial basis function (RBF) network-based switching law to strengthen the sliding mode control (SMC) tracking capacity for systems with uncertainties and disturbances. First, SMC discrete equivalent control law is designed on the basis of the nominal model of the system and the adaptive exponential reaching law, and subsequently, stability of the algorithm is analyzed. Second, RBF network is used to form the switching law in a direct and online manner with sliding-mode-related inputs and by approximating evaluation function; and the method to adjust its parameters is devised. Finally, comparable experiments are carried out to verify the application of the proposed approach to an inner-axis driven by a direct current (DC) torque motor through extra-low speed servo for a high precision flight simulator, and the axis works under deteriorating conditions such as periodically fluctuating torques of motor, nonlinear friction, and time-varying model parameters. The results show that the combined SMC can effectively improve the servo performance, for instance, to a stable 0.000 08 (°)/s speed response, the tracking error would be within 0.000 08° in 98% of operating times. Moreover, the hybrid nature of the approach imparts the RBF network the features of removing offline training and ease to set initial parameters.