Algorithm Research Of Exponential Sliding Mode Reaching Law For Discrete-time Uncertain System

The main content of this paper is to introduce two discrete sliding mode reaching laws applicable to different control system types.One of the discrete sliding mode reaching law is to employ an exponential term(1-e^{-log2（1+s（k））}in the sliding mode controller gain.Since the controller gain is the function of the sliding mode variable s（k）,the controlled system can adapt to the change of the sliding mode variable.When the system trajectories enter into the boundary layer of the sliding mode switching surface,the proposed new discrete sliding mode reaching law can make the system trajectories move smoothly around the sliding mode hyper-plane until the system trajectories reach the equilibrium point.The control algorithm has higher control performance for the case which change rate of the system disturbance is slow,but the control performance is suppressed for the case which the disturbance change rate is fast.However,most of the early proposed sliding mode reaching laws are based on the assumption that the rate of change of external disturbance is slow,but this situation rarely occurs in the actual control system.In order to solve the above problems,the fourth chapter of this paper proposes a piecewise discrete exponential sliding mode reaching law,this piecewise discrete sliding mode reaching law consists of two parts.When the system trajectories are far away from the sliding mode switching boundary layer,the traditional exponential sliding mode reaching law with sign function is employed.,the aim of this is to make the system trajectories reach the sliding mode hyperplane as fast as possible;when the system trajectory reaches the sliding mode switching boundary layer,the sign function in the sliding mode reaching law is replaced by the tangent function.The biggest advantage of the improvement is that the approaching rate of the system trajectories decreases as the system trajectories approach the sliding mode hyperplane.When system trajectories reaching the sliding mode hyperplane,the approach rate is zero,which greatly suppress the chattering of discrete system trajectory in the sliding mode hyperplane.Especially in the case of change rate of disturbance is fast,the chattering will be aggravated.The above theoretical results were verified by simulation experiments.The above two discrete sliding mode reaching laws are rigorously mathematically proven,and they all enable the system to satisfy the sliding mode approaching conditions.In the fifth chapter of this paper,the discrete sliding mode reaching law of the third chapter is applied to the permanent magnet synchronous motor speed control system.By comparing with the simulation results of other sliding mode reaching law algorithms,it is found that the permanent magnet synchronous motor control system utilizes the discrete sliding mode approach law proposed in this paper has better system performance.