Sliding Mode Control For Discrete-time System

Variable structure control (VSC) is essentially a special kind of nonlinear feedbackcontrol, reflected in the control of discontinuity. Sliding mode of VSC is easily tocome true in physics and its invariance is well known. The reason is its invariancewhen systems were affected by parameter perturbation and external interference. VSChave been widely used in many applications, such as robots, aircrafts, powergenerator and DC and AC motors and so on. The research on discrete systemsbecomes the main object of study. Chattering is a main obstacle to the application ofVSC of discrete control systems. Therefore the main works is discrete systems. Avariable structure controller is designed, which can weaken the chattering, improvethe control quality, control system close to the origin diminishingly, and make thesystem stable.The main works are summarized as follows:Firstly, the development of sliding mode control and the broad research situationabout VSC for discrete-time system are introduced. The basic definitions, principlesand methods about VSC for discrete-time systems are summarized. The cause of thesystem’s chattering is analyzed and solutions are given.Secondly, the slide mode control problem is considered for a class of time-delaydiscrete-time system. The original discrete system with time-delay is simplified to alinear discrete system without time-delay. A new variable structure control strategy isdesigned for this simplified discrete system. The control algorithm divides the controlprocess into two phases. When the system trajectory is outside of the givenneighborhood, the control law is used to drive the trajectory monotonically toward theswitching surface. When the trajectory is inside the neighborhood, the control lawdrives the trajectory to the switching surface precisely in one step. We focused on thestudy of weakening chattering of discrete system and the control algorithm wasproposed. The variable structure control system designed by using this control lawcan not only reach the switching surface in finite pace, but also can decreasinglyapproach to origin, and the system is stable. The system chattering caused by thediscontinuity of the discrete system is weakened and the system can keep fastreaching speed. The numerical results and simulation examples are given.Thirdly, a class of discrete-time system is considered and a variable structure control design method is proposed. To reduce the chattering of discrete-time slidingmode control, the reaching law is constructed. A variable structure controller isdesigned, which can weaken the chattering, improve the control quality, controlsystem close to the origin diminishingly, and make the system stable. The numericalresults and simulation examples are given.Fourthly, the slide mode control problem is considered for discrete-time systems. Adiscrete reaching law was presented to deal with the flaw which exits in the GAO’sreaching law. The chattering of the reaching law was analyzed, the controller based onthe reaching law is designed and the controller can effectively weaken chattering.