Research On Sliding-mode Control Of Nonlinear Uncertain Discrete Time Systems With Time-varying Delay

As we all know,sliding mode variable structure control has strong robustness to uncertain factors such as internal parameter uncertainty and external interference.Therefore,this method has been one of the research hotspots in the field of control since it was proposed in the 1950 s.Sliding-mode control has been widely used and studied in continuous systems.At the same time,with the development and application of computer technology,sliding-mode control in discrete time systems has been paid more and more attention.Due to the limitations of the adoption process,there is generally no ideal sliding mode.So it is not guaranteed that the sliding mode is accurately reachable.Therefore,the characteristics,existence conditions and accessibility conditions of the discrete sliding mode are completely different from the continuous case.In addition,there are various uncertain factors unavoidable in the actual application system such as time-varying time lag,nonlinear interference,actuator failure and so on,which will also affect the performance of the control system,and may even lead to system instability.The research on the sliding mode control method of nonlinear uncertain discrete time-varying time-delay systems has very important theoretical value and practical significance.The main research work of this paper is summarized as follows:The first chapter,on the basis of searching and studying many excellent documents,first introduces the research background and significance of the paper,then introduces the status of sliding mode variable structure control,and summarizes the main research directions of the discrete-time system sliding mode variable structure control,integral sliding mode variable mode control,sliding mode reliable control of structural actuator failure and other sliding mode variable structure control.The second chapter mainly introduces the basic knowledge and related lemma.First of all it introduced the fundamental knowledge of sliding mode variable structure control theory,then discusses the steps and sliding mode surface of sliding mode control design method,and then introduces the discrete sliding mode control principle,the existence conditions,accessibility and design method.Finally it also introduces the Lyapunov stability theory and linear matrix inequality(LMI)theory and related lemma.For the sliding mode control problem of a class of nonlinear uncertain discretetime-varying time-delay systems,a state observer is constructed to estimate the state of the system under study,and an integrated sliding mode surface is designed based on the estimated state to make the entire dynamic process completely robust with the external disturbances in the third chapter.By using Lyapunov stability theory and linear matrix inequality(LMI)technique,sufficient conditions for the asymptotic stability of sliding mode dynamic systems are given.A corresponding sliding mode controller is designed,and a saturation function is introduced into the controller to eliminate the chattering of the system,and simulation examples are used to verify the effectiveness of the proposed method.In the fourth chapter,for a class of nonlinear uncertain discrete time-delay systems reliable sliding mode control problems that the actuators may be down conditions,the expression of actuator failure model is given,integral sliding mode surface and sliding mode control are designed.Based on the Lyapunov stability theory and linear matrix inequality(LMI)technique,the sufficient conditions for the robust stability of the sliding mode dynamic system gradually is given.It is proved that the designed sliding mode control scheme can guarantee the accessibility of the sliding mode under the influence of actuator fault.Finally,the main research work of this paper is summarized,and further research direction is proposed.