Sliding Mode Control And Stability For Nonlinear Systems

In engineering practice,mathematical models of controlled objects are often inadequate or inaccurate.Moreover,actual systems are usually inevitably affected by the time delay,parameter changes,uncertainties and external interference,which makes the analysis of systems more complicated.Sliding mode control,with its unique robustness to parameter changes and the external disturbances,and its invariance to parameter uncertainties has shown strong power in handling control problem of nonlinear systems.It provides a convenient and effective method for the robust design of nonlinear systems with uncertainties,time delay,and external interference.Therefore,this paper focuses on the sliding mode control of nonlinear systems and studies its sliding mode control problems and stability for different types of nonlinear systems.Finally,the sliding mode control method designed in this paper is applied to the RLC circuit system,the inverted pendulum system,and the DC motor system,and the design method of the optimal sliding mode controller based on performance indicator for active suspension system is given.The simulation results show that the control effect is good.The main achievements of this paper are as follows.1)The sliding mode control problem for nonlinear systems with the time-varying delay,parameter uncertainties,Markov switching and Lévy noise is considered.Lévy noise with Poisson point process with jumps is introduced on the basis of conventional continuous Brownian noise.Combined with the adaptive control method,the known upper bound of the nonlinear function is removed.Furthermore,based on the Lyapunov stability theory,the adaptive sliding mode controller is designed to ensure the mean square exponential stability of the closed-loop system.2)The sliding mode control problem for nonlinear systems with the time-varying delay is discussed.The adjustable parameter is introduced to remove the constraint of the upper bound of the derivative of the time-varying delay.Based on the Lyapunov stability theory,the sliding mode controller is designed to make the closed-loop system asymptotically stable.At the same time,by restoring to double-integral calculations,the integral mean-value theorem and the zero-point existence theorem,the process of further converting the global asymptotic stability conditions into the global mean square exponential stability conditions is given.3)The sliding mode control problem for nonlinear systems with Markov switching,mode-dependent time-varying delay,and stochastic noise is investigated.Based on the concept of the It?process,the stochastic sliding surface is introduced to remove the conventional assumption imposed on the system.Furthermore,based on the Lyapunov stability theory,the sliding mode controller is designed to make the mean square exponential stability of the closed-loop system.4)The application research and the design of sliding mode controller are carried out for the four types of practical systems of RLC circuit system,inverted pendulum system,DC motor system and active suspension system.First,the sliding mode control design methods of Chapters 2,3,and 4 are applied to the circuit system,the inverted pendulum system,and the DC motor system,respectively.Finally,the design method of the optimal sliding mode controller based on H_? performance index is given for the active suspension system.