Research On Sliding Mode Control Theory And Application In Nonlinear Systems

The sliding mode control(SMC)theory has gained broad attention and research because of its significant robustness.Compared to the conventional sliding mode method,the terminal sliding mode(TSM)and higher-order sliding mode(HOSM)methods have more advantages,such as convergence time,relative order restriction,and chattering attenuation.Their theoretical systems have been preliminarily established,but some issues still need further study,for example,the application of TSM control in certain nonlinear systems,and the adaptive method of super-twisting algorithm(STA).In this research,the robust and adaptive control of these methods are studied,and they are applied to some nonlinear systems,such as robots and aircrafts.The research work and innovation points mainly include the following aspects:(1)The boundary layer approach was used to reduce the chattering of nonsingular TSM(NTSM)control.The ultimate bound estimation of sliding mode was given through the convergence analysis,which was more accurate than the range of boundary layer.The numerical simulation show the validity of the theoretical estimation.(2)The robust and adaptive NTSM control was developed for a class of second-order uncertain systems in which the input coefficient was unknown(except the bound information).First,a new fast NTSM was designed.It improves the performance of sliding surface and avoids the singularity problem.Second,a robust NTSM controller was designed,which extended the application of NTSM control.Then,an adaptive control scheme with double sliding modes was designed to combine the NTSM control with adaptive technique.Finally,the effectiveness of the robust controller and adaptive control scheme was verified through a variable length inverted pendulum model.(3)The TSM control was developed for a class of uncertain systems with input nonlinearity.The affection of system uncertainties and input nonlinearity was compensated simultaneously.First,fast TSM controllers were designed for first-order and second-order uncertain systems with dead zone and sector nonlinearity.Second,a fast TSM controller was given for a class of first-order systems with dead zone and saturation.The stability of closed-loop system was guaranteed under the limited input.Finally,the validity of proposed controllers was confirmed by numerical examples and a dynamic model of aircraft.(4)The robust control issue of a second-order sliding mode algorithm based on finite-time Lyapunov stability was studied to enhance its robustness against system uncertainties.A TSM disturbance observer and an adaptive first-order sliding mode compensator were designed for this algorithm.The proposed method was applied to trajectory tracking control of a wheeled mobile robot.The stability and robustness of closed-loop system were guaranteed under parameter perturbation and external disturbances.(5)The parameters selection and adaptive method of STA were studied.First,a new parameter domain was obtained through the Lyapunov function analysis.Furthermore,a nonlinear adaptive law was proposed to improve the transient performance,in which the gain adjusting rate was affected by the system state.Second,the adaptive law was modified to provide non-overestimated control gain in the whole control process.The high peak of control gain is avoided,and the input amplitude is also reduced.Finally,simulation analysis was carried on numerical examples and a two-link robot manipulator model.