Research On Adaptive Sliding Mode Control Of Uncertain Systems Based On Barrier Function

In actual industrial production,the system is often affected by uncertain factors such as unknown external disturbances and system internal changing parameter.In this context,how to control the uncertain system has always been one of the important research directions in the field of control.There always has some errors between the actual system and the mathematical model obtained by modeling.The errors are caused by unknown external disturbances and system dynamics that cannot be modeled.Sliding mode control is one of the important methods of contemporary control theory.Due to its relatively simple implementation method and strong robustness to uncertainty and disturbances,it has been extensively studied,and many eye-catching results have been obtained.Equipment manufacturing,power grids,motor control and many other fields have universal applications.Traditional sliding mode control methods often need to assume that the upper bound information of the interference and the upper bound information of the derivative of the disturbances are known.However,the magnitude of the parameter uncertainty and the magnitude of the disturbance boundary of the actual system are often unknown,which is to a large extent.The above limits the practical application of the sliding mode control method.For this reason,this paper will carry out research work on nonlinear systems with unknown or partly unknown upper bound information of model uncertain parameters and disturbance upper bound information,and merge adaptive control,barrier function and sliding mode control methods to obtain a barrier function-based.The adaptive sliding mode control law.The main content and innovations of the article are as follows:Firstly,considering the n-th order nonlinear system with uncertain model parameters,the sliding mode control method of the nonlinear system where the uncertain parameters and the boundary of the disturbance are partly unknown are studied.Select sliding variables,design an adaptive sliding mode control law based on barrier functions to compensate for unknown external disturbances and system uncertain parameters,and use the Lyapunov stability criterion to prove that the sliding mode variables asymptotically and stably converge to the preset neighborhood.Secondly,considering the nonlinear system with unknown control direction,the control method of the nonlinear system with unknown parameter boundary size and unknown control direction is explored.The hyperplane is introduced,and an adaptive Super-Twisting control law based on the barrier function is designed to control the system state.Through the hyperplane convergence to a constant,it is indirectly obtained that the sliding mode variable asymptotically converges to the preset neighborhood,and then Lyapunov is used for stability.The criterion verifies that the control law meets the preset requirements.Thirdly,considering nonlinear systems with model uncertain parameters,the sliding mode control of nonlinear systems with unknown model parameters and disturbances is studied.The adaptive sliding mode control law and the Super-Twisting control law based on barrier functions are designed to control the system state,and the concept of "fixed convergence time" is introduced.When the time is greater than the "fixed convergence time",the sliding mode variable converges stably to the preset value.Set within the neighborhood and will not exceed.Finally,according to the Lyapunov stability criterion,it is proved that the control law can make the system asymptotically converge.The above work content has the following innovations: the adaptive sliding mode control law based on the barrier function does not need to assume that the upper bound information of the system uncertainty and disturbances is known,and does not need to use a low-pass filter;the sliding mode variable is limited Time converges within a preset zero neighborhood and no longer exceeds it,and the size of this neighborhood is not affected by the boundary information of interference and system uncertainty;the control gain parameter of the proposed control law will not be overestimated,This largely avoids chattering.