Observer-Based Sliding Mode Controller Design For A Class Of Uncertain Nonlinear Systems

The control of nonlinear systems has been a research focus.In the industry systems,there are always uncertain factors that make the system not keeping stable or not reaching the desired target.Therefore,the problems of disturbances for nonlinear system have become more and more important.Sliding mode control has attracted much attention because of superior robustness in dealing with the control problems of uncertain systems.This paper focuses on the control of a class of uncertain nonlinear systems under the influence of disturbances.According to the different characteristics of system states and disturbances,the system is considered into three cases,and different types of sliding mode control methods are designed.The paper proposes a method of sliding mode control with double power reaching law based on disturbance observer when the system states are known.Firstly,a super twisting disturbance observer is designed to estimate the unknown disturbances.Then,combining with the structure of the systems and the estimation of the disturbances,a linear sliding mode surface is adopted,and a double power reaching law sliding mode controller is designed.Finally,the method is applied to the magnetic levitation system.Compared with the traditional sliding mode control,this method does not need the upper bound of the disturbances and has better performance.However,the states of the system are usually unknown,so it is necessary to consider the case of unknown states.When the system states are unknown and the disturbances of each subsystem are linear correlation,an approach of terminal sliding mode control based on reduced order observer is presented.Firstly,a reduced order observer is designed to estimate the states.Secondly,the super twisting observer is used to reconstruct the disturbances.Then,an integral sliding mode surface is designed.Combining with the terminal sliding mode control theory,a terminal sliding mode controller is introduced to make the states moving along the surface.This method can make the system states reaching the sliding mode surface in a finite time.However,it is a harsh condition that the disturbances are linear correlation,so it is worth to investigate the independent disturbances.In the case of unknown states and independent disturbances of each subsystem,this paper also proposes a global terminal sliding mode control method based on sliding mode observer.Firstly,a sliding mode observer is designed to estimate both states and disturbances.Secondly,a global integral sliding mode surface is presented and a global terminal sliding mode surface is employed.Then,combining with the estimations of the system states and the disturbances,a global terminal sliding mode controller is introduced to make states reaching the surface in a finite time.The proposed sliding mode observer has a lower chattering problem than the traditional sliding mode observer,which makes control performance better.