Research On Terminal Sliding Mode Control For Second-Order Nonlinear Uncertain Systems

At present,most of the equipment installed in industrial fields such as process equipment,robot and automobile assembly line and so on,from the angle of dynamics,are belong to the second-order nonlinear uncertain systems(SONUS).In general,the control for SONUS is usually achieved by designing controller so as to complete the production task accurately.So,the research on the controller design and control theory of SONUS is significant to achieve great operation of industrial equipments.In this paper,we regard SONUS as the research object,use some methods including Lyapunov stability theory,MATLAB numerical simulation and the classical terminal sliding mode control(TSMC)theory,so as to do some deep research about controller design of SONUS.According to the proposed problem,this article firstly presents a discontinuous fast terminal sliding mode surface,a TSMC based on state observer,a TSMC with state observer and disturbance observer and finally a TSMC based on continuous reaching law with adaptive boundary layer.The main works of this paper are as follows:According to the traditional terminal sliding mode control,singularity is always existed.In this paper,two kinds of sliding mode surfaces are proposed which include: a mixed fast terminal sliding mode surface and a discontinuous fast terminal sliding mode surface.Then,we show the estimated convergence time of system states on these two sliding mode surfaces.Finally,the simulation can confirm that system state on discontinuous fast terminal sliding mode surface has stronger robustness in condition of nonsigularity and superior dynamic performance.Noted that all of aforementioned design are based on an assumption that the second-order state is measurable.However,in practice,some second-order states are not measurable.This case can lead to failure of controller design.So,this paper shows two kinds of state observers: high-gain observer and terminal sliding mode observer,so as to estimate second-order unmeasurable signal.After the stability confirmation,the final simulation results verify that terminal sliding mode observer has better observation performance in comparison with highgain observer.Moreover,the external disturbance in system is always existing.It can lead to important influence for controller and state observer.Therefore,in this paper,we show two disturbance observers: an adaptive RBF network disturbance observer and a finite time disturbance observer.They can estimate outside disturbance accurately and offset controller so as to overcome their negative influence.After the stability confirmation,the simulation results finally prove that the finite time disturbance observer can achieve better estimation.Also,higher precision,stronger robustness can be obtained after controller combines with disturbance observer.Finally,what we need to consider is how to design controller so as to achieve continuous input,avoid chattering and obtain higher control precision simultaneously.Therefore,we firstly propose a continuous reaching law with adaptive boundary layer.Then,we design a new TSMC based on this reaching law.After stability confirmation,the simulation results show that this TSMC can avoid chattering and achieve continuous input,prior precision and stronger robustness in comparison with TSMC with traditional continuous reaching law.