Study On Application Of Non-Smooth Control Theory

Non-smooth control is a very important issue in nonlinear control field,which has received and is increasingly receiving a great deal of attention since its control methods can not only improve the convergence and disturbance rejection properties of the closed-loop systems,but also be applied to more general systems.However,there are still many open problems in this field.In this dissertation,based on the analysis of differential equations and homogeneity,continuous(and non-smooth)finite-time controllers via state or output feedback are proposed.The main control design techniques used in this research are:adding a power integrator,disturbance observer and sliding mode control techniques.In this dissertation we have mainly studied three problems of non-smooth control for nonlinear systems,with two in robot manipulator systems and one in train systems.The main research results and contributions are listed as follows:(1)For the position tracking control problem of robot manipulator systems,finite-time tracking control scheme is presented.The manipulator model is constructed in two degree of freedom(2-DOF).Then,a global finite-time state feedback control scheme is designed based on adding a power integrator technique.Compared with the conventional backstepping control scheme,the proposed control scheme provides a faster convergence rate for the tracking error system and a higher tracking accuracy.Finally,simulation results show the effectiveness of the proposed control scheme.(2)For the position tracking control problem of rigid manipulator systems with mismatched disturbances,a finite-time tracking control is developed via a composite control method for the first time.The manipulator model is constructed in two degree of freedom(2-DOF).Then,the proposed composite controller is designed based on finite-time disturbance observer and adding a power integrator technique.The controller design consists of two steps.Firstly,finite-time disturbance observer is designed which guarantees that the disturbances can be estimated in a finite time.Secondly,a finite-time composite controller is developed based on adding a power integrator approach and the estimates of the disturbances.Finite-time stability analysis for the augmented system is presented by means of Lyapunov stability theorems,which shows that the position tracking error is regulated to zero in finite-time even in the presence of mismatched disturbances.Under the proposed composite controller,the manipulator position can track the desired position in a finite-time.Finally,simulation results show the effectiveness of the proposed control scheme.(3)The last application is the position tracking control problem of train systems with uncertainties and disturbances.In order to achieve these goals,a finite-time trajectory tracking control scheme is presented for the first time.First of all,general description of the train system model is constructed.Then,a control scheme is designed based on integral-type non-singular terminal sliding-mode control(NTSMC).There are two remarkable features of the proposed method.First,the proposed TSMC is driven directly from the sliding mode reachability condition,and no saturation function term is applied.Second,in order to reduce the chattering,a boundary layer neighboring the sliding manifold method(saturated finite-time function)can be adopted in the proposed TSMC to remove the chattering.Compared with the conventional sliding mode control method(which achieves asymptotical stability results),the proposed control scheme can provide a faster convergence and the train's position and velocity tracking errors converge to zero in finite time,while the singularity problem is avoided.Finally,simulation results are presented to illustrate the effectiveness of the proposed method.