Research And Application Of Traditional And Higher-order Sliding Mode Control

Control in the presence of uncertainty is one of the main topics of modern control theory. In the formulation of any control problem there is always a discrepancy between the actual plant dynamics and its mathematical model used for the controller design. These discrepancies mostly come from external disturbances, unknown plant parameters, and unmodeled dynamics. Sliding mode control (SMC), one of the most significant branches in modern control theory, turns out to be characterized by high simplicity and invariance property which lies in its insensitivity to matched uncertainties when in the sliding mode. Thus, it has been widely implemented in many real systems such as robots, aeronautical and space vehicles.Traditional and higher order sliding mode (HOSM) control are investigated, and partial achievements are applied to robots and aircraft control. The main research contents and contributions are listed as follows:(1) For the traditional sliding mode tracking control of a class of uncertain nonlinear systems using boundary layer or power reaching rate law to suppress chattering, the steady-state error bounds are studied when use Slotine form sliding surface and integral sliding surface, respectively. Using the method of BIBO stability, the steady-state error bounds are obtained. Compared with the results reported in literatures, the steady-state error bounds in this dissertation is more accurate. Furthermore, by specifying the tracking error that is required, an appropriate saturation function or power reaching law to suppress chattering is designed without simulation experiments. A case study of an n-link robot manipulator model is presented to demonstrate the effectiveness of the analysis.(2) In order to decrease the steady-state error, many scholars introduced integral term in the sliding surface design. However, with the existence of large initial error, integrator windup would occur and give rise to overshoots and even lead to instability. Therefore, to promote the performance of traditional integral sliding mode control, a new nonlinear saturation function is proposed, which enhances small errors and be saturated with large errors in shaping the tracking errors. While maintaining the tracking accuracy of the traditional integral sliding mode control, this approach provides better transient performances. Using Lyapunov stability theory and LaSalle invariance principle, we proved that the proposed approach ensures the zero steady-state error in the presence of a constant disturbance or an asymptotically constant disturbance. Furthermore, global nonlinear integral sliding mode control is proposed to provide a framework for eliminating the reaching phase, so that a sliding mode exists throughout the entire response.(3) The finite time convergence of the second order sliding Super-Twisting algorithm is analyzed using a non-smooth quadratic-like Lyapunov function. For the constant disturbance, the finite time convergence is proved through Lyapunov equation, and the optimal estimation of the convergence time is presented. For the time varying disturbance, the finite time convergence of Super-Twisting is guaranteed when the parameters satisfy the algebraic Riccati equation, and the estimation of the convergence time is provided. Finally, based on the non-smooth quadratic-like Lyapunov function, adaptive Super-Twisting algorithm is proposed that continuously drives the sliding variable and its derivative to zero in the presence of the disturbance with the unknown bounded variation.(4) It is proved that power rate reaching law, in essential, is second order sliding mode which has perfect reaching quality but poor robustness. Therefore, a robust second order sliding mode control scheme for first order dynamic systems is proposed. The controller has finite time convergent property and contains two parts. A part is fast power reaching law which is used to stabilize sliding variable and its derivative to zero in finite time without disturbance. The other part is a non-homogeneous disturbance observer, which can provide for exact estimation of the sufficiently smooth disturbance in finite time. As a result, a continuous second order sliding mode is established in finite time. Compared our method with the smooth second order sliding mode proposed by Shtessel in the Automatica, a better transient performance is obtained by our method. Simulation results using a tailless aircraft model show good performance even in actuator failure scenarios which validates the effectiveness and feasibility of the proposed method.(5) Using homogeneity and adaptive sliding mode concept, a robust adaptive second order sliding mode control scheme is proposed, and the bounds of uncertainties are not required to be known in advance. Power function in the homogeneous system is replaced by a proposed nonlinear function, thus, a fast convergence rate is guaranteed for any distance from equilibrium point. The convergence rate of the second order sliding mode can be hastened through tuning the controller parameters, and the robustness is ensured. The method is evaluated in simulations on an Omni-directional Mobile Robot (Nubot).(6) Based on homogeneity and finite-time convergent Lyapunov function, a robust adaptive arbitrary order sliding mode control method is proposed. It is shown that the problem is equivalent to the finite time stabilization problem for a perturbed chain of integrators. The control law contains two parts: the nominal part, which is designed using homogeneity technique and finite-time Lyapunov stability theory, respectively, achieves finite time stabilization of the chain of integrators without uncertainties; the compensating part, which is designed using adaptive sliding mode, rejects bounded uncertainties, and the bounds of uncertainties are not required to be known in advance. As a result, a finite time convergent arbitrary order sliding mode is established. An illustrative example of a wheeled mobile robots control shows the applicability of the method.