Adaptive Second-Order Sliding Mode Controller Design Subject to Mismatched Uncertainties
针对存在失配不确定性的滑模控制系统，提出一种新型自适应二阶滑模控制律，通过三层嵌套自适应机制和修正加幂积分器方法，实现有限时间内的实际二阶滑模，并通过仿真验证有效性。
In this article, a novel adaptive second-order sliding mode (ASOSM) control law is constructed for a general category of sliding mode control (SMC) systems with mismatched uncertainties, including a nonvanishing external disturbance. This innovative control design proposal is accomplished through three key mechanisms. First, the new sliding mode dynamics subject to mismatched uncertainties is derived by selecting the appropriate sliding variables, which can significantly increase the uncertainties existing in the control input channel and relax the strict requirement on the relative degree assumption of the sliding variable. Second, a novel ASOSM controller, which contains some adaptive parameters generated via a three-layer nested adaptive mechanism, is constructed by utilizing the modified adding power integrator (API) approach and the adaptive control technique. Third, the practical finite-time stability of the closed-loop sliding mode system is confirmed by means of the systematic Lyapunov stability theory. The technical advancement of the developed adaptive control scheme lies in its ability to effectively deal with a more general sliding mode dynamics containing multiple uncertainties and guarantee that the practical second-order sliding mode (SOSM) is established in a finite time. Finally, simulation results, incorporating a practical application case, are provided to illustrate the effectiveness of the designed adaptive control scheme.