不确定欠驱动系统的高阶自适应Super-Twisting滑模控制

High-Order Adaptive Super-Twisting Sliding Mode Control for Uncertain Underactuated Systems

为实现一类不确定欠驱动系统在未知干扰情况下的鲁棒控制,针对传统滑模控制中存在的抖振问题,提出一种基于二次型Lyapunov函数的二阶Super-Twisting自适应滑模控制策略.首先,控制器的不连续项采用二阶Super-Twisting算法,将不连续控制作用在滑模量的二阶导数.然后,针对滑模面受不确定干扰影响的情况,为调节参数设计一种自适应律方法,该方法不受传统二阶滑模控制中干扰项的一阶导数边界已知的条件限制,保证滑模面在有干扰情况下的收敛,削弱控制器输入的抖振现象.最后,以两轮自平衡车为实验对象验证该方法,并与传统滑模及普通二阶滑模方法做仿真对比.仿真结果表明文中所提的二阶自适应滑模控制方法在控制效果和降低抖振方面表现更优.

To achieve good robustness against disturbances for a class of uncertain underactuated systems,a second-order adaptive sliding mode control method is proposed based on quadratic Lyapunov function to reduce the inherent chattering of conventional sliding mode control（ SMC）. Firstly,a second-order super-twisting algorithm is used by the discontinuous part of controller,which acts on the second-order derivative of sliding mode variables. Secondly,as for the effects of unknown disturbances on sliding mode surface,an adaptive law is designed to adjust the parameters. This method eliminates the restriction of the first derivative of disturbances boundary being known in the traditional second-order sliding mode control,which not only keeps convergence of sliding mode surface but also reduces chattering. Finally,a two-wheeled self-balancing cart is used to test the proposed approach. The simulation results show that compared with conventional SMC and ordinary second-order SMC,the proposed method outperforms the above methods on effectiveness and reducing chattering.