针对传统趋近律抖振大、趋近速度不快的缺陷,提出了一种新的离散趋近律。通过在指数趋近律切换项系数中加入非线性函数,实现了切换项系数随运动点到切换面的距离从大到小逐步变化,加快了趋近速度并降低了抖振,间接提高了系统鲁棒性。仿真结果证明,离散非线性指数趋近律具有良好的趋近品质,对确定性系统和不确定系统都有良好的控制效果。

A new discrete-time nonlinear exponentially approaching law is proposed to overcome the shortcomings of the traditional approaching law. A nonlinear function is adopted in the switching coefficients in the approaching law, to simulate the real situation that the distances of the switching coefficients from the system mobile point to the sliding surface decrease step by step, with the approaching speed improved and the chattering depressed, thus to improve the robust performance of the system indirectly. The simulation results show the superiority of the discrete-time approaching law, with better controlling performance for deterministic and non-deterministic systems alike.