基于趋近律方法的Delta算子滑模变结构控制系统

针对高速信号不确定滑模变结构控制系统的抖振问题，提出一种基于Delta算子离散化方法的不确定Delta算子系统的滑模变结构控制器。基于反正切函数给出了一种改进的Delta算子离散趋近律，将系统的不确定部分用其上、下确界代替，然后设计滑模变结构控制律。仿真结果表明了该方法的可行性和有效性，对内部参数摄动和外部干扰具有良好的完全鲁棒性。因此，基于该趋近律方法设计的滑模变结构控制系统既能在有限时间内快速趋近切换面，又最终稳定于平衡状态。

Delta operator sliding mode variable structure control system based on reaching law method

Concerning the chattering problem of Sliding Mode Variable Structure Control (SMVSC) for Delta operator system with uncertainties, a sliding mode variable structure controller based on Delta operator discrete method was designed. A modified discrete reaching law for Delta operator system was proposed based on arc tangent function. The system uncertainty was substituted with its least upper bound and greatest lower bound, and then the SMVSC law was designed. The simulation result illustrates the feasibility and validity of the proposed method, and shows it has a good complete robustness for the internal parameter perturbation and external disturbance. Therefore, the SMVSC system based on the proposed reaching law method can not only quickly reach the region of the switching plane in finite time, but also is stable in the equilibrium state.