滑模控制快速分段幂次趋近律设计与分析

针对滑模变结构控制中出现的抖振问题,提出了一种分段幂次趋近律。该趋近律采用分段函数方式设计,具有较快的收敛速率、较多的调节参数,并且针对不同阶段的趋近律分开设计互不影响。理论证明了该趋近律达到滑模面时无抖振、固定时间收敛,详细推导出了收敛时间的表达式。在系统存在不确定性和外界干扰时能收敛于干扰稳定界,求出了干扰稳定界范围,给出了各参数对收敛速率和干扰稳定界的影响程度。以小卫星姿态机动控制为例,通过对比仿真实验,证明了所提趋近律的优越性。

Rapid piecewise power reaching law of sliding mode control design and analysis

A piecewise power reaching law of sliding mode control is proposed to solve the chattering problem. The reaching law is designed by piecewise function. It has a faster convergence speed and more adjustment parameters, and the reaching law of different stages does not interfere with each other. It is proved that the system has no chattering phenomenon and can converge in fixed time, and the convergence time is derived in detail. In the presence of uncertainties and external disturbances, the system can converge to the disturbance stability boundary, and the range is given. The influence of parameters on the reaching speed and disturbance stability boundary is given. The proposed reaching law is applied in the attitude control system of small satellite. Simulation results show the superiority of the proposed reaching law.