High-frequency control switching, chattering, limits the practical application of sliding mode controllers. This paper proposes an enhanced reaching law, viz., Fractional Power Rate Reaching Law (FPRRL), for the design of sliding mode controllers to mitigate the chattering problem. Controller gains are selected to accommodate variations in switching function dynamically to prevent over-actuation near the sliding surface, which is the primary reason for chattering. Chattering mitigation is achieved without compromising other attributes of sliding mode control. Performance enhancements in the attributes, viz., reaching time, robustness, and reduced chattering magnitude have been established through the methodical analysis of the new reaching law. The proposed control strategy is then bench-marked with the state of the art reaching law methods through simulations by considering a twin-rotor MIMO system control problem.

高频控制开关，颤振限制了滑模控制器的实际应用。本文针对滑模控制器的设计提出了一种增强的到达定律，即分数功率到达率定律（FPRRL），以减轻抖动问题。选择控制器增益以动态地适应开关功能的变化，以防止在滑动表面附近发生过驱动，这是造成颤动的主要原因。在不损害滑模控制的其他属性的情况下，可以减轻抖动。通过对新的到达律的系统分析，已经确定了属性的性能增强，即到达时间，鲁棒性和减小的震颤幅度。