Filter-Based Adaptive Sliding Mode Control with Unknown Disturbance

Low pass filter (LPF) is an effective approach to suppress chattering of sliding mode control (SMC). However, in current LPF-based SMC, the upper bound of the disturbance or its derivative is needed to be known a priori. As a result, due to the constant control gain, chattering still occurs on the sliding mode even under minor external disturbance. In this paper, to cancel the requirement for the upper bound of the disturbance or its derivative, a leakage-type (LT) adaptive law is developed to approximate the amplitude of the disturbance and its derivative in finite time. Thanks to the LT algorithm, the chattering is further removed when the system is on the sliding mode. By using LT adaptation, a type of LPF-based adaptive SMC is proposed. Explicitly, a linear out-layer sliding function is introduced to realize the asymptotical convergence of the system to a small neighborhood around zero. Lyapunov analysis and simulations verify the superiorities of the developed method.