New algorithms of adaptive switching gain for sliding mode control: Part II - Real case

Based on new results on ideal adaptive sliding mode control (ASMC) design for nonlinear systems with uncertainties discussed in Part I of the present contribution, we extend the new designs to the real case in this paper (Part II) by using boundary layer method and filtered rate of the sliding variable. These modifications are proposed to enhance accuracy without overestimation of the uncertainty magnitude and to suppress the chattering phenomenon, often magnified within real measured signals. In fact, the new adaptation laws are designed in ways to assign a minimum admissible value to the switching gain. The robustness is proven using the Lyapunov stability criterion combined with an intuitive analysis of the control behavior. Simulation results are performed to demonstrate the effectiveness of the proposed algorithm.