Smooth Higher-Order Sliding Mode Control of a Class of Underactuated Mechanical Systems

This paper investigates the application of smooth higher-order sliding mode (HOSM) control to a class of underactuated mechanical systems. Underactuated mechanical systems have increasing practical importance, but their strong nonlinear behavior and increased vulnerability to uncertainties due to the absence of actuators for some of the configuration variables make the control design problem a challenging task. Sliding mode control (SMC) has the most effective role in controlling such strong nonlinear uncertain systems. However, the standard SMC has chattering in the control action, which is undesired and practically not applicable, especially in mechanical control systems. To achieve smooth control and robustness needed for underactuated mechanical systems, smooth HOSM control laws based on the Super-Twisting Algorithm and the Smooth Super-Twisting Algorithm are proposed. Closed-form analytic expressions are derived for performance design parameters of the sliding surface. These expressions determine the performance of the sliding mode dynamics and also guarantee its stability. For comparison of the results, a standard SMC law is also presented and its merits/demerits are discussed. The design procedure is illustrated by applying it to two well-known cases of the Beam-and-Ball system and the Cart-Pole system as representative examples of the class. Numerical simulation results verify the enhanced control performance and robustness of the theoretical work.