Sliding Mode Control of Underactuated Nonlinear Systems Based on Piecewise Double Power Reaching Law

A sliding mode control (SMC) strategy using novel piecewise double power reaching law (PDPRL) for a class of fourth-order nonlinear underactuated systems (USs) is proposed to realize simultaneous control of the unactuated and the actuated part. A novel PDPRL is designed in the form of a piecewise function to reduce the chattering produced by SMC. The fixed-time convergence characteristic and the existence of maximum convergence time independent of the initial value of the sliding mode surface for the PDPRL are analyzed. Considering the uncertainties of model parameters and external disturbance in the USs, a supertwisting disturbance observer (STDO) is provided to accurately estimate the disturbance in real time, and the estimated value is compensated to the controller. The underactuated inverted pendulum system is taken to verify the effectiveness of the devised strategy, and the simulation results show that the proposed strategy can reduce chattering, suppress the disturbance, and enhance the robustness of the system.