Novel Dynamic-Sliding-Mode-Manifold-Based Continuous Fractional-Order Nonsingular Terminal Sliding Mode Control for a Class of Second-Order Nonlinear Systems

A novel dynamic-sliding-mode-manifold-based continuous fractional-order nonsingular terminal sliding mode control is proposed for a class of second-order nonlinear systems. By designing the parameter in the continuous fractional-order nonsingular terminal sliding mode manifold as an exponential function of the tracking error, a dynamic sliding mode manifold can be obtained by adjusting the parameter online. Even if reference signals change, the parameter does not need repetitive offline optimization. By combining the fast-terminal-sliding-mode-type reaching law, the system states are attracted to the manifold quickly, enhancing the controller's robustness. When a large initial error exists, the control system can still accelerate response and reduce overshoot simultaneously owing to the dynamic changing characteristic of the manifold. The stability and finite-time convergence of the closed-loop system are proven by the Lyapunov stability theory. Simulation results on SISO and MIMO nonlinear systems show that for different reference signals, the proposed method has a better tracking performance than the general fractional-order nonsingular terminal sliding mode control.