Predefined-Time Barrier Function Adaptive Sliding-Mode Control and Its Application to Piezoelectric Actuators

This paper reports the design and validation of a novel predefined-time barrier function adaptive sliding-mode control (PTBFASMC) strategy for robust control of disturbed systems. The PTBFASMC strategy is established by integrating the time base generator (TBG) along with the barrier function. Unlike existing similar works, the proposed method enables global predefined-time convergence, i.e., the system trajectory returns to the ultimate bound even if an escape occurs at a certain time instant. Besides, the convergence time can be predefined by the user, which is independent of the initial conditions and disturbance. Moreover, the reaching phase is eliminated and the magnitude of initial control output is zero. Another attractive feature of the proposed method lies in that the ultimate bound can be predefined, i.e., the ultimate bound is independent of the upper bound of disturbance. To avoid large control magnitude, a modified control strategy is provided, which extends the proposed scheme to different scenarios. The stability of the control system is demonstrated, and its superiority is verified through numerical simulations and experimental investigations on a piezoelectric actuator.