Saturation-Tolerant Predefined Space-Time Super Twisting Control and Its Application to Piezoelectric Fast Steering Mirror

In this article, we report a new saturation-tolerant predefined space-time super twisting control (SPSSTC) method for the saturated systems. The SPSSTC method is constructed on the basis of the time-based barrier function and saturation-tolerant indicator. Different from the existing super twisting controllers, the presented method ensures the saturation-tolerant predefined space-time convergence, i.e., the sliding variable enters into a saturation-tolerant predefined space within a predefined time in spite of the presence of input saturation. In addition, both the convergence accuracy and time are able to be explicitly assigned ahead of time regardless of initial condition, lumped uncertainty, and other parameters. Besides, the saturation-tolerant indicator, which is produced by an auxiliary system, can flexibly adjust the saturation-tolerant predefined space based on input saturation. Moreover, the reported method reduces the overestimation of the control gain from the initial moment. The stability of the control system is confirmed based upon the Lyapunov method, and the effectiveness of the reported method is verified by simulations and experimental investigations on a piezoelectric fast steering mirror.