Saturation-Tolerant Prescribed Instant Adaptive Integral Sliding Mode Control

This paper proposes the design and verification of a new saturation-tolerant prescribed instant control (SPIC) scheme dedicated to the systems with input saturation. The SPIC scheme is constructed by integrating a saturation-tolerant factor along with the reference convergence differential function (RCDF). The main benefit of the proposed scheme lies in that it achieves an extraordinary accuracy on time, i.e., the system state converges to the saturation-tolerant prescribed trajectory at an exact prescribed instant even if input saturation occurs. Besides, the convergence time can be pre-selected by the user, which has no dependency on the initial condition and other control parameters. In addition, an auxiliary system is established to generate the saturation-tolerant factor, which bridges a link between the saturation-tolerant prescribed trajectory and input saturation tactfully. Namely, the saturation-tolerant prescribed trajectory can be flexibly adjusted according to the saturation-tolerant factor when input saturation occurs or disappears. Furthermore, disturbance is adaptively tackled by designing a saturation-tolerant prescribed instant adaptive integral sliding mode control (SPIAISMC) scheme. It ensures the SPIC with a prescribed accuracy in the presence of disturbance and input saturation. The stabilities of the control systems are proved in theory. Finally, the superior properties of the proposed schemes are tested by simulations and experimental studies on a nanopositioning stage.