Fixed-Time Third-Order Super-Twisting-like Sliding Mode Motion Control for Piezoelectric Nanopositioning Stage

This paper presents a novel third-order super-twisting-like integral sliding mode controller (3-ISMC) for trajectory tracking of nanopositioning applications. Different from traditional sliding mode control methods presenting with chattering problems, the proposed approach provides continuous control inputs, which brings much convenience for practical applications. Moreover, the fixed-time convergence of the proposed 3-ISMC is guaranteed independently of initial conditions. The estimation of the fixed convergence time and stability are derived based on the Lyapunov method. Simulation results demonstrate that the proposed controller exhibits chattering free and quick transient response performance for a piezoelectric nanopositioning system under model uncertainties and external disturbances.