Disturbance Observer-Based Sliding Mode Control of a Piezoelectric Nano-Manipulator

This paper is concerned with the ultra high precision tracking control problem of a class of hysteretic systems with both external disturbances and model uncertainties. By integrating a time rate function of the input into the classical Prandtl-Ishlinskii operators, a rate-dependent Prandtl-Ishlinskii model is introduced to compensate the rate-dependent hysteresis of such systems. Furthermore, the resulting inverse compensation error is considered, and a finite-time convergent disturbance observer-based sliding mode control methodology is proposed to improve both the tracking accuracy and transient performance. In this control methodology, a finite-time convergent disturbance observer is employed to estimate various disturbances for accurate eliminations, where the inverse compensation error is regarded as a bounded disturbance. Meanwhile, a novel sliding mode controller is designed to achieve the finite-time stability of the closed-loop system. In particular, it can be proved that both the sliding variable and disturbance estimated error can converge to zero in a finite time. Finally, the proposed control architecture is applied to a PZT (piezoelectric transducer) actuated servo stage, where good hysteresis suppression capability and excellent tracking performance are demonstrated in the experimental results.