Integrated PID-Based Sliding Mode State Estimation and Control for Piezoelectric Actuators

Tracking control of piezoelectric actuators (PEAs) has stimulated the development of various advanced control schemes that utilize the feedback of PEA system states for improved control performance. Among them, the one based on the concept of sliding mode has been shown promising due to its robustness to matched uncertainties, but leaving the required state estimation to be desired. Previous studies show that the PEA can be modeled as a linear dynamic system with matched uncertainties. On this basis, this paper presents the development of a novel observer based on the concept of proportional-integral-derivative-based (PID-based) sliding mode, in which the switching function is replaced by a PID regulator. The novel observer, referred to as the PID-based sliding mode observer (PIDSMO), relaxes the observer matching condition as required in the use of the unknown-input observers. The PIDSMO is then integrated with the PID-based sliding mode controller (PIDSMC) to form a novel integrated PID-based sliding mode observer-controller (PIDSMOC) for PEA tracking control. Experiments performed on a PEA showed that the PIDSMO can accurately estimate the PEA states and that the integrated PIDSMOC can achieve better tracking control performances as compared to the PIDSMC with α-β filter control scheme.