Compound Estimation-Based Output-Feedback Hysteresis Compensation and Sensor Fault-Tolerant Control Strategy: Application to Piezoelectric Micropositioning Stage

A piezoelectric micropositioning stage (PMPS), which is a type of piezoelectric-driven system, exhibits hysteresis characteristics that affect its positioning precision. In addition, the system is sensitive to disturbances, such as environmental noise, system uncertainties, and sensor uncertainties or faults. This study investigated a new hysteresis-compensation fault-tolerant control strategy for a PMPS. To compensate for the hysteresis caused by the piezoelectric actuator, an observer-based hysteresis compensator (HC) was proposed to avoid the need to model the hysteresis and calculate the hysteresis inverse. Subsequently, an extended state observer (ESO) was constructed to simultaneously estimate the unmeasurable states and generalized disturbances, including the HC compensation error, external disturbances, and uncertainties. The HC and ESO constitute a new compound estimation method to further enhance estimation performance. Moreover, to address sensor faults, a reconstruction sensor was developed to reconstruct the feedback loop and mask faults. Furthermore, a Nussbaum function was incorporated into the fault-tolerant controller to address the unknown actuator gain caused by hysteresis and hence avoid singularities that could occur in the controller design because of the adaptive estimation of the unknown gain. Finally, comparative experiments were conducted on the PMPS to demonstrate the effectiveness of the developed control method.