Discrete-Time Output Feedback Sliding Mode Control of Piezoelectric-Actuated Hybrid Isolator for Vibration-Sensitive Instruments

Vibrations significantly impact the working environment of high-precision instruments and degrade their accuracy. Due to its advantages of adaptability and reliability, the piezoelectric-actuated hybrid isolator (PAHIS) is employed to suppress vibrations for vibration-sensitive instruments. In this study, a discrete-time output feedback sliding mode control (SMC) method is designed for PAHIS with uncertainties and disturbances. Firstly, the fuzzy logic systems (FLSs) are employed to approximate the uncertainties in the system. Then, the state observer, combined with the FLSs, is adopted to estimate the system states. Thus, the state estimation information is obtained using only measurable system output. Additionally, a disturbance observer is adopted to estimate the matched and mismatched disturbances induced by vibrations. Subsequently, based on the estimated states, disturbances, and approximated uncertainties, a novel sliding mode surface (SMS) is designed to address the mismatched disturbances and uncertainties, which will improve the vibration isolation performance of the proposed controller. Furthermore, a modified reaching law is designed to improve convergence speed and reduce chattering, validated through simulation. The stability of the closed-loop system and the effectiveness of the proposed method against mismatched uncertainties and disturbances are proven. Finally, experiments are conducted to verify the performance of the proposed scheme.