Nonsingular Terminal Sliding-Mode Controller Based on Extended State Observer for Two-Mode Vibration of a Piezoelectric Plate: Design, Analysis and Experiments

Abstract

Considering the internal and external disturbances, i.e. coupling effect, model uncertainties, and external excitation of an all-clamped piezoelectric plate, a two-loop nonsingular terminal sliding-mode controller (NTSMC) based on extended state observer (ESO) is developed to suppress the two-mode structural vibration. First, a state space model of the structure is established based on system identification with an auxiliary variable method. Second, a three-order ESO of each individual mode is drawn to estimate and compensate the lumped disturbances via feedforward channel in real-time. Third, the NTSMC based on ESO for each single mode is designed to obtain vibration suppressing performance. In addition, the two-mode vibration control is decoupled into single-mode independent control through the proposed ESO. The stability of whole closed-loop system is analyzed by using a Lyapunov stability criterion. Finally, the experimental platform based on NI-PCIe device for a piezoelectric structural vibration control is set up to verify the effectiveness and superiority of the proposed two-mode vibration control method. Compared with the conventional ESO-based sliding-mode control (SMC) method, the experimental results of two-mode structural vibration demonstrate that the vibration suppression performance of first two modes is improved from 8.94[Formula: see text]dB to 11.7[Formula: see text]dB and 9.2[Formula: see text]dB to 14.75[Formula: see text]dB, respectively.