Considering the problems of total disturbances, i.e., higher harmonics, model uncertainties and external excitations in a practical vibration control system, a compound vibration suppression method is proposed for an all-clamped plate, which combines sliding mode control (SMC) with reduced-order extended state observer (RESO). First, a state space model of the all-clamped plate with inertial actuator is established. Second, a RESO is designed to estimate the system state variables and total disturbances in real time. In addition, the total disturbances can further be attenuated by RESO through a feedforward compensation part. Third, a sliding mode controller based on the estimation values is designed for a vibration control system. The Lyapunov stability theorem is further applied to prove the stability of the whole closed-loop vibration control system with the proposed controller. Finally, vibration control experiment equipment is built based on the NI-PCIe acquisition card, inertial actuator and acceleration sensor to verify the vibration suppression performances of the proposed method. The experimental results show that the amplitude value of vibration has been reduced by 75.2% with the proposed method, while the amplitude value is reduced by 54.5% with the traditional sliding mode control method based on an extended state observer (SMC-ESO). The comparative experimental results illustrate that the proposed method has excellent anti-disturbance and vibration suppression performances.

In this paper, we mainly aimed to design a reduced-order extended state observer-based active vibration controller for a structural vibration control system with total disturbances, i.e., model uncertainties, higher harmonics, and external excitations. A reduced-order extended state observer (RESO)-based nonsingular terminal sliding mode vibration control (RESO–NTSMVC) method is proposed for the vibration suppression of an all-clamped plate structure with an inertial actuator. First, a second-order state space model of the thin plate, with an inertial actuator, was established by solving the dynamic partial differential equation and analyzing the physical model. Second, the total disturbances, i.e., model uncertainties, higher harmonics, and external excitations, were estimated and compensated for by using a RESO via a feedforward part. Third, a NTSMVC based on an estimated value was designed to obtain a fast-tracking rate and effective vibration suppression performance. In addition, the stability of the closed-loop system was proven by using a Lyapunov stability criterion. Finally, a semi-physical experimental instrument was built based on the MATLAB/Simulink real-time environment and the NI-PCIE6343 acquisition card to verify strong anti-disturbance performance and effective vibration control performance of the designed method. The experimental comparison results showed that the vibration amplitudes of the proposed method could be reduced by 11.7 dB, when the traditional extended state observer-based nonsingular terminal sliding mode vibration control (ESO–NTSMVC) method achieved a control effect of only 6.5 dB. The comparative experimental results showed that the proposed method possessed better vibration suppression performance and anti-disturbance performance.

This paper proposes an improved nonlinear extended state observer (NLESO)-based dynamic sliding mode control strategy to address total disturbances, including modeling uncertainties, higher-order harmonics, external excitations, and random noise in an all-clamped piezoelectric plate. Modal analysis is conducted using a laser vibrometer to identify the natural frequencies and mode shapes for optimal actuator and sensor placement. An improved NLESO with a new nonlinear error feedback function xal ( xal -ESO) is developed for accurate state and disturbance estimation with enhanced noise suppression. A dynamic sliding mode surface (DSMC) based on the xal -ESO is designed to reduce high-frequency chattering and enhance vibration suppression performance. Simulation results show that the proposed xal -ESO outperforms traditional ESOs in estimation accuracy and noise suppression. Finally, experimental comparisons of vibration control performance are conducted on a MATLAB/Simulink real-time platform with an NI PCIe-6343 data acquisition card among the xal -ESO + DSMC, fal -ESO + DSMC, and LESO + DSMC schemes. The results demonstrate that the proposed xal -ESO + DSMC exhibits strong disturbance rejection capability.