An Enhanced Time Delay Smith Predictor of Sliding Mode Structural Vibration Controller Based on Extended State Observer

Considering the total disturbances such as system time delay, model uncertainty, actuator effect and dynamic nonlinearities, a composite control strategy is proposed to suppress vibrations in an all-clamped plate structure, which combines sliding mode control based on extended state observer with time delay compensation (TDCSMCESO). First, a second-order state-space representation of the all-clamped plate, equipped with an inertial actuator, is formulated through the analysis of the dynamic partial differential equation and the physical model of the thin plate. Second, due to the inevitable system time delay and the noise amplification of the traditional differentiator, an enhanced differentiator is proposed to make the system without time delay. Additionally, a sliding mode control approach based on extended state observer (SMCESO) is designed to estimate and compensate for the total disturbance through a feedforward mechanism. Third, the closed-loop system’s stability is established through the application of the Lyapunov stability method. Finally, a semi-physical experimental platform utilizing an NI-PCIe6343 acquisition card and Matlab/Simulink environment is constructed to assess and compare the effectiveness of the proposed TDCSMCESO with SMCESO and traditional predictor-based SMCESO (PSMCESO). Comparative experiments show that the TDCSMCESO controller exhibits improved disturbance resistance and vibration reduction capabilities.