ADRC for a piezoelectric plate with delays and disturbances via frequency response method: Design, analysis and experiments

Abstract

A large number of uncertainties such as external excitement, model parameter perturbation, complex boundary conditions, time delays, seriously impact the operation of the piezoelectric plate structure. Therefore, an active disturbance rejection controller is designed and implemented based on an extended state observer to address such issues. The controller designed is analyzed in frequency-domain to address the time delays introduced by the sensors, actuators, communicational networks, computational delays, etc. Knowing that the accurate models are difficult to build, the Lissajous graphics and frequency test methods, hence, are implemented to estimate the delay and model parameters of the system. The stability characteristics and performance are verified via two intuitive frequency response methods, the small gain theorem and the Nyquist diagram. Bedsides, the relationship between time delays and control parameters is quantified, which enables controller parameters to be adjusted according to frequency index. This is the first attempt to use the small-gain theorem, which is favored for its numerical precision and computational efficiency, to analyze the active disturbance rejection control of time-delay systems. A case of a disturbed all-clamped piezoelectric plate with delays is, in particular, tested under a hardware-in-the-loop benchmark. Theoretical and experimental results show the effectiveness of the proposed approach to suppress the structure vibration in the presence of delays and disturbances.