Extended‐state‐observer‐based adaptive robust control of a single‐axis hydraulic shaking table

Abstract

The shaking table test has been widely recognized as one of the most reliable methods for assessing the dynamic response of structures and systems when exposed to a range of vibrations. Replicating these vibrations, recorded as acceleration signals, necessitates precise controller designs. However, traditional controller designs primarily rely on linear system assumptions, leading to complications in incorporating parametric uncertainty and uncertain non‐linearity. This paper presents a novel approach to the acceleration trajectory control problem of single‐axis hydraulic shaking table systems from a non‐linear perspective. This strategy employs a controller combined with an extended state observer (ESO) and adaptive control, offering a design that more closely reflects real‐world scenarios and requires less parameter adjustment. The ESO estimates the uncertain non‐linearity using the displacement signal, while the parametric uncertainty is tackled through adaptive control. The proposed controller's effectiveness is validated through theoretical proof using Lyapunov analysis. The analysis demonstrates that asymptotic tracking performance is guaranteed when the uncertain non‐linearity is time‐invariant. Moreover, with time‐variant uncertain non‐linearity, the controller can also ensure both prescribed transient tracking performance and final tracking accuracy. Comparative experiment results underscore the superior performance of the proposed controller.