Active Vibration Control Based on Static Anti-windup Compensator and Unknown Input Observation

Abstract

In this paper, the windup problem is addressed for disturbance rejection control (DRC) based on an unknown input observer (UIO). The proposed combination aims at dealing with actuator input nonlinearities in active vibration control (AVC) to provide a useful tool for systems under unknown environmental stimuli. Accordingly, first, assuming the governing dynamics of the plant to be smooth and differentiable around the equilibrium points, a UIO is designed such that the two transfer functions from disturbance/control input to observation residuals are null. By aiming at rejecting the external perturbations in the plant output and the observation error dynamics, an improved form of the bounded real lemma is employed. Then, based on the Lipschitz condition and considering independent input disturbance signal (mismatch case) and measurement noise, DRC synthesis is formulated in linear matrix equality/inequality framework. To address the saturation of actuators, the developed controller is then augmented with a static anti-windup (AW) compensator in a linear fractional transformation (LFT) form. The proposed combination can be used as a low order yet effective method in model-based AVC of arbitrary mechanical/civil structures.