Cancellation of unknown multi-harmonic disturbances in multivariable flexible mechanical structures

Abstract

Active vibration control of flexible mechanical structures is a challenging field of research in control engineering due to typically high state-space dimensions of the plant models and the resulting multi-modal dynamical behavior. This work deals with the cancellation of unknown multi-harmonic disturbances in such flexible mechanical structures with multiple inputs and multiple outputs. The proposed control scheme exploits the passivity property of the closed-loop system to ensure robustness to unknown and slowly varying plant parameters. The controller design follows a decentralized control approach, which features a high flexibility in terms of the number of available actuators. However, the unknown disturbance frequency is estimated in a centralized way. Here, the frequency estimator switches between individual outputs based on the estimated amplitudes of the compensation scheme. This leads to an improved rate of convergence compared to a fixed output frequency estimator while retaining the high flexibility of the controller design regarding the number of available actuators. In this work, the local exponential stability of the respective nonlinear time-varying switched error dynamics is proven. Furthermore, measurements from an experimental test rig for electromagnetic stabilization of thin steel strips demonstrate the effectiveness and robustness of the proposed control scheme.