An LPV discrete-time controller for the rejection of harmonic time-varying disturbances in a lightweight flexible structure

In this work, control system design and implementation for active vibration control (AVC) of flexible structures with piezoelectric actuators is studied. The goal is to reduce the effect of harmonic disturbances with known time-varying frequencies acting on a system. As a test bed, a thin flexible aluminum cantilevered beam with two symmetrically bonded piezoelectric actuators is used. The harmonic excitation is generated by two DC motors each of them with an unbalanced mass. A discrete-time model is obtained through black-box system identification methods. The control algorithm design is based on a plant description with a disturbance model as a linear parameter varying (LPV) system in linear fractional transformation (LFT) form. This results in a gain-scheduled controller where the harmonic disturbance frequencies are the scheduling variables. The experimental real-time results show the effectiveness of the controller and its capability to suppress time-varying harmonic disturbances, whose frequencies are measured directly from the DC motors. The design method leads to a controller that stabilizes the closed-loop system even for arbitrarily fast changes in the disturbance frequencies. In the real-time experiment, the controller suppresses a disturbance consisting of two independent harmonics with frequencies that vary over a range of 15 Hz.