Active Control Experiment Study of a Flexible Beam with Multiple Time Delays

Abstract

In this paper, active control for vibration of a flexible beam with multiple time delays is studied numerically and experimentally. Piezoelectric (PZT) patches are used as actuators, and foil gauges were used as sensors. Firstly the motion equation of a flexible beam with multiple time delays and Piezoelectric patches is presented and written into a state space form. Then the state equation is discretized and transformed into a standard form without any explicit time delay by a particular augmentation for state variables. So time-delay controller could be designed based on the standard state equation using the discrete active control method. Finally, numerical and experimental studies are presented to verify the validity of the time-delay processing method using the discrete optimal control method and the discrete variable structure control method, respectively. An experimental setup is constructed using DSP TMS320F2812. The numerical and experimental results show that the proposed time-delay controller is effective in suppressing the beam vibration. It is also applicable to both shortand longtime delays.