Active vibration control of a flexible beam using a non-collocated acceleration sensor and piezoelectric patch actuator

In this paper, the design of an acceleration sensor based active vibration control for a cantilever beam with bonded piezoelectric patches is studied. The problem of phase hysteresis and time delay caused by the non-collocated sensor/actuator pairs is considered. The system's dynamic model considering the non-collocated placement of the acceleration sensor and the piezoelectric patch actuator is derived. The phenomenon of phase hysteresis and time delay degrades the performance of the control system, or even induces instability. To solve the problem, an acceleration sensor based proportional feedback control algorithm and a sliding mode variable structure control algorithm with phase shifting technology are proposed, for suppressing the first two bending modes vibration of the beam. The stability of the proposed controllers was theoretically analyzed. The modal frequencies, phase hysteresis loops and phase lag values due to non-collocated placement of the acceleration sensor and the piezoelectric patch actuator are experimentally obtained, and the phase lag is compensated by using the phase shifting technology. Experiments are conducted to compare the above two active vibration control algorithms. Experimental results demonstrate that the presented acceleration sensor based control methods are effective.