Phase delay control of a cantilever beam

This paper addresses a phase delay control for controlling low-frequency vibrations of a lightly damped beam using a piezoelectric actuator and a piezoelectric sensor. This controller is designed to behave like the velocity feedback controller at the frequencies of modes to be controlled. This controller is composed of a lowpass filter, a highpass filter, and all-pass filters. The lowpass and the highpass filters are supplemented for the robust stability of uncontrolled modes. The highpass filter also suppresses the amplification of the vibration around the frequency zero in the control system. The all-pass filters are designed to give desirable phase delay at the natural frequencies. The phase delay control is applied to vibration suppression of a cantilever beam with a piezoelectric actuator and a piezoelectric sensor. Experimental results show that the phase delay control works well.