Inverse shaper based active vibration control of flexible structures with a collocated sensor-actuator pair

We propose a new control design for active vibration suppression of flexible structures with a collocated sensor-actuator pair. The proposed controller is based on the inverse form of a well-known input zero vibration (ZV) shaper. The inverse ZV shaper is utilized with a serially interconnected all-pass filter. This way, the appropriate controller frequency response properties for vibration suppression of collocated flexible systems is achieved, when the controller is applied in the positive feedback path. We propose two different cost functions to optimize the parameters of the proposed controller for efficient vibration suppression. The performance of the controller is investigated in both frequency and time domains through the vibration control of a cantilever beam model with a collocated piezoelectric sensor-actuator pair. Furthermore, its performance is compared with a recently improved version of the positive position feedback controller, which is a state-of-the-art work. It is shown via the simulations that the proposed controller suppresses vibrations more efficiently.