Vibration suppression of flexible structures via adaptive positive position feedback

The control of flexible structures is often very tough because modal frequencies may vary in operation and are difficult to obtain accurately in advance. The variation in the modal dynamics may cause degradation in performance. This paper presents an adaptive positive position feedback method for controlling the vibration of a flexible beam with bonded piezoelectric sensors and actuators. Dynamics of an experimental flexible beam is modeled via finite element method. The proposed vibration controller combines the positive position feedback (PPF) with an online adaptive parameter estimator based on the gradient algorithm with parameter projection and a dead zone. Since the online estimator is able to identify the modal frequencies, the PPF controller is able to damp out the target modes quickly. Simulation results are presented to illustrate the effectiveness of the proposed control method.