Vibration damping of a flexible beam with saturated control

This paper contains a study on the vibration control of a flexible beam equipped with a piezoelectric actuator driven by a bounded control signal. This problem is tackled in two stages. First, a linear H_∞ synthesis with pole placement constraint is performed for the design of a controller permitting an efficient vibration damping. Then, an anti-windup compensator design is proposed by using two different approaches that are compared, in order to improve closed-loop performances in the saturated operating range. Because of experimental purposes of this work, the amplitude of the dead-zone signal should be bounded. So, among the main sought properties of this compensator, one consists in imposing a bound on the closed-loop dead-zone signal in order to avoid numerical problems that could arise during experimental implementation of the anti-windup compensator.