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Dealing with actuator saturation for active vibration control of a flexible structure piezo-actuated

We present a study on the active control of vibrations of a flexible mechanical structure in presence of saturation affecting the closed-loop control signal. The application we consider here is a system composed of a flexible beam with one edge clamped on a movable support and the other kinematically free. Two piezoelectric patches are bonded on the beam: one of them is used as an actuator and the other is used as a sensor. First, we show how we perform a linear ℋ2 synthesis for the design of a controller permitting the active vibration damping with good performances. Then, we analyse how a saturation of the control signal causes a degradation of these performances. The main goal of this work is to design an anti-windup compensator which, combined with the linear controller, permits to recover or to enhance some linear closed-loop performances in presence of this non-linearity.