Active vibration control of flexible structures under input saturation through delay-based controllers and anti-windup compensators

In this work, the problem of active vibration control of flexible mechanical structures is addressed through infinite and finite dimensional techniques. The compared approaches are adjusted for an output feedback controller based on delayed proportional actions,through a quasipolynomial-based approach, and an optimalH∞ controller design computed with an LMI approach.They are shown in order to analyze their capabilities to damp some vibrational modes in the frequency band with of interest, and to avoid the so called “spillover”phenomenon. These controllers are synthetized through a finite dimensional model, derived from a finite element analysis of the mechanical structure, combined with some reduction methods.The flexible structures considered here are, firstly, aflexible aluminium beam in the Euler-Bernoulli configuration,and secondly, an axysimmetric membrane. Bothof them are equipped with two piezoelectric patches that are bounded and collocated on each face of the structure.We intend to examine and discuss the aforementioned performances in both simulation and experimental environments.