Observer-based self sensing actuation of piezoelastic structures for robust vibration control

Abstract

This contribution is concerned with self-sensing actuation (SSA) for the adaptive vibration control of smart structures with piezoelectric actuators. The electro-mechanical model of a Kirchhoff plate equipped with two piezoelectric patches is rewritten in the form of an infinite dimensional port controlled Hamiltonian system with dissipation (PCHD) where collocation of input and output is achieved by SSA. In the case of piezoelectric actuators, self sensing requires a robust separation of electric current due to the direct piezoelectric effect from the measured electric current. Because of the unfavorable ratio of these two signals, the design of an approximate observer for the electric current due to the direct piezoelectric effect is proposed. The control design goal is the asymptotic suppression of a harmonic disturbance with unknown frequency, amplitude and phase. The control law is derived for the plant augmented by an appropriate exosystem, which models the properties of the disturbance. The novelty of this contribution is the extension of the control design methods from the finite dimensional case to the infinite dimensional one. The stability analysis for the infinite dimensional system is based on the concept of L2-stability and the small gain theorem. Vibration attenuation around a dominant eigenfrequency is demonstrated by simulation and experiment.