The damping of a truss structure with a piezoelectric transducer

This paper re-examines the classical problem of active and passive damping of a piezoelectric truss. The active damping strategy is the so-called IFF (integral force feedback) which has guaranteed stability; both voltage control and charge (current) control implementations are examined; they are compared to resistive shunting. It is shown that in all three cases, the closed-loop eigenvalues follow a root-locus; closed form analytical formulas are given for the poles and zeros and the maximum modal damping. It is shown that the performances are controlled by two parameters: the modal fraction of strain energy ν i in the active strut and the electromechanical coupling factor k. The paper also examines the damping via inductive shunting and the enhancement of the electromechanical coupling factor by shunting a synthetic negative capacitance. In the second part, a numerical example is examined and the analytical formulae are compared with predictions based on more elaborate models, including a full FE representation of the truss, the transducer, the electrical network and the controller. The limitations of the analytical formulae are pointed out.