The damping of a truss structure with a piezoelectric transducer

Abstract

This paper reexamines 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.

Butterworth Pattern-based Simultaneous Damping and Tracking Controller Designs for Nanopositioning Systems

“…This method has since been refined (Preumont et al, 2008) and applied to other resonant systems, such as nanopositioning stages (Fleming, 2010). IFF with tracking control has the same structure as IRC, see Figure 2A, where C d and Ct are both integral controllers.…”

“…Numerous damping controllers have been presented in the literature. Integral Force Feedback (IFF) (Preumont et al, 2008) and Integral Resonant Control (IRC) (Aphale et al, 2007) are simple, easy to design control schemes which provide guaranteed stability and excellent robustness. Positive Position Feedback (PPF) (Fanson and Caughey, 1990) and Positive Velocity and Position Feedback (PVPF) (Bhikkaji et al, 2007) use the feedback of position, and position and velocity, respectively, to achieve closed-loop pole placements, which increase damping.…”

Servo design and analysis for the Thirty Meter Telescope primary mirror actuators

“…[9] Alas, all of our approaches have been tried before, including force feedback, plus one more, an op-amp circuit providing negative capacitance. That too was tried, but was no better than the tuned circuit.…”

“…For the subsequent discussion consider the equations for a single PZT, which can be either the forcer or the sensor: [8], [9] 1 (1) The three equations are respectively the electrical, mechanical, and circuit equations. The non-dimensional term k 33 is commonly used to characterize the material, with close to one being good.…”

Generalized modal analysis for closed-loop piezoelectric devices

“…As a prerequisite to apply the methods though, the frequency response of the mechanical structure must be identified. Preumont et al (2008) address the problem of controlling the vibrations of large trusses. A quasi-static model of the actuator was considered, because in this case the dynamics of the piezoelectric actuator was much faster than that of the controlled structure.…”