Resonant control of structural vibration using charge-driven piezoelectric actuators

Abstract

Abstract-Driving piezoelectric actuators by charge, or current rather than voltage is known to significantly reduce the hysteretic nature of these actuators. Although this feature of piezoelectric transducers has been known to the researchers for some time, still voltage amplifiers are being used as the main driving mechanism for piezoelectric devices. This is due to the perceived difficulty in building charge/current amplifiers capable of driving highly capacitive loads such as piezoelectric actuators. Recently, a new charge amplifier has been proposed which is ideal for driving piezoelectric loads used in applications such as active damping of vibration. Consequently, it is now possible to effectively, and accurately control the charge deposited on the electrodes of a piezoelectric transducer, and thereby avoid hysteresis altogether. This paper further investigates properties of piezoelectric transducers driven by charge sources when used with resonant controllers for structural vibration control applications. The paper reports experimental results of a multivariable resonant controller implemented on a piezoelectric laminate cantilever beam.

Physical-model-based control of a piezoelectric tube for nano-scale positioning applications

“…It is known [28,29] that it is advantageous to drive piezoelectric transducers with current or charge rather than voltage; furthermore, the voltage v 2 can be measured with a high-impedance instrument. Taken together, this avoids non-linear and hysteresis effects [28,29] and the bond graph of Fig. 2 represents a linear system.…”

Multivariable PPF Control of an Active Structure

“…Ω is the 3 × 3 diagonal matrix with resonance frequencies of the beam as its diagonal elements, and D denotes the feed-through term D vv of the model, see (10). The design variables Γ, ∆ andΩ are 2 × 3, 3 × 3 and 3 × 3 matrices respectively, with Γ as defined in (23) and the matrices ∆ andΩ being diagonal.…”

“…In what follows, a PPF controller will be designed to damp these high amplitude vibrations in the beam. It is worth noting that the cantilever beams of the type to be used here are known to have models of the form (1), (2) and (4), see [9], and resonant controllers designed for them are known to have damped the vibrations to a reasonable extent, see [13] and [10].…”

“…The other higher order modes have been discarded (or not taken into account) as they are beyond the frequency regions of interest. Since the given data includes only three modes, it suffices to set N = 3, or consider a third order model of the form (8)- (10). A standard method to determine the model parameters {Ψ v1 k , Ψ v2 k , β k , γ k , ω k , ζ k } N k=1 and the feed-through terms D yw , D yv , D vw and D vv is to choose them as the minimizers of the cost function,…”

“…where G N ij (iω) are the FRFs corresponding to the multivariable state space model (8)- (10) and ω k denotes the frequency points where the non-parametric FRFs G ij (iω) are measured.…”