Piezoelectric Stack Actuators and Control System Design: Strategies and Pitfalls

Abstract

An evaluation is presented of two control strategies for piezoelectric stack actuators: voltage feedback control and charge feedback control. The study consists of two principal parts: an experimental determination of the nonlinearities inherent in piezoelectric actuators using different control strategies and an analysis of how those nonlinearities would affect the stability and performance of feedback control systems that utilize piezoelectric actuators. The voltage control response of the piezoelectric actuator tested was demonstrably more nonlinear than the same actuator with charge feedback circuitry. Nyquist design analysis reveals that these nonlinearities translate into lower stability margins and potential system performance for voltage control of piezoelectric actuators as compared to charge control. The improved system stability that can be achieved with charge control as compared to voltage control is demonstrated to be signi cant in multi-degree-of-freedom systems but almost negligible when the system dynamics are essentially single degree of freedom. NomenclatureA = stack cross-sectionalarea, m 2 C = series capacitance, F c D = modulus at constant electric displacement, Pa c E = modulus at constant electric eld, Pa D = electric displacement, coulomb/m 2 E = total electric eld, V/m e, d, h, g = piezoelectric constants F = force applied to tip mass, N G = voltage ampli er gain K c = controller subsystem K f = displacement feedback subsystem K g = gain margin, dB K m = stack/mechanism subsystem m = target mass, kg N = system describing model discrepancies n = number of stack layers Q t = total charge applied to stack, coulombs S = strain T = stress, Pa t = stack layer thickness, m V = voltage applied to stack, V V in = ampli er input voltage, V x = displacement, m v = phase margin, deg

Charge feedback-based robust position tracking control for piezoelectric actuators

“…Theorem 1: The controller given in (16), (21) and (32) ensures that |e(t)| ≤ ε as t → ∞ provided the control gain k r , introduced in (32), is sufficiently large, and hence, e(t) is practically regulated to zero. The controller also guarantees that all closed-loop signals remain bounded.…”

“…From (6) and (8), it is clear that q p (t), V c (t) ∈ L ∞ ; thus, from (16), it is clear that V (t) ∈ L ∞ . After utilising the above boundedness statements along with (1) and (7), it is clear thatÿ(t) ∈ L ∞ .…”

“…The main challenging issue in precision positioning with the PZTAs is the strong hysterical activity because of their composition from ferroelectric ceramic materials [16]. Specifically, an applied voltage is typically the input control signal which activates the PZTA.…”

“…In the event that the input control voltage is relatively large, the PZTA exhibits a significant amount of distortion because of the inherent hysteresis in the device, and this effect may reduce the stability of the system in feedback control applications [17]. Owing to this non-linear behaviour, the accuracy of the PZTAs are deteriorated in precise tracking control applications [16]. Hence, efficient non-linear control strategies are needed to ensure stability and to guarantee accurate tracking for the use of the PZTAs in micro/nanopositioning systems and tracking applications.…”

Resonant control of structural vibration using charge-driven piezoelectric actuators

“…In [5], the authors report experimental results to illustrate that when a piezoelectric stack actuator is being used in a feedback loop with a voltage amplifier the gain and phase margins of the system deteriorate significantly compared to the situation in which the same actuator is driven by a charge amplifier. In particular, the authors report 28% improvement in the phase margin by using charge as the driving mechanism.…”