A Digital Charge Amplifier Model for Hysteresis Reducing of Piezoelectric Actuators

Abstract

The piezoelectric actuators have high resolution, wide operating frequency and low power consumption, but they suffer hysteresis which affects their linearity. In this paper are presented comparatively the analog and digital techniques for improvement (reducing) of nonlinear behavior of this type of actuators using charge amplifiers. First an analog charge amplifier and its performance analysis are presented. Then a model of digital charge amplifier with linearity performance considerably improved (91% reduced), but which shows a pronounced drift is presented. In the last section several methods for drift reducing are presented and analyzed, one of them having a reduction with 87%. A number of functional diagrams and response graphs for the developed techniques and methods are presented. Introduction The application area of the piezoelectric actuators has been spectacular developed, especially due to their remarkable qualities. Compared to other nano-positioning actuators, these have high resolution, high force, wide operating frequency and low power consumption. It is enough to mention some of their applications [1, 2, 3]: in micro and nano-devices for mechanical positioning with below micrometrics accuracy (optical and electronics microscopy, high precision cutting devices (error correction), robotics and positioning of magnetic heads and optical recordingplayback); in deformable mirrors (adaptive optics systems); in ultrasonic motors; in the impact controlled on/off devices; in fuel injectors of diesel engines etc. But, the piezoelectric materials have important non-linear characteristics determi-ned by the existence of hysteresis and creep, which can reduce the positioning accuracy of a piezoelectric actuator. When it is applied to a piezoelectric actuator a sudden voltage, the length will quickly respond then it will change slowly due to the creep effect. Creep is the polarization result of the piezoelectric actuator which continues to change after the applied voltage reaches its final value. Commonly, this effect is an issue at low frequencies and it is not important for higher frequencies [4]. Hysteresis is another undesired effect: when the input voltage is gradually increased, the actuator displacement is different from when the voltage is decreased for the same voltage value applied. For hysteresis reducing, many techniques have been implemented: the model-based control [5]; the displacement feedback control [6]; the charge control [7]. Without going into details, it is worth mentioning that, none of these techniques do not provide an acceptably hysteresis dimi-nution to allow the piezoelectric actuators to do the very high precisions displacement. In this paper, a model of digital charge amplifier is presented. By this model, a significant reduction of the piezoelectric actuators nonlinear behaviour is obtained. 94 | T h e 3 9 t h A R A P r o c e e d i n g s In the following sections we present this digital model. The analog charge amplifier To make the transition to digital charge amplifier, we present a simple analog charge amplifier in this section. In Figure 1(a) the circuit diagram of this analog charge amplifier is shown. It contains a comparator (Ʃ) and amplifier (K), a stack piezoelectric (SP) with capacity, Cpa, a sensing capacitor with capacitance, CS. R1 is used to model the operational amplifier (OA) input terminal leakage, and R2 is due to the leakage of the sensing capacitor. The circuit feedback loop is used to equalize the reference voltage, Vr, with the actual voltage across the sensing capacitor. If the OA, SP and sensing capacitor would be ideal, R1 and R2 can be removed and ideal Laplace transfer function would be: