Sensorless model-based displacement estimator for piezoelectric actuator through a practical three-stage mechanism

Abstract

Piezoelectric elements (PEMs) are used in a variety of applications. In this paper, we developed a new simple sensorless method for a Piezoelectric Actuator (PEA), which includes piezostack elements and a three-stage amplification mechanism. This research focuses on a piezoelectric actuator that incorporates a three-stage amplification system, where the outcome of one stage serves as the input for the subsequent one. The actuator receives two types of inputs: the voltage applied to the piezoelectric elements and the mechanical load it carries. Its output is defined by the rotation angle observed at the end of the third amplification stage. To indirectly measure the actuator's displacement, a basic external circuit is utilized. The precise movement of these actuators is essential. To circumvent the high costs and limitations associated with highly accurate displacement sensors, there has been a growing interest in sensorless control methods. Certain electrical signals, when measured, can provide an estimation of displacement. However, induced voltage measurements are not effective for piezoelectric stacks. Two more promising measures are the voltage and current of the piezoelectric material. Given that the electrical charge on these actuators closely reflects their displacement with minimal hysteresis across a broad frequency spectrum, it's proposed that displacement can be effectively gauged through current measurements that assess charge. The core contribution of this paper is the introduction and validation, both theoretically and experimentally, of a hybrid algorithm that leverages these two electrical signals to enhance the accuracy of displacement estimates. This was confirmed using a laboratory setup. The primary benefit of this research is the presentation of a straightforward sensorless control algorithm, poised for further exploration within the realm of piezoelectric actuators. The simplicity of both the theoretical model and the sensorless technique facilitates their application across a diverse range of piezoelectric actuators and amplification systems, thereby streamlining the design, modeling, and control strategy development for various actuators. The innovation of this study stems from the application of an uncomplicated sensorless estimation algorithm, coupled with a system-level perspective on piezoelectric actuators. This approach utilizes a simple, adaptable model suitable for a wide array of applications and operational techniques.

Keywords: Amplification mechanism; Analytical models; Hysteresis; Modelling; Piezoelectric actuators; Sensorless estimation.

Fig. 1

Three-stage lever scheme (a) and picture (b) [1].

Fig. 2

Hybrid Sensorless Position Feedback Estimator scheme.

Fig. 3

The combined system scheme [1].

Fig. 4

The combined system model [1].

Fig. 5

Poled piezoelectric ceramic [49].

Fig. 6

Simulink piezostack model.

Fig. 7

Classical hysteresis curve of PEMs [53].

Fig. 8

Hysteresis Curves [1]. (a) Measured, (b) Norm down, (c) Norm up, (d) Norm both.

Fig. 9

The mechanical amplification [1].

Fig. 10

Piezoelectric actuator electromechanical coupling: (a) Electrical part, (b) coupling, (c) mechanical part [1].

Fig. 11

Measurement of output angle and current as results of the square input signal. (a) Vin = 120 V, (b) Vin = 100 V, and (c) Vin = 80 V.

Fig. 12

Charge Based Position Feedback Estimation Method scheme.

Fig. 13

Charge based transfer function parameters.

Fig. 14

Comparison of charge based estimation results Vs measured results. (a) Vin = 120V, (b) Vin = 100V, (c) Vin = 80V.

Fig. 15

Model Based Position Feedback Estimation Method scheme.

Fig. 16

Model based transfer function parameters.

Fig. 17

Comparison of model based estimation results Vs measured results. (a) Vin = 120V, (b) Vin = 100V, (c) Vin = 80V.

Fig. 18

Comparison of hybrid estimation results Vs measured results. (a) Vin = 120V, (b) Vin = 100V, (c) Vin = 80V.

Fig. 19

Comparison of charge based estimation results, model based estimation results, hybrid estimation results Vs measured results. (a) Vin = 120V, (b) Vin = 100V, (c) Vin = 80V.