Compensating Hysteresis and Mechanical Misalignment in Piezo-Stepper Actuators

TL;DR

This work addresses velocity ripples in piezo-stepper actuators caused by rate-dependent hysteresis and mechanical misalignments. It develops a unified feedforward framework that combines a rate-dependent hysteresis model, inverted in real time, with an iterative learning scheme to compensate for $oldsymbol{\alpha}$-domain disturbances using only current and position measurements. The rate-dependent model is low in parameters and implemented via LUTs, while the disturbance learning adapts shear references to minimize tracking error, with convergence guarantees under designed $L(q)$ and $Q(q)$ filters. Experimental validation shows substantial RMSD reductions across drive frequencies, enabling high-precision, long-stroke operation without reliance on expensive position sensors, and improving robustness to task changes. The approach is broadly applicable to piezo-steppers facing similar parasitics and supports real-time embedded implementation with reduced sensor needs.

Abstract

Piezo-stepper actuators enable accurate positioning through the sequential contraction and expansion of piezoelectric elements, generating a walking motion. The aim of this paper is to reduce velocity ripples caused by parasitic effects, due to hysteresis in the piezoelectric material and mechanical misalignments, through suitable feedforward control. The presented approach involves the integration of a rate-dependent hysteresis model with a position-dependent feedforward learning scheme to compensate for these effects. Experimental results show that this approach leads to a significant reduction in the velocity ripples, even when the target velocity is changed. These results enable the use of piezo-stepper actuators in applications requiring high positioning accuracy and stiffness over a long stroke, without requiring expensive position sensors for high-gain feedback.

Figures (14)

• Figure 1: Schematic of a piezo-stepper actuator. The clamps ($C_1$, $C_2$) press the shear elements ($S_1$, $S_2$) onto the mover. When a shear element $S_e$ is in contact with the mover, it expands or contracts laterally to push or pull the mover in the $x_1$ direction.
• Figure 2: Reference displacements for piezo elements to achieve a stepping motion. The clamps (,) press the shears (,) onto the mover one by one, and the shears drag the mover along in the lateral direction.
• Figure 3: Position error of the mover against the commutation angle $\alpha$, using voltage waveforms that scale with the references in Figure \ref{['fig:waveforms']}, for a range of constant drive frequencies between 0.4 Hz () and 100 Hz (), showing three steps per frequency. The data shows a direction-dependent error that remains consistent across steps, suggesting it is caused by $\alpha$-domain disturbances. Variations across drive frequencies are attributed to a combination of history-dependent hysteresis effects and lowpass effects of the capacitive position sensor.
• Figure 4: Schematic overview of the experimental setup. The lateral displacement $y$ of the mover is measured using a capacitive sensor via a parallel guide.
• Figure 5: Schematic depiction of feedforward control of a piezo-stepper actuator. The feedforward controller yields voltages based on a commutation angle $\alpha$. When applied to the piezo elements $e$, their individual motions $\dot{y}_e$ cause a displacement of the mover via kinematics $\kappa$. Mechanical misalignments in the piezo elements lead to a velocity disturbance $\dot{d}$.

Theorems & Definitions (2)

• Lemma 4.1
• Theorem 1