Robust reset control design for piezo-actuated nano-positioner in presence of hysteresis nonlinearity

TL;DR

This work addresses the DC-gain uncertainty caused by hysteresis in piezo-actuated nano-positioners and aims to achieve high bandwidth with robust phase margins. It proposes a robust framework that blends a linear controller with a complex-order element via a COS/CgLp reset strategy, analyzed through SIDF and HOSIDF. Theoretical results (Proposition 1 and Theorem 1) show that integrating a complex-order component can extend the maximum robust bandwidth beyond what linear designs allow, while a constrained optimization tunes the CgLp parameters. Simulation results validate the frequency-domain improvements and demonstrate about a 20% increase in average robust bandwidth, along with improved rise time and reduced tracking error. The approach offers practical guidance for achieving high-precision tracking in piezo-based nano-positioners under hysteresis nonlinearity.

Abstract

In this paper, a robust nonlinear control scheme is designed for the motion control of a class of piezo-actuated nano-positioning systems using frequency-domain analysis. The hysteresis, the nonlinearity in the piezoelectric material, degrades the precision in tracking references with high frequency contents and different travel ranges. The hysteresis compensation by the inverse model, as the state-of-the-art solution, is not reliable alone. Therefore, a control framework with robustness against the remaining nonlinearity is needed. It is shown that there is an unavoidable limitation in robust linear control design to improve the performance. A robust control methodology based on a complex-order element is established to relax the limitation. Then, a constant-in-gain-lead-in-phase (CgLp) reset controller is utilized to realize the complex-order control. The control design is based on the sinusoidal input describing function (SIDF) and the higher-order SIDF (HOSIDF) tools. A constrained optimization problem is provided to tune the control parameters. The achieved improvements by the CgLp control is validated by the simulation.

Figures (6)

• Figure 1: Experimental study of the nonlinearity in the piezo setup; (a) Hysteresis curves; (b) The DC gain
• Figure 2: The block-diagram of the control loop: the linear and nonlinear elements in the plant and the controller.
• Figure 3: The Bode plots of the plant and the open loop in the nominal and worst cases together with the Bode plots of the robust linear control and its elements.
• Figure 4: SIDF-based comparison of robust nonlinear control with linear controllers; (a) Open loop, (b) Sensitivity function, (c) Complementary sensitivity function.
• Figure 5: The HOSIDF-based validation of the designed control; (a) Open loop, (b) Sensitivity function, (c) Complementary sensitivity function.