Robust Feedforward-Feedback Control of a Nonlinear and Oscillating 2-DOF Piezocantilever

Abstract

Many tasks related to the micro/nanoworld require, not only high performances like submicrometric accuracy, but also a high dexterity. Such performances are only obtained using micromanipulators and microrobots with multiple degrees of freedom (DOF). Unfortunately, these multi-DOF systems usually present a strong coupling between the different axis making them very hard to control. The aim of this work is the modeling and control of a 2-DOF piezoelectric cantilever dedicated to microassembly/micromanipulation tasks. In addition to the coupling between the two axis, the piezocantilever is very oscillating and strongly nonlinear (hysteresis and creep). In the proposed approach, the nonlinearity and vibration are first compensated thanks to the feedforward technique. Afterwards, we derive a decoupled model in order to synthesize a linear robust H∞ controller. The experimental results show the efficiency of the proposed approach and their convenience to the micromanipulation/microassembly requirements. Note to Practitioners-The main motivation of this paper is the need of both high performances and high dexterity in micromanipulation and microassembly tasks. In such a case, not only a sub micrometric accuracy and stability are needed, but also numerous degrees of freedom. For that, in the literature, there exist piezoelectric based structures with two or more DOF. Unfortunately, the coupling between its axis, the nonlinearities (hysteresis and creep) and the structure vibration make them very difficult to control and therefore make performances lost. A classical feedback con troller can be employed but when the nonlinearities and vibration become strong, it is impossible to synthesize a linear controller. In this paper, we show that the combination of feedforward techniques, to minimize the nonlinearities and vibration, and feedback techniques makes possible to reach the high performances required in micromanipulation/microassembly. We notice that the proposed approach can also be applied to other nonlinear, oscillating and multi-DOF systems, such as piezotubes.