Continuous Path Tracking System of High Precision Stage Using Synchronous Piezoelectric Device Driver

This paper proposes a robust controller for a high precision stage using a synchronous piezoelectric device driver to attain both high speed and high accuracy. The proposed controller consists of a friction compensator, a robust feedback controller, and a continuous path tracking system. The friction compensator based on the well-known static model compensates the effect of friction. Stability of the control system is provided by the robust feedback controller based on the doubly coprime factorization and disturbance observer. The tracking performance is further enhanced by the continuous path tracking system. Effectiveness of the proposed controller is evaluated through simulation and experiments. Introduction The demand for high precision stages has grown rapidly in many fields of research and technology, such as in semiconductors manufacturing, robot systems, etc. In order to raise the quality of products, the industry, thus, is directed into the goal of high precision, and high speed motion control. To date, for sub-nanometer accuracy and resolution, ultrasonic motors using resonant vibrations of the piezoelectric elements have become a standard option [1]. However, the resonant vibrations reduce the nanometer-range positioning and increase the dead time consuming electric power. To overcome this problem, a synchronous piezoelectric device driver (SPIDER) employing the DC characteristics of the piezoelectric effects has developed. The scope of this paper is to propose a robust digital controller for a high precision stage using SPIDER to achieve both high speed and the nanometer regime positioning motion control capability. The proposed controller consists of a friction compensator, a robust feedback controller, and a continuous path tracking system. The friction compensator is based on the experimental friction model and it compensates for the nonlinear characteristic of friction. Stability of SPIDER system is provided by the robust feedback controller based on the doubly co-prime factorization and the disturbance observer. The tracking performance is further increased by the continuous path tracking system. The effectiveness of the proposed controller is evaluated by simulation and experiments. Fig. 1. Photograph of SPIDER. Advanced Materials Research Online: 2006-02-15 ISSN: 1662-8985, Vols. 11-12, pp 121-124 doi:10.4028/www.scientific.net/AMR.11-12.121 © 2006 Trans Tech Publications Ltd, Switzerland All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of Trans Tech Publications Ltd, www.scientific.net. (Semanticscholar.org-20/03/20,09:20:05) High Precision Stage Control System System Configuration. The proposed high precision stage has two main parts (1) the plant; and (2) the control system. The plant consists of SPIDER, a stage with an additional load of 20kg, a linear scale and a linear encoder as a position sensor with 20nm resolution. The control system is implemented by using a Pentium IV PC with a servo driver. The weight of the stage is approximately 1.2kg. The longitudinal feed of stage is 100mm. Operating Principle. The walking drive is a method to feed the stage over a linear guide by utilizing micro-deformations of SPIDER. Its principle is similar to walking motions of such animals as human beings, horses. Fig. 2 illustrates one complete cycle consisting of eight steps of the feed mechanism. System Identification. SPIDER system is a complicated system, where the structure of the system is hard to model mathematically, and the intermediate state variables are extremely difficult to measure. Therefore, we use the system identification method to determine SPIDER system's model [3]. Input data is the applied voltage to the actuator, and output data is the position signal of the stage. The corresponding transfer function of SPIDER is given by Eq. 1. 200.8) s(s 101.4 P(s) + = (1) Design of Robust Feedback Controller SPIDER system requires controllers to satisfy such requirements as high accuracy, small overshoot, and robustness. In addition, ease of controller design and adjustment are important in practical applications.We have proposed a robust feedback controller based on the doubly coprime factorization and the disturbance observer [4]. In Fig. 3, the inner loop system is the closed-loop system based on state feedback and state observer. The outer loop system is equivalent to the closed-loop system based on the disturbance observer. It is seen that the function g(z) is equivalent to a low-pass filter used to make the inverse of the nominal transfer function realizable. The controller C(z) is determined by the coprime factorization N(z), D(z), X(z), Y(z), and the function g(z) as shown in Eq. 4. The poles of state feedback and state observer are chosen by the coefficient diagram method [5]. In this work, the equivalent time constant and the stability index are chosen as τ = 0.1 and γi = [2.5 2 2], respectively. D(z) N(z) P(z) = (2) 1 D(z)Y(z) N(z)X(z) = + (3) N(z) 1 g(z) 1 g(z) Y(z) 1 Y(z) X(z) C(z) − + = (4) Fig. 2. Operating sequence of SPIDER. Fig. 3. Block diagram of the robust feedback controller. 122 AICAM 2005