Tracking Error Analysis for Feedback Systems With Hysteresis Inversion and Fast Linear Dynamics1

Author:

Edardar Mohamed1,Tan Xiaobo2,Khalil Hassan K.2

Affiliation:

1. Electrical and Electronic Engineering, University of Tripoli, Tripoli, Libya e-mail:

2. Electrical and Computer Engineering, Michigan State University, 428 S. Shaw Lane, East Lansing, MI 48824 e-mail:

Abstract

Analysis of closed-loop systems involving hysteresis is important to both the understanding of these systems and the synthesis of control schemes. However, such analysis is challenging due to the nonsmooth nature of hysteresis nonlinearities. In this paper, singular perturbation techniques are employed to derive an analytical approximation to the tracking error for a system consisting of fast linear dynamics preceded by a piecewise linear hysteresis nonlinearity, which is motivated by applications such as piezo-actuated nanopositioning. The control architecture considered combines hysteresis inversion and proportional-integral feedback, with and without a constant feedforward control. The analysis incorporates the effect of uncertainty in the hysteresis model, and offers insight into how the tracking performance depends on the system parameters and the references, thereby offering guidance in the controller design. Simulation and experimental results on a piezo-actuated nanopositioning system are presented to support the analysis. In particular, the control scheme incorporating the feedforward element consistently outperforms the classical PI controller in tracking a variety of references.

Publisher

ASME International

Subject

Computer Science Applications,Mechanical Engineering,Instrumentation,Information Systems,Control and Systems Engineering

Reference33 articles.

1. A Survey of Control Issues in Nanopositioning;IEEE Trans. Control Syst. Technol.,2007

2. Design, Identification, and Control of a Flexure-Based XY Stage for Fast Nanoscale Positioning;IEEE Trans. Nanotechnol.,2009

3. Inverse Feedforward Controller for Complex Hysteretic Nonlinearities in Smart-Material Systems;Control Intell. Syst.,2001

4. An Analytical Generalized Prandtlishlinskii Model Inversion for Hysteresis Compensation in Micropositioning Control;IEEE/ASME Trans. Mechatronics,2011

5. Mathematical Models of Hysteresis;IEEE Trans. Magn.,1986

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