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Technical Briefs

A Disturbance Attenuation Approach for a Class of Continuous Piecewise Affine Systems: Control Design and Experiments

[+] Author and Article Information
A. Doris

 Shell International Exploration and Production B.V., Keslerpark 1, 2288 GS Rijswijk, The Netherlandsapostolos.doris@shell.com

N. van de Wouw

Department of Mechanical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlandsn.v.d.wouw@tue.nl

W. P. M. H. Heemels

Department of Mechanical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlandsw.p.m.h.heemels@tue.nl

H. Nijmeijer

Department of Mechanical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlandsh.nijmeijer@tue.nl

J. Dyn. Sys., Meas., Control 132(4), 044502 (Jun 15, 2010) (7 pages) doi:10.1115/1.4001279 History: Received February 08, 2008; Revised July 29, 2009; Published June 15, 2010; Online June 15, 2010

We consider the disturbance attenuation problem for a class of continuous piecewise affine systems. Hereto, observer-based output-feedback controllers are proposed that render the closed-loop system uniformly convergent. The convergence property ensures, first, stability and, second, the existence of a unique, bounded, globally asymptotically stable steady-state solution for each bounded disturbance. The latter property is key in uniquely specifying closed-loop performance in terms of disturbance attenuation. Because of its importance in engineering practice, the class of harmonic disturbances is studied in particular and performance measures for this class of disturbances are proposed based on so-called generalized frequency response functions for convergent systems. Additionally, the derived control strategy is extended by including conditions that guarantee the satisfaction of a bound on the control input. The effectiveness of the proposed control design strategy is illustrated by the application of the results to an experimental benchmark system being a piecewise affine beam system.

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Copyright © 2010 by American Society of Mechanical Engineers
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Figures

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Figure 1

Photo of the experimental setup

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Figure 2

Experimental PWA beam system and its characteristic lengths and variables

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Figure 3

Open- and closed-loop steady-state responses of q¯mid(maxt∊[0 T]|q¯midω(t)|/R(ω)) using simulations and measurements.

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Figure 4

Experimental open- and closed-loop time responses of qmid(t) in steady-state for (a) R=16 N, ω/2π=20 Hz and (b) R=74 N, ω/2π=43 Hz

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Figure 5

The maximum absolute value of the actuator force

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