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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e-mail: apostolos.doris@shell.com
e-mail: n.v.d.wouw@tue.nl
e-mail: w.p.m.h.heemels@tue.nl
e-mail: h.nijmeijer@tue.nl
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July 2010
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A Disturbance Attenuation Approach for a Class of Continuous Piecewise Affine Systems: Control Design and Experiments
A. Doris,
e-mail: apostolos.doris@shell.com
A. Doris
Shell International Exploration and Production B.V.
, Keslerpark 1, 2288 GS Rijswijk, The Netherlands
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N. van de Wouw,
N. van de Wouw
Department of Mechanical Engineering,
e-mail: n.v.d.wouw@tue.nl
Eindhoven University of Technology
, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
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W. P. M. H. Heemels,
W. P. M. H. Heemels
Department of Mechanical Engineering,
e-mail: w.p.m.h.heemels@tue.nl
Eindhoven University of Technology
, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
Search for other works by this author on:
H. Nijmeijer
H. Nijmeijer
Department of Mechanical Engineering,
e-mail: h.nijmeijer@tue.nl
Eindhoven University of Technology
, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
Search for other works by this author on:
A. Doris
Shell International Exploration and Production B.V.
, Keslerpark 1, 2288 GS Rijswijk, The Netherlandse-mail: apostolos.doris@shell.com
N. van de Wouw
Department of Mechanical Engineering,
Eindhoven University of Technology
, P.O. Box 513, 5600 MB Eindhoven, The Netherlandse-mail: n.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 Netherlandse-mail: w.p.m.h.heemels@tue.nl
H. Nijmeijer
Department of Mechanical Engineering,
Eindhoven University of Technology
, P.O. Box 513, 5600 MB Eindhoven, The Netherlandse-mail: h.nijmeijer@tue.nl
J. Dyn. Sys., Meas., Control. Jul 2010, 132(4): 044502 (7 pages)
Published Online: June 15, 2010
Article history
Received:
February 8, 2008
Revised:
July 29, 2009
Online:
June 15, 2010
Published:
June 15, 2010
Citation
Doris, A., van de Wouw, N., Heemels, W. P. M. H., and Nijmeijer, H. (June 15, 2010). "A Disturbance Attenuation Approach for a Class of Continuous Piecewise Affine Systems: Control Design and Experiments." ASME. J. Dyn. Sys., Meas., Control. July 2010; 132(4): 044502. https://doi.org/10.1115/1.4001279
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