In linear systems, designers use zeros for loop-shaping and the attenuation of disturbances. For example, imaginary-axis zeros can be used to reject sinusoids at a specific frequency such as a 50 Hz or 60 Hz power line interference. If the disturbance is nonsinusoidal, repetitive control methods may be used but additional controller states for each harmonic are required. Thus, rejecting periodic disturbance that are nonsinusoidal with low controller order remains an open problem. In this paper, we constructively design low-order nonlinear dynamics that reject a nonsinusoidal disturbance. We identify a particular case of the nonlinear regulator theory wherein the Byrnes–Isidori PDE has a simple solution. This case leads to a constructive procedure for designing nonlinear zero dynamics in systems with input disturbances. The constructive procedure is accessible to designers who do not have experience with the nonlinear geometric control theory.
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e-mail: paden@engineering.ucsb.edu
e-mail: nasim@ece.ucsb.edu
e-mail: lgentili@deis.unibo.it
e-mail: lmarconi@deis.unibo.it
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July 2009
Technical Briefs
Designing Nonlinear Zero Dynamics to Reject Periodic Waveforms
Brad E. Paden,
Brad E. Paden
Department of Mechanical Engineering,
e-mail: paden@engineering.ucsb.edu
University of California, Santa Barbara
, Santa Barbara, CA 93106
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Nasim Mirnateghi,
Nasim Mirnateghi
Department of Mechanical Engineering,
e-mail: nasim@ece.ucsb.edu
University of California, Santa Barbara
, Santa Barbara, CA 93106
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Luca Gentili,
Luca Gentili
CASY-DEIS,
e-mail: lgentili@deis.unibo.it
University of Bologna
, Va Risorgimenio, 2, 40136 Bologna, Italy
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Lorenzo Marconi
Lorenzo Marconi
CASY-DEIS,
e-mail: lmarconi@deis.unibo.it
University of Bologna
, Va Risorgimenio, 2, 40136 Bologna, Italy
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Brad E. Paden
Department of Mechanical Engineering,
University of California, Santa Barbara
, Santa Barbara, CA 93106e-mail: paden@engineering.ucsb.edu
Nasim Mirnateghi
Department of Mechanical Engineering,
University of California, Santa Barbara
, Santa Barbara, CA 93106e-mail: nasim@ece.ucsb.edu
Luca Gentili
CASY-DEIS,
University of Bologna
, Va Risorgimenio, 2, 40136 Bologna, Italye-mail: lgentili@deis.unibo.it
Lorenzo Marconi
CASY-DEIS,
University of Bologna
, Va Risorgimenio, 2, 40136 Bologna, Italye-mail: lmarconi@deis.unibo.it
J. Dyn. Sys., Meas., Control. Jul 2009, 131(4): 044504 (4 pages)
Published Online: May 20, 2009
Article history
Received:
June 25, 2007
Revised:
January 14, 2009
Published:
May 20, 2009
Citation
Paden, B. E., Mirnateghi, N., Gentili, L., and Marconi, L. (May 20, 2009). "Designing Nonlinear Zero Dynamics to Reject Periodic Waveforms." ASME. J. Dyn. Sys., Meas., Control. July 2009; 131(4): 044504. https://doi.org/10.1115/1.3117187
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