Technical Briefs

Designing Nonlinear Zero Dynamics to Reject Periodic Waveforms

[+] Author and Article Information
Brad E. Paden

Department of Mechanical Engineering, University of California, Santa Barbara, Santa Barbara, CA 93106paden@engineering.ucsb.edu

Nasim Mirnateghi

Department of Mechanical Engineering, University of California, Santa Barbara, Santa Barbara, CA 93106nasim@ece.ucsb.edu

Luca Gentili

CASY-DEIS, University of Bologna, Va Risorgimenio, 2, 40136 Bologna, Italylgentili@deis.unibo.it

Lorenzo Marconi

CASY-DEIS, University of Bologna, Va Risorgimenio, 2, 40136 Bologna, Italylmarconi@deis.unibo.it

J. Dyn. Sys., Meas., Control 131(4), 044504 (May 20, 2009) (4 pages) doi:10.1115/1.3117187 History: Received June 25, 2007; Revised January 14, 2009; Published May 20, 2009

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.

Copyright © 2009 by American Society of Mechanical Engineers
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Figure 1

Disturbance rejections problem with linear plant

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Figure 2

Visualization of the construction of γ for the case of scalar-valued d(⋅)

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Figure 3

Nonlinear notch filter

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Figure 4

Response of nonlinear notch filter to matching periodic waveform

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Figure 5

Framework for regulation with nonlinear plant

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Figure 6

Nonlinear regulator as applied to the disturbance cancellation problem



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