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Effects of Delays, Poles, and Zeros on Time Domain Waterbed Tradeoffs and Oscillations

Leong, Yoke Peng and Doyle, John C. (2017) Effects of Delays, Poles, and Zeros on Time Domain Waterbed Tradeoffs and Oscillations. IEEE Control Systems Letters, 1 (1). pp. 122-127. ISSN 2475-1456. doi:10.1109/LCSYS.2017.2710327.

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his letter aims for a simple and accessible explanation as to why oscillations naturally arise due to tradeoffs in feedback systems, and how these can be aggravated by delays and unstable poles and zeros. Such results have been standard for decades using frequency domain methods, which yield a rich variety of familiar “waterbed” tradeoffs. While almost trivial for control experts, frequency domain methods are less familiar to many scientists and engineers who could benefit from the insights such tradeoffs can provide. So here we present an entirely time domain model using discrete time dynamics and l1 norm performance. A simple waterbed effect is that imposing zero steady state response to a step naturally create oscillations that double the response to periodic disturbances. We also show how this tradeoff is further aggravated not only by unstable poles and zeros, but also delays, in a way clearer than in the frequency domain versions.

Item Type:Article
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URLURL TypeDescription
Leong, Yoke Peng0000-0001-8560-8856
Doyle, John C.0000-0002-1828-2486
Additional Information:© 2017 IEEE. Manuscript received March 6, 2017; revised May 1, 2017; accepted May 18, 2017. Date of publication June 1, 2017; date of current version June 9, 2017. This work was supported in part by AFOSR, and in part by NSF. Recommended by Senior Editor F. Blanchini.
Funding AgencyGrant Number
Air Force Office of Scientific Research (AFOSR)UNSPECIFIED
Subject Keywords:Robust control, optimal control, linear systems
Issue or Number:1
Record Number:CaltechAUTHORS:20170614-164911018
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Official Citation:Y. P. Leong and J. C. Doyle, "Effects of Delays, Poles, and Zeros on Time Domain Waterbed Tradeoffs and Oscillations," in IEEE Control Systems Letters, vol. 1, no. 1, pp. 122-127, July 2017. doi: 10.1109/LCSYS.2017.2710327
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:78227
Deposited By: Kristin Buxton
Deposited On:15 Jun 2017 21:06
Last Modified:15 Nov 2021 17:37

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