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On the achievable delay margin using LTI control for unstable plants.

Middleton, Richard H. and Miller, Daniel E. (2007) On the achievable delay margin using LTI control for unstable plants. IEEE Transactions on Automatic Control, 52 (7). pp. 1194-1207. ISSN 0018-9286

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Abstract

Handling delays in control systems is difficult and is of long-standing interest. It is well known that, given a finite-dimensional linear time-invariant (FDLTI) plant and controller forming a strictly proper stable feedback connection, closed-loop stability will be maintained under a small delay in the feedback loop, although most closed loop systems become unstable for large delays. One previously unsolved fundamental problem in this context is whether, for a given FDLTI plant, an arbitrarily large delay margin can be achieved using LTI control. Here, we adopt a frequency domain approach and demonstrate that, for a strictly proper real rational plant, there is a uniform upper bound on the delay that can be tolerated when using an LTI controller, if and only if the plant has at least one closed right half plane pole not at the origin. We also give several explicit upper bounds on the achievable delay margin, and, in some special cases, demonstrate that these bounds are tight.

Item Type: Article
Additional Information: "©2007 IEEE. Reprinted from IEEE Transactions on Automatic Control. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE." http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4268385&isnumber=4268363
Keywords: Closed loop systems; Delays; Feedback; Frequency-domain analysis; Linear systems; Multidimensional systems; Stability; LTI control; Closed-loop stability; Control systems; Delay handling; Delay margin; Feedback loop; Delay; Feedback stability; Finite-dimensional linear time-invariant controller; Frequency domain approach; Plant stability; Time delay; Delay margin; Frequency domain; Linear systems; Hamilton Institute.
Subjects: Science & Engineering > Hamilton Institute
Science & Engineering > Computer Science
Item ID: 1709
Identification Number: 10.1109/TAC.2007.900824
Depositing User: Hamilton Editor
Date Deposited: 02 Dec 2009 10:50
Journal or Publication Title: IEEE Transactions on Automatic Control
Publisher: IEEE
Refereed: Yes
URI:

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