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Best achievable tracking performance in sampled-data systems via LTI controllers.

Chen, Jie and Hara, Shinji and Qiu, Li and Middleton, Richard H. (2008) Best achievable tracking performance in sampled-data systems via LTI controllers. IEEE Transactions on Automatic Control, 53 (11). pp. 2467-2479. ISSN 0018-9286

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Abstract

In this paper we study the problem of tracking a step reference signal using sampled-data control systems. We are interested in the tracking performance, defined as the integral square of the tracking error response between the system’s output and the reference input. This performance is deemed the best achievable by a sampled-data controller with a linear time-invariant discrete-time compensator if it is the minimal attainable by all such controllers that stabilize the system. Our primary objective is to investigate the fundamental tracking performance limit in sampled-data systems, and to understand whether and how sampling and hold in a sampled-data system may impose intrinsic barriers to performance. We consider two tracking performance measures, with one defined with respect to the unit step signal, and another with respect to a delayed step signal and averaged over one sampling period. We derive an analytical closed-form expression in each case for the best achievable performance. The results show that a performance loss is generally incurred in a sampled-data system, in comparison to the tracking performance achievable by analog controllers. This loss of performance, as so demonstrated by the expressions, is attributed to the non-minimum phase behaviors as well as the intersample effects generated by samplers and hold devices. Thus, sampled-data controllers do result in an additional performance limit, which is seen as a necessary tradeoff for other advantages offered by this class of controllers.

Item Type: Article
Additional Information: "©2008 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=4700850&isnumber=4700835
Keywords: Discretization; Frequency-domain lifting; Intersample effects; Non-minimum phase zeros; Performance limit; Sampled-data systems; Tracking; Compensation; Discrete time systems; Linear systems; Signal sampling; Tracking; Closed-form expression; Error response tracking; Linear time-invariant; Discrete-time compensator; Sampled-data control system; Step reference signal tracking problem; Hamilton Institute.
Subjects: Science & Engineering > Computer Science
Science & Engineering > Hamilton Institute
Item ID: 1695
Identification Number: 10.1109/TAC.2008.2006924
Depositing User: Hamilton Editor
Date Deposited: 01 Dec 2009 11:07
Journal or Publication Title: IEEE Transactions on Automatic Control
Publisher: IEEE
Refereed: Yes
URI:

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