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Research Papers

Suitability of Redesigned Digital Control Systems Having an Interval Plant via an Evolutionary Approach

[+] Author and Article Information
Chen-Chien Hsu1

Department of Applied Electronics Technology, National Taiwan Normal University, 162 He-Ping East Road, Section 1, Taipei 10610, Taiwanjhsu@ntnu.edu.tw

Tsung-Chi Lu

Posiflex Technology Inc.,6, Wu-Chuan Rd., Wu-Ku, New Taipei City 24886, Taiwan222888@ms64.url.com.tw

1

Corresponding author.

J. Dyn. Sys., Meas., Control 133(4), 041007 (Apr 08, 2011) (11 pages) doi:10.1115/1.4003569 History: Received February 06, 2010; Revised January 14, 2011; Published April 08, 2011; Online April 08, 2011

In this paper, a quantitative index is proposed to address the performance evaluation and design issues in the digital redesign of continuous-time interval systems. From the perspective of signal energy, a worst-case energy resemblance index (WERI), defined as the ratio of the worst-case continuous signal energy (WCSE) of the continuous-time interval system over the worst-case discrete sequence energy (WDSE) of the redesigned digital system, is established for evaluating the closeness of the system performance between the redesigned digital control system and its continuous-time counterpart. Based on the WERI, performance of the redesigned digital systems can be evaluated for different discretization methods at different sampling times. It is found that no discretization method outperforms the others for all sampling times. Because of serious nonlinearities and nonconvexity involved, the determination of WCSE and WDSE is first formulated as an optimization problem and subsequently solved via an evolutionary algorithm. To guarantee stability of the redesigned digital system, the largest sampling time allowed is also evolutionarily determined to establish a sampling-time constraint under which robust Schur stability of the redesigned digital system can be ensured. For design purposes, sampling time required can be determined according to the user-specified WERI, which serves as a performance specification for fine tuning the performance of the redesigned digital control system.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

Continuous-time control system with an interval plant

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Figure 2

Redesigned digital control system of Fig. 1

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Figure 3

Sampled-data representation of Fig. 2

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Figure 4

Discrete representation of Fig. 3

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Figure 5

Evolutionary framework of the GA-based approach to determine the largest sampling time allowed

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Figure 6

Flowchart of the proposed GA-based approach to determine the largest sampling time allowed

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Figure 7

WERI plot within the stable sampling-time range in Example 1

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Figure 8

Worst-case step responses of the redesigned digital control system for all discretization methods at T=0.1 in Example 1

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Figure 9

Worst-case step responses of the redesigned digital control system for different discretization methods with WERI=80%

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Figure 10

Worst-case step responses using backward integration with different WERIs

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