Abstract
This paper presents a digital controller design methodology for multivariable analog systems represented by minimally realizable multiple input–output time-delay transfer function matrices with long time delays. First, the analog transfer function matrix with multiple input–output time delays is minimally realized and represented by a delay-free state-space model and a multiple output-delay function. For a specific multiple time-delay transfer function matrix with complex poles, a minimal realization scheme is newly proposed. Then the minimized delay-free state-space model is utilized for linear quadratic regulator (LQR) design. Furthermore, the designed analog LQR is digitally redesigned via a predictive state-matching method for finding a low-gain digital controller from the pre-designed high-gain analog controller. For implementation of the digitally redesigned controller, a digital observer is constructed for the multiple time-delay system with long time delays. An illustrative example is given to demonstrate the effectiveness of the proposed method.
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Acknowledgements
This work was supported in part by the US Army Research Office under grant W911NF-06-1-0507, the National Science Foundation under grant NSF 0717860, the research contract 1440234, and the National Science Council of Republic of China under contract NSC99-2221-E-006-206-MY3.
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Wang, HP., Gu, X., Xie, L. et al. Digital Controller Design for Analog Systems Represented by Multiple Input–Output Time-Delay Transfer Function Matrices with Long Time Delays. Circuits Syst Signal Process 31, 1653–1676 (2012). https://doi.org/10.1007/s00034-012-9393-2
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DOI: https://doi.org/10.1007/s00034-012-9393-2