QFT template generation for time-delay plants based on zero-inclusion test |
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Authors: | Chyi Hwang Shih-Feng Yang |
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Affiliation: | a Department of Chemical Engineering, National Chung Cheng University, Chia-Yi 621, Taiwan;b Department of Information Management, Transworld Institute of Technology, Douliu 640, Taiwan |
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Abstract: | Plant template generation is the key step in applying quantitative feedback theory (QFT) to design robust control for uncertain systems. In this paper we propose a technique for generating plant templates for a class of linear systems with an uncertain time delay and affine parameter perturbations in coefficients. The main contribution lies in presenting a necessary and sufficient condition for the zero inclusion of the value set f(T,Q)={f(τ,q): τT[τ−,τ+], qQ∏k=0m−1[qk−,qk+]}, where f(τ,q)=g(q)+h(q)e−jτω*, g(q) and h(q) are both complex-valued affine functions of the m-dimensional real vector q, and ω* is a fixed frequency. Based on this condition, an efficient algorithm which involves, in the worst case, evaluation of m algebraic inequalities and solution of m2m−1 one-variable quadratic equations, is developed for testing the zero inclusion of the value set f(T,Q). This zero-inclusion test algorithm allows one to utilize a pivoting procedure to generate the outer boundary of a plant template with a prescribed accuracy or resolution. The proposed template generation technique has a linear computational complexity in resolution and is, therefore, more efficient than the parameter gridding and interval methods. A numerical example illustrating the proposed technique and its computational superiority over the interval method is included. |
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Keywords: | Value set Plant template Zero-inclusion test Quantitative feedback theory Time-delay systems Parametric uncertainties |
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