Controllability of Processes with Large Singular Values

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• 作者：Thomas McAvoy and Richard D. Braatz
• 刊名：Industrial & Engineering Chemistry Research
• 出版年：2003
• 出版时间：November 26, 2003
• 年：2003
• 卷：42
• 期：24
• 页码：6155 - 6165
• 全文大小：194K
• 年卷期：v.42,no.24(November 26, 2003)
• ISSN：1520-5045

文摘

The singular-value decomposition has been used to analyze the robustness of closed-loop systemsand to determine whether any controllability problems can be expected. Past controllabilityconditions have been derived in terms of the condition number and the minimum singular valueof the process and the condition number of the controller transfer function matrix, in terms ofpotential sensitivities of the closed-loop system to model uncertainties or problems with saturationof the manipulated variables. This paper considers processes with a large maximum singularvalue. It is shown that the closed-loop control of such processes can result in poor transientperformance as a result of valve accuracy considerations, even if the condition number is smalland the minimum singular value is large, which would indicate no performance limitationsaccording to existing controllability criteria. Further, processes with large singular values canbe prone to sensor saturation. This indicates that the magnitude of all of the singular valuesshould be considered when assessing the controllability of a process. A new interaction tool basedon output correlation is introduced to help select measurements and manipulated variables thathave a good range of singular values for practical application. The approach proposed isillustrated on two simple examples and on the Tennessee Eastman process.