Wiener-Hopf approach to trade-offs between stability margin and performance in two- and three-degree-of-freedom multivariable control systems

J. J. Bongiorno, Farshad Khorrami, T. C. Lin

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Abstract

Trade-offs between stability margin and performance are considered in two- and three-degree-of-freedom multivariable control systems using a Wiener-Hopf design approach. Maximum improvement in an approximate measure of stability margin is achieved at the expense of a prescribed increase in the quadratic cost functional measuring system performance. In order to attain an analytical solution to this fundamental trade-off problem, the approximate measure of stability margin chosen is also a quadratic cost function. A novel approach is introduced which allows structured perturbations in the coprime polynomial matrix fraction description of the plant transfer matrix to be taken into account. As a consequence, it is believed that the use of an approximate measure of stability margin is mitigated. Moreover, if needed, the solution obtained could serve as a very good initial one from which to search for better solutions iteratively.

Original languageEnglish (US)
Pages (from-to)1337-1366
Number of pages30
JournalInternational Journal of Control
Volume68
Issue number6
StatePublished - Dec 1997

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Multivariable control systems
Cost functions
Polynomials

ASJC Scopus subject areas

  • Control and Systems Engineering

Cite this

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abstract = "Trade-offs between stability margin and performance are considered in two- and three-degree-of-freedom multivariable control systems using a Wiener-Hopf design approach. Maximum improvement in an approximate measure of stability margin is achieved at the expense of a prescribed increase in the quadratic cost functional measuring system performance. In order to attain an analytical solution to this fundamental trade-off problem, the approximate measure of stability margin chosen is also a quadratic cost function. A novel approach is introduced which allows structured perturbations in the coprime polynomial matrix fraction description of the plant transfer matrix to be taken into account. As a consequence, it is believed that the use of an approximate measure of stability margin is mitigated. Moreover, if needed, the solution obtained could serve as a very good initial one from which to search for better solutions iteratively.",
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