Complex structured singular value analysis using fixed-structure dynamic D-scales |
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Authors: | Wassim M. Haddad Emmanuel G. Collins Jr. Raymond Moser |
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Affiliation: | 1. School of Aerospace Engineering , Georgia Institute of Technology , Atlanta, GA, 30332-0150, USA E-mail: wm.haddad@aerospace.gatech.edu;2. Department of Mechanical Engineering , Florida A&3. M - Florida State 2525 Pottsdamer St., Tallahassee, FL, 32310-6046, USA E-mail: ecollins@eng.fsu.edu;4. Department of Mechanical and Aerospace Engineering , Florida Institute of Technology , Melbourne, FL, 32901, USA |
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Abstract: | Models of systems are always inexact. Hence, to better predict the performance of a system it is necessary to take into account uncertainty in a nominal model of a system. The structured singular value was developed to nonconservatively analyze robust stability and performance for systems with multiple-block uncertainty. In practice, optimization techniques are used to compute an upper bound on the structured singular value. For dynamic uncertainty with bounded magnitude and arbitrary phase (i.e., "complex uncertainty"), the standard approach to computing an upper bound involves finding diagonal scaling matrices D(jω) that minimize σmax (D(jω)G(jω)D-1(jω)) over a (theoretically) infinite number of frequencies. The order of the corresponding stable, minimum phase, rational function D(s) (if it exists) is hence arbitrary, which can lead to very high order controllers when D(s) is used for controller synthesis. This paper develops a fixed-structure approach to computing an upper bound for the complex structured singular value. In particular, by relying on results from mixed-norm H2/H∞ analysisD(s) is a priori constrained to be a rational matrix function of a chosen order and a new approach to computing an upper bound on the structured singular value is developed. The results are illustrated using two examples which clearly demonstrate the suboptimality of standard curve fitting. The proposed approach can be extended to mixed uncertainty and structured singular value controller synthesis without D — K type iteration. |
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Keywords: | H2/H∞ performance robust stability and performance structured singular value |
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