Robust Controller Design Using Normalized Coprime Factor by Duncan C. McFarlane, Keith Glover

By Duncan C. McFarlane, Keith Glover

This monograph issues the layout of suggestions controllers for multivariable linear dynamic platforms. the actual procedure is to contemplate a coprime issue description of the plant's move functionality and to symbolize a relatives of platforms via perturbing the numerator and denominator. The layout of controllers to robustly stabilize one of these kin is posed as an H? optimization challenge and a few particular strategies are received. equally, methods for lowered order modelling and controller layout are derived. eventually, the implications are exploited to provide a scientific loop shaping keep an eye on approach layout process that's assessed on numerous aerospace examples. The booklet could be applicable for complicated undergraduate or graduate sessions requiring just a first direction in state-space tools. It additionally supplies a superb advent to multivariable keep watch over and using H? methods.

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Extra info for Robust Controller Design Using Normalized Coprime Factor Plant Descriptions

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O ° . ~ ° ° ~ ° ~ ° ° . . . oo° . . . w ~ o o o o . o o o . . . . . ° H ~ - ° * ~ - ' ~ ' ~ * ~ ° ~ ° ~ ° ~ ° ~ ° ~ ° ~ ° * ° ° ~ ' ' - * ° ° ° ° ~ ° ° ° ~ ° * ° ~ ° ° ~ * ~ * ° ° ~ - ~ ° ~ - ° ~ ` ~ . 1 The Normalized L C F Robust Stabilization Problem 'Let (IV, 2(¢) be a normalized left coprime factorization of G. ~), such that GA = (/'1}/"+ A M ) - I ( / ~ + AN) can be stabilized by a single controller, K , for all A E DC~ is given by e.... 3) where K is chosen over all stabilizing controllers.

I t ]W1 idI "I I z -I i L~ ....... I w ,! ~ i P :i +( ;' z l P 2 I + L J u i i! ooooo.. . . . . o o . . ~ . . . . . . . . . . . . . . . 12. ,i,, exactly, and we will consider an iterativc procedure here. For this purpose we introduce the so called Sub-Optimal Hoo Problem, that of finding a stabilizing controller, K , such that for 7 > 7-~in, II~'KP, K)Iloo < 7. 11), and parametrize all such controllers. We review this work next, and then outline an iterative procedure for estimating %,a,,.

1 Background For the presence of modelling error to play a part in controller analysis and design, it is necessm'y to construct some form of mathematical model to represent the error. The modelling should be based on the information available about the uncertainty, or, if this is unavailable, on reasonable assumptions about its magnitude. A key assumption in all modelling of system errors is that the uncertain part of a process can bc modelled separately from the known part of the process, as represented by the nominal model.

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