By Duncan C. McFarlane, Keith Glover
This monograph issues the layout of suggestions controllers for multivariable linear dynamic platforms. the actual technique is to contemplate a coprime issue description of the plant's move functionality and to symbolize a kin of platforms by means of perturbing the numerator and denominator. The layout of controllers to robustly stabilize one of these relatives is posed as an H? optimization challenge and a few particular options are bought. equally, systems for lowered order modelling and controller layout are derived. eventually, the consequences are exploited to provide a scientific loop shaping keep watch over method layout strategy that's assessed on a number of aerospace examples. The ebook should be applicable for complex undergraduate or graduate sessions requiring just a first path in state-space equipment. It additionally provides an outstanding creation to multivariable keep watch over and using H? methods.
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Additional resources for Robust Controller Design Using Normalized Coprime Factor Plant Descriptions
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,,. The derivation of this procedure is outlined in Doyle et al (1988), and presents significant simplifications over earlier procedures (scc, for example, Doyle, 1984, Foo and Postlcthwaite, 1984, KwM~crnaak, 1985, Safonov, Jonekhcere, Verm~ and Limebccr, 1987, and Francis, 1987) in terms of computational requirements.
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. 7. I The remainder of this chapter is concerned with obtaining a solution for e,na, in this 53 normalized left coprimc factorization robust stabilization problem, and characterizing all controllers for tiffs problem.
By this me~hod, the minimmn achicvable 7 can bc cvaluatcd to within a designcr selected I;olcrance/z. 17 In the case rn 2 = Pi and P2 = nil (corresponding to P i 2 and P21 being square in thc standard plant, P ) it is possiblc to find 7,,,i,, cx~ctly, as is outlincd, for examplc, in Limcbcer and Hung, (1987). Hcncc the itcratlve procedure outlincd abovc can be avoidcd. 5 exist cven if thc above dimcnsionM equalitics do no~ hold. Summary This chaptcr has providcd a gcncrMized framework for thc analysis and synthe- sis of robustly stabilizing controllers.
Robust Controller Design Using Normalized Coprime Factor Plant Descriptions by Duncan C. McFarlane, Keith Glover