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SUMMARY:Polynomial Equation Approach to Linear Control System Design.
DTSTART:20120316T101500
DTSTAMP:20260408T132620Z
UID:b627f2ddbdc160f6b935fc985651db0c01bb56d8b5137e16a69b899b
CATEGORIES:Conferences - Seminars
DESCRIPTION:Pr. V. Kucera\, Faculty of Electrical Engineering. Masaryk Ins
 titute of Advanced Studies\, Czech Techn\nPolynomial techniques have made 
 important contributions to systems and control theory. Engineers in indust
 ry often find polynomial and frequency domain methods easier to utilize th
 an state equation based techniques. Control theorists show that results ob
 tained in isolation using either approach are in fact closely related. Pol
 ynomial system description provides input-output models for linear systems
  with rational transfer functions. These models display two important syst
 em properties\, namely poles and zeros\, in a transparent manner. A perfor
 mance specification in terms of polynomials is natural in many situations\
 ; see pole allocation techniques. A specific control system design techniq
 ue\, called polynomial equation approach\, was developed in the 1960s and 
 1970s. The distinguishing feature of this technique is a reduction of cont
 roller synthesis to a solution of linear polynomial equations of specific 
 (Diophantine or Bezout) type. In most cases\, control systems are designed
  to be stable and to meet additional specifications\, such as optimality a
 nd robustness. It is therefore natural to design the systems step by step:
  stabilization first\, then the additional specifications each at a time. 
 For this it is obviously necessary to have any and all solutions of the cu
 rrent step available before proceeding any further. This motivates the nee
 d for a parametrization of all controllers that stabilize a given plant. I
 n fact this result has become a key tool for the sequential design paradig
 m. The additional specifications are met by selecting an appropriate param
 eter. This is simple\, systematic\, and transparent. However\, the strateg
 y suffers from an excessive grow of the controller order.\nThis seminar is
  a guided tour through the polynomial control system design. The origins o
 f the parametrization of stabilizing controllers\, called Youla-Kucera par
 ametrization\, are explained. Historical and personal notes are added. Sta
 ndard results on pole placement and H2 control are summarized. New and exc
 iting applications of the parametrization result are then discussed: stabi
 lization subject to input constraints\, output overshoot reduction\, fixed
  order controller design\, and robust stabilization.
LOCATION:ME C2 405
STATUS:CONFIRMED
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