Péter Gáspár, Zoltán Szabó, József Bokor

Discrete Feedback Systems 2.

Modern Control


A.4.4 Youla parameterization

Figure A.7: Youla parametrization
 
Theorem A.4 (Youla Parameterization) Consider the feedback system shown in Figure A.6. Let G=NrDr-1=Dl-1Nl be right and left coprime factorizations over RH, respectively. Let Ur, Vr, Ul, and Vl be RH matrices satisfying the Bezout identity
 
VrUr-NlDlDr-UlNrVl=I00I
(A.78)
 
then the following statements are equivalent:
  1. K is internally stabilizing.
  2. K has a left coprime factorization of the form
 
K=K4-1K3
(A.79)
 
where
 
K4-K3=I-QVrUr-NlDl
(A.80)
 
and Q is any RH transfer function matrix such that the required inverse exists.
3. K has a right coprime factorization of the form
 
K=K1K2-1
(A.81)
 
where
 
K1K2=Dr-UlNrVlQI
(A.82)
 
and Q is any RH transfer function matrix such that the required inverse exists.
 

Discrete Feedback Systems 2.

Tartalomjegyzék


Kiadó: Akadémiai Kiadó

Online megjelenés éve: 2019

ISBN: 978 963 454 373 2

The classical control theory and methods that we have been presented in the first volume are based on a simple input-output description of the plant, expressed as a transfer function, limiting the design to single-input single-output systems and allowing only limited control of the closed-loop behaviour when feedback control is used. Typically, the need to use modern linear control arises when working with models which are complex, multiple input multiple output, or when optimization of performance is a concern. Modern control theory revolves around the so-called state-space description. The state variable representation of dynamic systems is the basis of different and very direct approaches applicable to the analysis and design of a wide range of practical control problems. To complete the design workflow, finally some introduction into system identification theory is given.

Hivatkozás: https://mersz.hu/gaspar-szabo-bokor-discrete-feedback-systems-2//

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