Paper Info
Title
Strong stability of a coupled system composed of impedance-passive linear systems which may both have imaginary eigenvalues
Abstract
We consider coupled systems consisting of a well-posed and impedance passive linear system (that may be infinite dimensional), with semigroup generator A and transfer function G, and an internal model controller (IMC), connected in feedback. The IMC is finite dimensional, minimal and impedance passive, and it is tuned to a finite set of known disturbance frequencies ω <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">j</sub> , where j E {1, ... n }, which means that its transfer function g has poles at the points iω <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">j</sub> . We also assume that g has a feedthrough term d with Re d > 0. We assume that Re G(iω <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">j</sub> ) > 0 for all j ϵ {1, ... n} and the points iω <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">j</sub> are not eigenvalues of A. We can show that the closed-loop system is well-posed and input-output stable (in particular, (I + gG) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup> E H <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sup> and also G(1 + gG) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-l</sup> E H <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sup> ). It is also easily seen that the closed-loop system is impedance passive. We show that if A has at most a countable set of imaginary eigenvalues, that are all observable, and A has no other imaginary spectrum, then the closed-loop system is strongly stable. This result is illustrated with a wind turbine tower model controlled by an IMC.
Year
DOI
Venue
2018
10.1109/CDC.2018.8619326
2018 IEEE Conference on Decision and Control (CDC)
Keywords
Field
DocType
impedance-passive linear systems,imaginary eigenvalues,internal model controller,IMC,finite set,closed-loop system,transfer function,disturbance frequencies,coupled system stability,observability,wind turbine tower model,feedback
Countable set,Finite set,Observable,Linear system,Control theory,Computer science,Mathematical analysis,Electrical impedance,Transfer function,Semigroup,Eigenvalues and eigenvectors
Conference
ISSN
ISBN
Citations 
0743-1546
978-1-5386-1396-2
0
PageRank 
References 
Authors
0.34
19
2
Name
Order
Citations
PageRank
Xiaowei Zhao1269.65
George Weiss29412.48