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A Partially Augmented Lagrangian Method for Low Order H-Infinity Controller Synthesis Using Rational Constraints
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
2011 (English)Report (Other academic)
Abstract [en]

When designing robust controllers, H-infinity synthesis is a common tool touse. The controllers that result from these algorithms are typically of very high order, which complicates implementation. However, if a constraint on the maximum order of the controller is set, that is lower than the order of the (augmented) system, the problem becomes nonconvex and it is relatively hard to solve. These problems become very complex, even when the order of the system is low.

The approach used in this work is based on formulating the constraint onthe maximum order of the controller as a polynomial (or rational) equation.This equality constraint is added to the optimization problem of minimizingan upper bound on the H-innity norm of the closed loop system subjectto linear matrix inequality (LMI) constraints. The problem is then solvedby reformulating it as a partially augmented Lagrangian problem where theequality constraint is put into the objective function, but where the LMIsare kept as constraints.

The proposed method is evaluated together with two well-known methodsfrom the literature. The results indicate that the proposed method hascomparable performance in most cases, especially if the synthesized con-troller has many parameters, which is the case if the system to be controlledhas many input and output signals.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press , 2011. , 7 p.
Series
LiTH-ISY-R, ISSN 1400-3902 ; 3008
Keyword [en]
H-infinity synthesis, Augmented Lagrangian, Linear systems
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:liu:diva-67021ISRN: LiTH-ISY-R-3008OAI: oai:DiVA.org:liu-67021DiVA: diva2:406256
Funder
Swedish Research Council, 60519401
Available from: 2011-03-30 Created: 2011-03-25 Last updated: 2014-06-18Bibliographically approved

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Ankelhed, DanielHelmersson, AndersHansson, Anders
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