Change search
ReferencesLink to record
Permanent link

Direct link
On design of low order H-infinity controllers
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
2011 (English)Doctoral thesis, monograph (Other academic)
Abstract [en]

When designing controllers with robust performance and stabilization requirements, H-infinity synthesis is a common tool to use. These controllers are often obtained by solving mathematical optimization problems. The controllers that result from these algorithms are typically of very high order, which complicates implementation. Low order controllers are usually desired, since they are considered more reliable than high order controllers. However, if a constraint on the maximum order of the controller is set that is lower than the order of the so-called augmented system, the optimization problem becomes nonconvex and it is relatively difficult to solve. This is true even when the order of the augmented system is low.

In this thesis, optimization methods for solving these problems are considered. In contrast to other methods in the literature, the approach used in this thesis is based on formulating the constraint on the maximum order of the controller as a rational function in an equality constraint. Three methods are then suggested for solving this smooth nonconvex optimization problem.

The first two methods use the fact that the rational function is nonnegative. The problem is then reformulated as an optimization problem where the rational function is to be minimized over a convex set defined by linear matrix inequalities (LMIs). This problem is then solved using two different interior point methods.

In the third method the problem is solved by using a partially augmented Lagrangian formulation where the equality constraint is relaxed and incorporated into the objective function, but where the LMIs are kept as constraints. Again, the feasible set is convex and the objective function is nonconvex.

The proposed methods are evaluated and compared with two well-known methods from the literature. The results indicate that the first two suggested methods perform well especially when the number of states in the augmented system is less than 10 and 20, respectively. The third method has comparable performance with two methods from literature when the number of states in the augmented system is less than 25.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press , 2011. , 135 p.
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1371
Keyword [en]
H-infinity synthesis, linear systems, linear matrix inequalities, rank constraints, optimization, rational constraints, interior point methods
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:liu:diva-67869ISBN: 978-91-7393-157-1OAI: oai:DiVA.org:liu-67869DiVA: diva2:413954
Public defence
2011-06-10, Visionen, Hus B, Campus Valla, Linköpings universitet, Linköping, 10:15 (English)
Opponent
Supervisors
Available from: 2011-05-11 Created: 2011-05-01 Last updated: 2011-07-01Bibliographically approved

Open Access in DiVA

On design of low order H-infinity controllers(762 kB)4622 downloads
File information
File name FULLTEXT01.pdfFile size 762 kBChecksum SHA-512
449a2d724c2015301a59a90ca4356bc613a2a45a3bd738a8cb6634c4bda5d59dc1d36c4eb6016abf309277f89040f441b13425345e8a1542aaa6f6f51511b5e9
Type fulltextMimetype application/pdf
Errata List(104 kB)50 downloads
File information
File name ERRATA01.pdfFile size 104 kBChecksum SHA-512
17f3e42bd38e636e21e04bcbd551d0b832517d48cf0cfe847a6e4f6f08ffd0d1122fbb5e1043fba38a0c31676a144c7be0333b78ef430771c4422e29f82f4d35
Type errataMimetype application/pdf
cover(71 kB)39 downloads
File information
File name COVER01.pdfFile size 71 kBChecksum SHA-512
4a1622ebb393211fe9c5fabf3ccdec646d5e474aa8cf646434b5b1c6a8ac9932305421e179c94c77186f184f4a5f165241e94e70f9b5a018b2c61c8eac303be0
Type coverMimetype application/pdf

Search in DiVA

By author/editor
Ankelhed, Daniel
By organisation
Automatic ControlThe Institute of Technology
Control Engineering

Search outside of DiVA

GoogleGoogle Scholar
Total: 4622 downloads
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

Total: 1308 hits
ReferencesLink to record
Permanent link

Direct link