On low order controller synthesis using rational constraints
2009 (English)Licentiate thesis, monograph (Other academic)
In order to design robust controllers, H-infinity synthesis is a common tool to use. 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 plant, the problem is no longer convex and it is then relatively hard to solve. These problems become very complex, even when the order of the system to be controlled is low.
The approach used in the thesis is based on formulating the constraint on the maximum order of the plant as a polynomial equation. By using the fact that the polynomial is non-negative on the feasible set, the problem is reformulated as an optimization problem where the nonconvex polynomial function is to be minimized over a convex set defined by linear matrix inequalities.
To solve this optimization problem, two methods have been proposed. The first method is a barrier method and the second one is a method based on a primal-dual framework. These methods have been evaluated on several problems and compared with a well-known method found in the literature. To motivate this choice of method, we have made a brief survey of available methods available for solving the same or related problems.
The proposed methods emerged as the best methods among the three for finding lower order controllers with the same or similar performance as the full order controller. When the aim is to find the lowest order controller with no worse than +50% increase in the closed loop H-infinity norm, then the three compared methods perform equally well.
Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press , 2009. , 87 p.
Linköping Studies in Science and Technology. Thesis, ISSN 0280-7971 ; 1398
H-infinity synthesis, Linear Matrix Inequalities, rank constraints, polynomial constraints, interior point methods
IdentifiersURN: urn:nbn:se:liu:diva-17002Local ID: LiU-TEK-LIC-2009:6ISBN: 978-91-7393-669-9OAI: oai:DiVA.org:liu-17002DiVA: diva2:201266
2009-03-27, Visionen, Hus B, Campus Valla, Linköpings universitet, Linköping, 10:15 (Swedish)
Forsgren, Anders, Professor
Hansson, Anders, ProfessorHelmersson, Anders, Professor