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Low order sampled-data H∞ control
University West, Department of Engineering Science, Division of Automation and Computer Engineering.ORCID iD: 0000-0001-5608-8636
Chalmers University of Technology, Control Engineering Lab, Göteborg, Sweden.
2003 (English)In: Decision and Control, 2003. Proceedings. 42nd IEEE Conference on, 2003, Vol. 3, 2308-2313 Vol.3 p.Conference paper, Published paper (Refereed)
Abstract [en]

A method for obtaining low order sampled-data H∞ controllers is presented. The method is mainly based on a parametric static feedback controller for a plant that is augmented with the controller dynamics. The design of a full-order controller is a convex problem, while the optimisation problem for lower order controllers is non convex. The proposed method starts with design of a full-order sampled-data controller using Riccati equations. Then this controller is reduced by an ordinary model reduction technique, and the reduced controller is used as an initial value for an iterative procedure using linear matrix inequalities (LMIs) in the search for an optimal controller. The matrix inequalities are in fact linear in either the Lyapunov matrix or the static controller matrix, why the solution to the non convex problem fundamentally is given by a bilinear matrix inequality (BMI). The order of the controller is reduced until the closed loop performance degrades too much. Simulations are shown for the control of a time delayed SISO-plant where the controller order can be reduced from 8th to 3rd order. Results are also shown from control of a MIMO-model of a jet engine where the reduction is successful from 15th to 4th order. It is argued that the non convexity is handled efficiently since the procedure uses a model reduction of the full-order controller as initial value.

Place, publisher, year, edition, pages
2003. Vol. 3, 2308-2313 Vol.3 p.
Keyword [en]
H∞ control, Lyapunov methods, MIMO systems, Riccati equations, closed loop systems, concave programming, control system synthesis, delay systems, feedback, jet engines, linear matrix inequalities, reduced order systems, sampled data systems, LMI, MIMO-model, bilinear matrix inequality, closed loop performance, control system design, controller dynamics, full-order sampled-data controller, jet engine, optimal controller, optimisation problem, ordinary model reduction technique, parametric static feedback controller, sampled-data H controllers, static controller matrix, time delayed SISO-plant, Adaptive control, Degradation, Delay effects, Design methodology, Design optimization, Optimal control
National Category
Control Engineering
Research subject
ENGINEERING, Manufacturing and materials engineering
Identifiers
URN: urn:nbn:se:hv:diva-7884DOI: 10.1109/CDC.2003.1272963OAI: oai:DiVA.org:hv-7884DiVA: diva2:845771
Conference
Decision and Control, 2003. Proceedings. 42nd IEEE Conference on
Available from: 2015-08-13 Created: 2015-08-12 Last updated: 2015-08-13Bibliographically approved

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