Bounded linear stability region in Linear Matrix Inequalities for a multivariable object

• Autorzy: Rybczak M.
• Języki publikacji: EN

Abstrakty

EN

This paper is devoted to the concept of stability in linear matrix inequalities. Especially to the analysis of a bounded stability region for a multivariable 3DOF system. The study is focused on two different, user defined, bounded LMI regions where poles are calculated with the use on an algorithm and placed in the left half plane of complex variable plane s. It is shown that in the studied case the shape of the region is irrelevant compared to the location of region bounds. And more specifically only the active bounds where the poles are located on it’s limits are significant to controller operation.

Słowa kluczowe

EN

LMI; LMI Regions; multivariable system; stability in LMI; LMI in ships

• Wydawca: Wydawnictwo Naukowe Akademii Morskiej w Szczecinie
• Czasopismo: Zeszyty Naukowe / Akademia Morska w Szczecinie
• Rocznik: 2014
• Tom: nr 39 (111)
• Strony: 133--139
• Opis fizyczny: Bibliogr. 13 poz., rys.

Twórcy

autor

Rybczak M.

• Gdynia Maritime University, Department of Vessel Automation 81-225 Gdynia, ul. Morska 81–87

Bibliografia

• 1. BOYD S., GHAOUI L., FERON E., BALAKRISHNAN V.: Linear Matrix Inequalities in System and Control Theory. Society for Industrial and Applied Mathematics, SIAM, Philadelhia 1994.
• 2. BACHELIER O., BOSCHE J., MEHDI D.: On Pole Placement via Eigenstructure. Assignment Approach IEEE Trans. Aut. Control 9, vol. 51, 2006, 1554–1558.
• 3. GUANG-REN DUAN, HAI-HUA YU.: LMIs in Control Systems. CRC Press, 2013.
• 4. GIERUSZ W.: Simulation model of the shiphandling training boat “Blue Lady”. Int. IFAC Conference Control Applications in Marine Systems CAMS’01, Scotland, Glasgow 2001.
• 5. DE CAMPOS V.A.F., DA CRUZ J.J., ZANETTA L.C. JR.: Robust Control of Dynamical Systems Using Linear Matrix Inequalities and Norm-Bounded Uncertainty Journal of Control. Automation and Electrical Systems Vol. 25, Issue 2, April 2014, 151–160.
• 6. KACZOREK T.: Basics of control theory. Wydawnictwa Naukowo-Techniczne, 2nd ed., Warszawa 2005 (in Polish).
• 7. KOZIŃSKI W.: Controller design. Chosen classical and optimization methods. Oficyna Wydawnicza Politechniki Warszawskiej. 1st ed., Warszawa 2004 (in Polish).
• 8. SCHERER C., WIELAND S.: Linear Matrix Inequalities in Control. Society for Industrial and Applied Mathematics, Delft Center for Systems and Control Delft University of Technology, The Netherlands, 2005.
• 9. KACZOREK T.: Vectors and matrices in automation and electrotechnics. Wydawnictwa Naukowo-Techniczne, 2nd ed., Warszawa 1998 (in Polish).
• 10. GIERUSZ W.: Synthesis of multivariable systems of precise ship motion control with the aid of selected resistant system design methods. Akademia Morska w Gdyni, 2005 (in Polish).
• 11. http://users.isy.liu.se/johanl/yalmip/ – LMI preprocesor
• 12. http://sedumi.ie.lehigh.edu/ – special toolbox in Matlab
• 13. GIERUSZ W., POMIRSKI J., RAK A.: Control system for trials on material ship model. Polish Maritime Research, Special Issue S1(74), Vol. 19, 2012, 25–30.