Abstract
This article presents a convex optimization approach in the synthesis of H2 delay independent observer-based controller for the control of linear systems with uncertain delay in measurements. The motivation for this technique is highlighted by the sensitivity of stability of the conventional linear quadratic regulator (LQR) against such delay in the example of drive train anti-jerk control in vehicles with electric single-wheel drives. The stability constraint for this approach guaranteeing the asymptotic stability of the closed loop system is derived from Lyapunov-Krasovskii functional and then specified in terms of LMIs. The related H2 performance is achieved by minimizing a chosen quadratic cost functional which is convex in matrix variables associated with LMIs. An observer-based controller which guarantees asymptotic stability and H2 performance is developed and its effectiveness is demonstrated in the active damping control of drive train oscillation.
Zusammenfassung
Dieser Beitrag behandelt eine Methode der konvexen Optimierung zur Synthese eines dynamischen Reglers für lineare Systeme mit verzögerten Messausgängen. Dabei wird die H2-Regelgüte mitberücksichtigt. Diese Methode wurde für die aktive Drehschwingungsdämpfung von elektrischen Einzelradantrieben entwickelt, um auch bei Verzögerungen in der Übertragung der Drehzahlsignalen ein stabiles Regelverhalten sicherzustellen. Die Stabilitätsbedingung des Regelkreises wird bei der vorgestellten Methode aus dem Lyapunov-Krasovskii-Funktional abgeleitet und anschließend in Linear-Matrix-Inequalities (LMIs) spezifiziert. Die H2-Regelgüte des Regelkreises wird durch die Minimierung eines quadratischen Kostenfunktionals gewährleistet, welches konvex in den Matrizenvariablen der LMIs ist. Die Anwendbarkeit dieser Art der Reglersynthese für aktive Drehschwingungsdämpfungsprobleme in elektrischen Einzelradantrieben wird anhand von Beispielrechnungen veranschaulicht.
About the authors
Dipl.-Ing. Khang Zhun Yeap graduated with Diplom in Mechatronics and Microsystem Engineering from University of Applied Sciences Heilbronn in 2008 and received his second Diplom in Engineering Cybernetics from University of Stuttgart in 2011. He is currently working as a research assistant in the Institute of Mechatronics in Mechanical and Automotive Engineering, University of Kaiserslautern. His research area is the active damping control of drive train oscillations in electric cars and research interests are robust control design techniques.
Gottlieb-Daimler-Straße 42, 67663 Kaiserslautern, Germany. Telephone: +49-631-2054301. Fax: +49-631-2054301
Prof. Dr.-Ing. Steffen Müller graduated with Diplom in Aerospace Engineering and received his doctorate from the Technical University of Berlin. From 2000 to 2001, he was a post-doctoral researcher at the University of California, Berkley. From 2001 to 2008, he held various positions in the BMW Group Research and Innovation Centre, Munich. Since 2008, he is leading the Institute of Mechatronics in the Department of Mechanical and Process Engineering at the University of Kaiserslautern. His research interests are chassis, drive train and vehicle control, vehicle electrification, driver assistance systems and vehicle automation.
Gottlieb-Daimler-Straße 42, 67663 Kaiserslautern, Germany. Telephone: +49-631-2053230. Fax: +49-631-2054301
Dr.-Ing. Jochen Rauh received his Diplom in Engineering Cybernetics and acquired his doctorate in the field of Technical Dynamics under supervision of Prof. Schiehlen at University of Stuttgart, and is working for Daimler AG since 1987. Presently, he is manager of Vehicle Dynamics System Analysis at Daimler's Group Research and Advanced Engineering Centre for Chassis and Driver Assistance Systems. Main foci of his work are analysis and functional development of vehicle dynamics properties of chassis systems in simulation, at the driving simulators, and in prototype vehicles.
Hans-Klemm-Straße 45, 71034 Böblingen, Germany. Telephone: +49-7031-4389627. Fax: +49-711-3052-114-195
©2014 Walter de Gruyter Berlin/Boston
