Jeong H. Kim Engineering Building, Rm. 1110
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301 405 4471
Booz Allen Hamilton Distinguished Colloquium in Electrical and Computer Engineering
"Modeling, Interconnection, and Energy Flow for Dynamical Systems"
Dr. Jan Willems
K.U. Leuven, Belgium
Modern engineering systems are open, modular, dynamic, and show a large degree of connectivity. These features, combined with the ever increasing computing power, in principle allow to model complex systems accurately, using tearing, zooming, and linking. However, this program requires an appropriate methodology and the right mathematical concepts for the notion of an open dynamical system, for interconnection of systems, and for the interconnection architecture. We show that defining a system in terms of its behavior and interconnection as variable sharing overcomes the inadequacies of input/output thinking and signal flow graphs as the basis for modeling physical systems. We also discuss the energy flow in interconnected systems, taking electrical circuits and 1-D mechanical systems as paradigmatic examples. We define a port as a set of terminals that satisfy certain conditions, which we call the port-Kirchhoff laws. For ports, and only for ports, we define the power and the energy which flows into a system. Since a port involves more than one terminal, power and energy are not ‘local’, but involve ‘action at a distance’. Moreover, we cannot speak about the power and the energy flow along any set of terminals. We discuss the nature of ports for electrical and for mechanical systems, we derive an expression for motion energy that is not frame dependent. We end by proving that a connected RLC circuit forms a 1-port. One of the conclusions is that terminals are for interconnection, but that ports govern energy flow. In open systems energy rarely flows between subsystems along the interconnection interface.
Reference: ‘The behavioral approach to open and interconnected systems’, Control Systems Magazine, volume 27, pages 46-99, 2007.
Jan C. Willems was born in Bruges in Flanders, Belgium. He received the Ph.D. degree in electrical engineering from MIT in 1968. He was an assistant professor in the department of electrical
engineering at MIT from 1968 to 1973, when he was appointed Professor of Systems and Control in the Mathematics department of the University of Groningen. In 2003, Professor Willems became emeritus. Presently he is guest professor at the K.U. Leuven, Belgium. He served terms as chairperson of the European Union Control Association and of the Dutch Mathematical Society (Wiskundig Genootschap). He has been on the editorial board of a number of journals, in particular, as managing editor of the SIAM Journal of Control and Optimization and of Systems & Control Letters. In 1998, he received the IEEE Control Systems award. His research area is Systems and Control Theory. He worked on stability of feedback systems, on the theory of dissipative systems, and on geometric control and other topics in linear systems theory. He developed the behavioral approach to dynamical systems and control. A complete CV and a list of publications may be found at http://homes.esat.kuleuven.be/%7Ejwillems/
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