Plenary Lecture

New Results on Selective Modal Analysis of Dynamic Systems



Professor Eyad H. Abed
Institute for Systems Research
Electrical and Computer Engineering
University of Maryland
College Park, MD 20742 USA

Abstract: One of the most powerful (and simple) tools in the study of linear systems is the concept of system modes and the circle of ideas known as modal analysis. Although modal analysis is a very well-studied subject, in this lecture we discuss some new insights into an important topic within modal analysis, namely the topic of modal participation factors. Participation factors were introduced three decades ago as a scale-free measure of the degree of participation of system modes in system states, and of the degree of participation of system states in system modes. Participation factors are a main building block in Selective Modal Analysis, which addresses such issues as model order reduction and placement of actuators and sensors in large-scale systems. In particular, these tools are commonly used in the analysis and design of electric power networks and in the placement of measuring devices and controllers for large power networks. In this work, we take a new approach to the defin!
ition of participation factors. The approach employs defining participations by viewing the system initial condition as either unknown but bounded, or random. In the former case, participation factors are defined by taking a mathematical average over the set of possible initial conditions. In the latter case, participation factors are obtained by taking a mathematical expectation over the assumed random initial condition. We find that this new approach leads to the common formula for participation factors for measurement of modes in states, but that this formula is no longer an accurate measure for participation of states in modes. Implications for the monitoring and control of complex uncertain systems that may be bordering on instability are discussed.

Brief Biography of the Speaker:
Eyad H. Abed is Professor of Electrical and Computer Engineering and Director of the Institute for Systems Research at the University of Maryland, College Park, USA. He completed the S.B. degree at MIT and the M.S. and Ph.D. degrees at the University of California, Berkeley, all in electrical engineering. His research includes contributions on the control of nonlinear systems exhibiting bifurcation and chaos, singular perturbation analysis and reduced-order modeling, nonlinear stability and stabilization, linear robust stability, and applications in several areas including gas turbine jet engine dynamics and control, electric power system dynamics and control, computer network congestion control, and radar system dynamics. He is a recipient of the Presidential Young Investigator Award from the National Science Foundation, the O. Hugo Schuck Best Paper award from the American Automatic Control Council, a Senior Fulbright Scholar Award, the Outstanding Systems Engineering Faculty Award of the Institute for Systems Research, the Alan Berman Research Publication Award from the Naval Research Laboratory, and two teaching awards from the University of Maryland. He is a Fellow of the IEEE, and serves as Vice President for Financial Activities of the IEEE Control Systems Society.