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Unformatted text preview: 6.241 Dynamic Systems and Control Lecture 17: Robust Stability Readings: DDV, Chapters 19, 20 Emilio Frazzoli Aeronautics and Astronautics Massachusetts Institute of Technology April 6, 2011 E. Frazzoli (MIT) Lecture 17: Robust Stability April 6, 2011 1 / 15 Motivation All analytical methods for control design are based on a model of the system to be controlled. Such a model does not necessarily represent a perfect description of the system, for several reasons, for example: The complexity of a real physical system can not be handled well by mathematical models. Even in the case in which a perfect model can be designed for a given system, in general the same model is not a perfect description under all operating conditions. The experimental identification of a systems model (including validation of a mathematical model) is very dicult for openloop unstable plants, for obvious reasons. Even for stable plants, an accurate experimental measurement of highfrequency behavior is very hard to get. Certain characteristics of the model may not be amenable to easy control design (e.g., nonlinearities, or very high order or fast dynamics). In these cases, it may be preferable to formulate a simple linear model of the system, that can be used as the basis for control design. E. Frazzoli (MIT) Lecture 17: Robust Stability April 6, 2011 2 / 15 1 2 System uncertainty and uncertainty models P P Uncertainty model System uncertainty nominal system "real" system Still, even though a perfect model of the system is not available, it is desired to design an automatic control system that performs according to some specifications not only for the given model, but also for the real system. In order to take such uncertainty into account, we will first come up with an uncertainty model, consisting of A nominal model; A set of models that is guaranteed to contain the system uncertainty, and is easier to handle. and then design a control system that meets the stability and performance specifications not only for P , but also for all other possible models in the uncertainty model....
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This note was uploaded on 01/12/2012 for the course ECE 6.241j taught by Professor Prof.emiliofrazzoli during the Spring '11 term at MIT.
 Spring '11
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