A Time-Varying System - Missile Dynamics

Spyros Andreou

Abstract


Most of the control theory is developed around time-invariant systems where the state matrix A consists of scalars which are not functions of time. However, many physical systems are naturally modeled with the elements of the state matrix A depending on time. One example is the dynamics of a missile. Time- varying systems also arise when non-linear systems are linearized about a trajectory. In this work, the state-transition matrix is studied for time-varying systems in order to reach a general solution. The computational effort is significantly more complicated that the time-invariant case. There are many different methods in the literature for finding the state-transition matrix and one of them is adopted. Finally, a case study of Missile Dynamics will be analyzed and simulated in MATLAB.

Keywords


state transition matrix, time-varying system, missile dynamics

References


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Lygeros_J. and Ramponi F., Lecture Notes on Linear System Theory, Automatic Control Laboratory, ETH Zurich, Switzerland, September 22, 2013.

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Palm III W. J., A Concise Introduction to MATLAB, McGraw-Hill, New York, 2008.

www.egr.msu.edu/classes/me851/jchoi/lecture/Lect_24.pdf & www.egr.msu.edu/classes/me851/jchoi/lecture/Lect_23.pdf

http://en.wikibooks.org/wiki/Control_Systems/Time_Variant_Systen_Solutions


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