Numerical Simulation for Solving Control Systems of High Dimension
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Date
2020-02-26
Authors
Sawafta, Hadeel Monther Fathi
Journal Title
Journal ISSN
Volume Title
Publisher
جامعة النجاح الوطنية
Abstract
In this thesis we have introduced some definitions in control theory including
dynamical system, Laplace transformation, Lyapunov equations, stability, con trollability, observability and their Gramians, we focus our attention mainly on
the numerical methods for solving control systems of high dimension. These
methods are: the balanced truncation method and the singular perturbation ap proximation method.
The mathematical framework of these numerical methods together with their
properties will be presented. These numerical methods will be clarified by some
numerical examples .
The two methods give us the same error bounds. For the balanced truncation
method the error is small at high frequencies and large at low frequencies, but
for the singular perturbation approximation we have large error at high frequen cies and small error at low frequencies.