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Update Control_systems.md
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GerritKuik committed Mar 13, 2024
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(control_systems)=
exercise(control_systems)=
# Control systems

In this chapter a number of basic principles of control systems are covered. The following will be discussed:
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$$
\begin{split}
{\rm Re} [ A ( \omega ) ] &= \frac{\omega^2 \tau^2}{1 + \omega^2 \tau^2} = \frac{1}{1 + \left( \frac{1}{\omega \tau} \right)^2},\; {\rm and} \\
{\rm Im} [ A ( \omega ) ] &= \frac{\omega \tau}{1 + \omega^2 \tau^2} = \frac{1}{1 + \frac{1}{\omega \tau} + \omega \tau}.
{\rm Re} [ A ( \omega ) ] &= \frac{\omega^2 \tau^2}{1 + \omega^2 \tau^2},\; {\rm and} \\
{\rm Im} [ A ( \omega ) ] &= \frac{\omega \tau}{1 + \omega^2 \tau^2}.
\end{split}
$$ (eq:ch7-15)
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