Analysis of Dynamic Systems

Schedule:

  • Getting started
  • Introduction
  • Mathematical bases
  • Bode diagrams
  • Modeling with linear elements
  • State variables
  • Block diagrams
  • Time response
  • Frequency response
  • Stability
  • Root Locus
  • Final project
  • Course evaluation

Mathematical bases

  • Complex Variable Theory.
  • Differential equations.
  • Laplace transform.
  • Theory of matrices.
  • Bode diagrams.

Complex Variable

The complex variable $s$ has two components:

  • $\sigma$: The real part
  • $\omega$: The imaginary or complex part

So, $s = \sigma + j \omega$.


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from IPython.display import SVG
SVG('img/intro_fig7.svg')


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image/svg+xml Complex plane J 1 1 s = 1 + 1

Functions of a Complex Variable

$G(s)$ is a function of the complex variable $s$, when for each value of $s$ there exists a corresponding value (or several) of $G(s)$.

$$G(S)=Re (G) + J Im (G)$$

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from IPython.display import SVG
SVG('img/intro_fig8.svg')


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image/svg+xml s G(s)

For example:

$$G(s)=\frac{1}{s(s+1)}$$

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Image(filename='img/output1.jpg')


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Image(filename='img/output2.jpg')


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Image(filename='img/output3.jpg')


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Image(filename='img/output4.jpg')


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