[SOLVED] Lecture 10

Lecture 10
Examples of Bode diagrams

Recap of Bode diagrams

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Bode via Matlab
Examples of Bode diagrams Conclusions

Bode via Matlab
To get the magnitude in decibels, use magdB=20*log10(mag)
For this transfer function: use
num=[0 0 25]
den=[1 4 25]
bode(num,den)
title(of G(s)=25/(s^2+4s+25))

Bode diagram of a positive constant
Time response

Bode diagram of a negative constant
Time response

Bode diagram of a differentiator
Time response

Bode diagram of an integrator
Time response

Bode diagram of a real zero term
Time response

Asymptotic behaviour
For small frequencies the system behaves like positive constant gain
For large frequencies the system behaves like a differentiator:

A useful relationship
For reciprocal factors, Bode diagrams just need to change sign:

Bode diagram of a real pole term
For instance, we have for
For exercise find the time response of the system as we did in previous examples.

A second order system

Summary of common cases
Taken from Goodwin, Graebe and Salgado, Control system design.

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