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Nov 7, 2014

Lag Compensator design with Bode plot

The post below has been copied from: http://thebeautifullmind.com/2012/05/23/an-introduction-to-compensator-design-with-matlab/
Please note that in case you find this helpful, please cite  the above source and not this blog post.     

The steps to design the lag Compensator are
  1. Determine K from the error constatns given
  2. Sketch the bode plot
  3. Determine phase margin if it is not satisfactory design lag compensator
  4. take  as the required phase margin to that add a tolerance of 5 so that new phase margin is
    $\gamma_{n}=\gamma_{d}+5$
  5. Find new gain cross over frequency $\omega_{gcn}$ which is the frequency corresponding to $\gamma_n$ of previous step for that find
    $\phi_{gcn}=\gamma_n - 180$ from the bode plot determine $\omega_{gcn}$corresponding to $\phi_{gcn}$
  6. Determine gain corresponding to $\omega_{gcn}$ from bode plotlet it be A db
  7. a lag compensator has the form
    $\frac{(s+\frac{1}{T})}{(s+\frac{1}{\beta T})}$

  8. $\beta=10^{\frac{A}{20}}$ since
    $A = 20log\beta$

  9. $T= \frac{10}{\omega_{gcn}}$
  10. form the complete transfer function with the lag compensator added in series to th original system
  11. plot the new Bode plot and determine phase margin and observe that it is the required phase margin
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