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Nov 7, 2014

Lead Compensator Design

he post below has been copied from: http://thebeautifullmind.com/2012/05/24/lead-compensator-design-with-bode-plot/
In case you find this helpful, please acknowledge the blog above and not this one. The post has been reproduced to help my students understand the concepts and for no other reason.   

The steps to design the Lead Compensator are:
  1. Determine K from the error constants given
  2. Sketch the bode plot
  3. Determine phase margin 
  4. The amount of phase angle to be contributed by lead network is
    $\phi_m=\gamma_{d}-\gamma + \epsilon$, where $\gamma_d$ is the required phase margin and $\epsilon$ is 5 initially. if the angle is greater than 60then we have to design the compensator as 2 cascade compensator with lead angle as $\phi_m/2$
  5. calculate
    $\alpha=\frac{1-sin(\phi_m)}{1+sin(\phi_m)}$ from bode plot find $\omega_m$ such that it is the frequency corresponding to the gain
    $-20log(1/\sqrt(\alpha))$
  6. calculate
    $T=\frac{1}{\omega_m \sqrt(\alpha)}$
  7. a lead compensator has the form
    $\frac{(s+\frac{1}{T})}{(s+\frac{1}{\alpha T})}$
  8. form the complete transfer function with the lead compensator added in series to th original system
  9. plot the new Bode plot and determine phase margin and observe that it is the required phase margin
  10. if not satisfactory repeat steps from step 4 by changing value of $\epsilon$ by 5
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