Binoy's Tech Blog: Control Systems

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The purpose of this blog is purely to serve as a compilation of good technical material for my students. No financial or other motives are involved. Most of the content in this blog has been reproduced from other sources. I have made every attempt to mention the source link at the beginning of each blog. All readers are requested to kindly acknowledge that source and not this blog, in case you find the post helpful. However, I have not been able to trace the source links for some of my older posts. I wish to emphasize that this is not intentional and any help in this regard would be appreciated.

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:

Determine K from the error constants given
Sketch the bode plot
Determine phase margin
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 $\phi_m/2$
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
$-20log(1/\sqrt(\alpha))$
calculate
$T=\frac{1}{\omega_m \sqrt(\alpha)}$
a lead compensator has the form
$\frac{(s+\frac{1}{T})}{(s+\frac{1}{\alpha T})}$
form the complete transfer function with the lead compensator added in series to th original system
plot the new Bode plot and determine phase margin and observe that it is the required phase margin
if not satisfactory repeat steps from step 4 by changing value of $\epsilon$ by 5

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

Determine K from the error constatns given
Sketch the bode plot
Determine phase margin if it is not satisfactory design lag compensator
take as the required phase margin to that add a tolerance of 5 so that new phase margin is
$\gamma_{n}=\gamma_{d}+5$
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 $\phi_{gcn}$
Determine gain corresponding to $\omega_{gcn}$ from bode plotlet it be A db
a lag compensator has the form
$\frac{(s+\frac{1}{T})}{(s+\frac{1}{\beta T})}$
$\beta=10^{\frac{A}{20}}$ since
$A = 20log\beta$
$T= \frac{10}{\omega_{gcn}}$
form the complete transfer function with the lag compensator added in series to th original system
plot the new Bode plot and determine phase margin and observe that it is the required phase margin