- #1

paul2211

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The theoretical question for which I am having trouble. When designing a controller to compensate a process using Bode Plots, why does my book seem to just use the forward loop gain rather than the transfer function (of an unity feedback system)?

i.e. For a forward path of Gc(s) and G(s) with unity feedback, the book's example seems to just overlay these two bode plots to meet the design requirements. Why did it not find the transfer function, and instead just uses the forward loop gain? (Or I am totally misunderstanding what my book does)

1. Homework Statement

1. Homework Statement

Design a phase lead / lag controller so that G(jω) = 300,000/s(s+360) will have a Phase Margin (PM) of 60 degrees and have high frequency (ω >= 1000 rad/s) gain <= -20 dB

## Homework Equations

L(s) = Gc(s)G(s), where Gc(s) = K(s+z)/(s+p) as a Lead/Lag compensator

The picture of the control system I am referring to is: http://wps.prenhall.com/wps/media/objects/1468/1503802/ch10mc3.gif

Please ignore the equations as this is not the question I am doing.

## The Attempt at a Solution

Solving for ωcrossover using the uncompensated system:

0 ≈ 20log(833.333/(ω^2/360)

ω = 548 rad/s

Plugging into phase: Ang G(s) = 0 - 90 - atan(ω/360) = -146 degrees. PM uncompensated = -146 + 180 = +34 degrees.

Cannot use phase lead compensator with the phase peak at 548 rad/s because it will increase magnitude's gain at high frequencies. Uncompensated gain is at -13 dB at 1000 rad/s, so I must decrease high frequency gain.

This means I will need a phase lag compensator, which decreases the gain at high frequencies.

Now I am stuck. I cannot design a lag compensator at the original crossover ω = 548 rad/s because it will decrease the PM. So I essentially need to design something that will decrease the crossover frequency using the magnitude plot.

The way my professor does in class seems more like an art than science. I feel like this will need MATLAB to do. My prof hinted that these types of questions will be on the final, so are there any hints/systematic ways to design these controllers?

Thanks so much!