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I am trying to design a closed loop system with a PI controller. I have plotted root loci before, but in those, I had assumed that the controller was only Proportional. This gave a characteristic equation of the form:

1 + K*(n(s)/d(s)) = 0

where K is the proportional controller gain, which was varied to plot the root locus.

However, with a PI controller, there are two gains Kp and Ki, so how do I plot the root locus since both of them can be varied?

Francis Vellara
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  • If you were going to draw a block diagram of a PI controller, what would it look like? Could you use properties of control block diagrams to reduce any equations? (I’m asking these questions to you as hints) –  Sep 10 '20 at 04:25
  • **1**) What do you think the resulting locus will look like and **2**) how are you planning to use it for design? – AJN Sep 10 '20 at 04:36
  • Are you going to use software to plot the locus(numerical)? Or manually on own and paper(analytical expression)? – AJN Sep 10 '20 at 04:37
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    You could fix one and plot the locus of the other, then repeat. – copper.hat Sep 10 '20 at 04:56

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