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# PI Controller and Nyquist Analysis

(Complete problem with equations found in attachment).

Problem 1

A very common industrial controller is the proportional and integral (PI) controller. It has
a transfer function,

, kp is the proportional gain, Ti is the "reset time"

For an integrating process, P(s) = 2/s, investigate the positive root locus for
a) fixed Ti = 10 and varying kp.

b) fixed kp = 10 and varying Ti.

Problem 2

a) For each of the three loop transfer functions L(s) listed below, sketch the
Nyquist locus. In each case, determine the range (or ranges) of gain K for stability.

b) For each of the two loop transfer functions L(s) listed below, sketch the Nyquist locus. In each case, label the regions of stability appropriately (you don't have to calculate ranges of K).

c) What is the pole-zero plot that corresponds to the Nyquist Plot below?

(Complete problem with equations found in attachment).

#### Solution Summary

The solution solves all questions provided in the document regarding the PI controller and nyquist analysis.

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