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Electrical Engineering - Root locus

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(b) A particular system has the open loop transfer function:

g(s) = (s+4)/((s+1)(s-2))

sketch the root locus for this system

(c) The system is placed in a feedback control system as shown in Figure Q6. Determine the gain, k, which would result in marginal stability. Determine the frequency of oscillation which would result for this gain. What would be the effect of increasing the gain above this value

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(See attached file for full problem description)

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A comprehensive solution of root locus is provided. A diagram as well as equations to support the solution are provided. The solution is two pages in an attachment.

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Solution
(b)
1. Locate the poles and zeros of on the s-plane.
Poles are -1 and +2. Zeros is -4.

2. Determine the asymptotes of root loci.
Angle of asymptotes
when is number of poles and is number of zeros.

3. Find the breakaway and break-in points.
The ...

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