Question: Problem 3. Simple Root locus (4 pts.) 1 Consider this plant: G(s) = (s+a) Assume that we are closing a feedback loop around this

Problem 3. Simple Root locus (4 pts.) 1 Consider this plant: G(s)

Problem 3. Simple Root locus (4 pts.) 1 Consider this plant: G(s) = (s+a) Assume that we are closing a feedback loop around this system in our usual unity-feedback form with a positive gain K. R K G(s) Y We want to find the root locus for this system. You should do this problem entirely by pencil and paper, but you can use MATLAB to check your answer after you are done. (If you do this, the MATLAB check should not be submitted.) Hint: Feel free to make approximations regarding the magnitude of certain pole components if you need to calculate any angles by hand. a. Find the closed-loop transfer function and the closed loop pole. b. Sketch the path of the closed loop pole as K varies from K = 0 to K =8. Note: For this first order plant under proportional control, this is all the information we need to construct the root-locus.

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