Question

5. A milling machine has the following open-loop transfer function: (s 1)(s+3) Draw a block diagram describing a negative feedback system that includes a plant a) with transfer function of Gi(s) and a cascade proportional controller with a gain of K. b) Write the closed-loop transfer function for such a negative feedback system c The plant has poles that are solutions to P(s) 0 and zeros that are the solutions to Z(s)-0. Write an equation involving K, P(s) and Z(s) that holds for the closed-loop poles d) By substituting in for P(s) and Zs) or otherwise, deduce the position of the closed- loop poles when K-0. e Draw the root locus for Gi(s). Clearly indicate the positions of the closed-loop poles when K is infinite. f) Is the closed-loop system stable for all values of K?

Answer 1

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er Poles aa al-Sニー2,-2,-1,-2,-2,-2. to al of Poten aie6 k +3) (s+2) poles S-2,-2,-2,-2,-2 '-2 a, p- 2

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