Consider the feedback system in Figure 26. r 마 k G(s) Figure Q6: Feedback system In the case when (52 - 2s+2) G(8) = (5

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Consider the feedback system in Figure 26. r 마 k G(s) Figure Q6: Feedback system In the case when (52 - 2s+2) G(8) = (5 + 1)(8 + 25 + 2) and when kis positive: a) Sketch the root locus of the closed loop system. To assist in this 1) compute the open loop poles and zeros (3 marks) II) calculate the portion of the locus lying on the real axis (3 marks) ii) calculate the angles the asymptotes make with the real axis and also the value of the centroid (2 marks) iv) calculate the point at which the locus breaks away from the real axis (4 marks) V show that the angle of departure of the locus from the complex poles is 180 (4 marks) Use the above information, together with the fact that the angle of arrival of the locus at the complex zeros is 200, to complete the diagram (4 marks)