Answer Happy

Consider the generic feedback system shown in Figure 4, where G(s) is the plant's transfer function and C(s) is the controller's transfer function (8) G(s) Figure 4 The plant G(s), which is open-loop unstable, and the Controller C(s) are even as follows: (+)(+10) (5-2015+20 C(s) = (1) where k>O is a proportional gain. Study the root-locus of the feedback system through the following steps (a summary of the rules for rent locus construction is given at the end of the examination paper): state the open-loop poles and pers. [25 marks 00 determine the regions of the focus lying on the real axis. [1.5 marks) ENGD3113 - Examination Paper 2021/2022 draw an approximate root-locus diagram, 14 marks] (iv) determine the point at which the root-focus re-enters the real axis and the cartesponding value of £. Your answer should be justified. (4 marks] Hint: the re-entry point is one of these three points:-15.15.-7.15,5 I knowing that the root locus intersects the imaginary axis at the points=15.5). find the corresponding value of £. [marks] (vi) on the basis of the root locus obtained, discuss the variation in the properties of the feedback system (es. Oscillatory behaviour and stability) for different intervals of values of k. 19 marks]