2. For the position control system shown in Figure 1, find the following: R(s) K (s + 3)(s + 4) s2 - 4s + 13 c(s). Figur
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2. For the position control system shown in Figure 1, find the following: R(s) K (s + 3)(s + 4) s2 - 4s + 13 c(s). Figur
2. For the position control system shown in Figure 1, find the following: R(s) K (s + 3)(s + 4) s2 - 4s + 13 c(s). Figure 1: Block diagram of a position control system (a) Plot the root locus of the system using MATLAB. [5 marks) (b) From the root locus, determine the following: i. The range of K for the system to be stable. ii. The value of K that makes the system marginally stable and the corresponding frequency of oscillation. iii. The range of K for the system to be unstable. [11 marks] (c) Plot the transient response for each of the cases above, selecting the appropriate K for each of the cases (b)(i) and (b)(ii) using MATLAB. [6 marks)
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