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# (Solved): A dynamic system in a negative unity feedback configuration has the root locus, shown in Fig. Use t ...

A dynamic system in a negative unity feedback configuration has the root locus, shown in Fig. Use the given root locus plot to answer the following questions: (a) What are the open-loop poles and zeros of this system? (b) Is the open-loop transfer function stable? (c) For what range of values of the gain \( K \) is the closed-loop system stable? (d) For \( K=15 \) : - What are the closed-loop poles? - What are the dominant poles (if exist)? - What is the settling time? - What is the peak time? - What is the max. overshoot? (e) For what value of \( K \) does the closed-loop system have a minimum settling time? (f) For what value of \( K \) does the closed-loop system have a minimum peak time? (g) For the value of \( K \) in (f): - List all the poles of the closed-loop system - What is the natural frequency of the dominant poles of the system? (h) For what value(s) of the gain \( K \) does the closed-loop system have two real repeated poles? (i) For the value(s) of \( K \) in (h) list the other poles (j) For what range of \( K \) all poles of the system are complex? (k) What is the minimum closed-loop steady-state error for the step input? (l) What value of \( K \) will yield a minimum closed-loop steady-state error for ramp input? Figure 4

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