A closed-loop control system is shown in Figure 4, where G(s) is the transfer function of the system,G.(s) is the transfer function of the controller, D(s) is a disturbance, R(s)

and Y(s) are the input1and output, respectively. The open-loop system is unstable with a transfer function of G (s)(1/s-Y)'= where y is 6 The objectives of the controller, G.(s), are to make the closed-loop system stable and at the same time to minimize the effect of the disturbance. Ks+yConsider a proportional-integral (PI) controller with a transfer function G.(s)Answer theSfollowing questions: Determine a suitable value of K so that the closed-loop system is stable. Note: you need to justify the choice of your designed gain K. Find the steady-state error for the case whereR(s) =1and D(s) = 0.S Find the steady-state output of the system when R(s)= 0 and D(s) = -S Base on the above analysis, explain whether the objectives of the controller have been met or not.

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