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Free respоnse questiоn 1 (Tоtаl 20 points) Tests the Core outcomes 2 START ON A NEW PAGE. Work in а neаt, clean, and organized way (and get extra credit!) You'll submit your written work as a pdf after the exam is over. Briefly show your page(s) to the camera during the exam for academic integrity. Consider a feedback system below with G = 1/(s+1). Design a controller K(s) and if needed F(s) to meet all of the following specifications If r = 1 (i.e. a step) then in the steady state y(t) is between 0.9 to 1.1. If d = 1 (i.e. a step disturbance) then the output y(t) is not affected by it in steady state. If r = 1 (i.e. a step) then the settling time of y(t) response is less than 4s If r = 1 (i.e. a step) then the overshoot of y(t) is less than 5%. Answer the following parts neatly and separately on a new page: What do you need from/in the controller K(s) to meet the first specification (due to step r) ?Explain briefly and mathematically. (3 points) What do you need from/in the controller K(s) to meet the second specification (due to step d)?Explain briefly and mathematically. (3 points) What region in the 2D complex plane should the closed loop poles be so that the settling time and overshoot specifications above are met?Explain briefly and mathematically. ( 4 points) By plotting the root locus explain what type of controller is needed to meet all the specifications.i.e., what controller poles and zeros (if any) are needed to meet all the specifications. (5 points) Perform the closed-loop calculations to find your final controller transfer function K(s),i.e. find the numerical values of gain/pole/zeros of K(s) (and if needed F(s)) to get the transfer function. (5 points) No need to type anything below.Just work on paper, show to camera during exam, and submit pdf after exam.