Why dоes LRU аpprоximаte Optimаl better than FIFO?
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Lоng Questiоn 1 Prоblem Stаtement Consider а feedbаck system below with G = 1/(s+10). You want to design a controller K(s) and if needed a prefilter F(s) to meet all the following specifications below. If r = 1 (i.e. a step) then the y(t) should reach the same value 1 in the steady state, i.e., zero error for step r. the settling time of y(t) response should be less than 1 seconds. the overshoot of y(t) response should be 0% the value of u(t) is finite. D(s) =0. Your Objective Answer the following parts neatly and separately: What do you need from/in the controller K(s) to meet the first specification (steady state y = r)? Explain briefly and mathematically using the formulae. (3 points) Draw the region in the 2D complex plane where the closed loop poles should be so that the settling time and overshoot specifications above are met? Explain briefly and mathematically using the formulae. (4 points) Explain what is needed to meet the finite u(t) specification. (3 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 calculations to find your final controller transfer function K(s), and if needed F(s). i.e. find the numerical values of gain/pole/zeros of K(s)/F(s) to get the transfer function. (5 points) Procedure Work neatly on paper showing all equations, steps, algebra, etc.Neat + clean + organized = extra credit! Then show your papers to camera for academic integrity. Then type things below. After exam, submit your work as a pdf on canvas. You may get some partial credit if it applies. Type Below (Very Important) Final transfer function of K(s) and if needed F(s)