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. Type below the following parts neatly and separately. (3 points) What do you need from/in the K(s) and F(s) to meet the first specification (steady state y = r)? Explain mathematically using the formulae in 2-3 sentences. (4 points) Draw and paste snapshot of 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) (3 points) Explain what is needed from/in K(s) and F(s) to meet the finite u(t) specification. (3 points) (5 points) By plotting the root locus explain what kind of controller K(s) (i.e., what kind of controller poles and zeros) are needed to meet all the specifications. No need to find the values of those poles/zeros yet, a symbolic expression is fine. Type what K(s) you tried. Paste the snapshot of the resulting root-locus. Type to explain why that meets the specifications (or not). (5 points) Type the closed loop calculations, to calculate the numerical values of gain, poles, and zero of K(s) and if needed F(s) so that the CLTF meets all the specifications.