Lоng Questiоn 2 Prоblem Stаtement Consider а feedbаck system below with G = 6/(s+6) and H= 2/(s+2). You want to design a controller C(s) and prefilter F(s) to meet all the following specifications below. If r = t (i.e. a unit-sloped ramp) then the y(t) and r(t) should not be farther than 0.5 from each other for large times, i.e., steady state error < 0.5 error in y(t) due to a step disturbance d(u) should be zero! your controller can NOT have more number of zeros than poles, i.e. it must be proper. This is a strict requirement! For a very specific settling time and overshoot, I want the closed loop TF to have two repeated poles at -5. And no other closed loop poles and no closed loop zeros. Type below the following parts neatly and separately. (4 points) What do you need from/in the C(s) and F(s) to meet to meet the ramp error specification? Explain mathematically using the formulae in 2-3 sentences. (3 points) What do you need from/in the C(s) and F(s) to meet the disturbance error specification? Explain mathematically using the formulae in 2-3 sentences. (5 points) By plotting the root locus explain what kind of controller C(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 C(s) you tried. Paste the snapshot of the resulting root-locus. Type to explain why that meets the specifications (or not). (6 points) Type the closed loop calculations, to calculate the numerical values of gain, poles, and zero of C(s) and if needed F(s) so that the CLTF meets all the specifications. (2 points) What will be the overshoot in y(t) for step r(t)? Explain.