Consider the following feedback control systems: 1) Derive the relationship between E(S)/R(s). 2) Apply the input r(t)=2u(t) where u(t) is a step function (in Laplace is 1/s ). 3) Replace the input be a ramp function r(t)=tu(t) 4) Find the final values of E(s) in both cases (use limit s-> 0sR(s)E(s) where E(s) is computed in 1 and R(s) in the input in the Laplace domain). 5) Simulate the system using MATLAM with both inputs in 2 and 3. 6) Replace the controller 5 by 5/s and re-simulate the system. 7) Include your figures and your derivation for 1 in files