4. Consider a unity (negative) feedback control system whose open-loop transfer function is given by the following. 2 G(s) = s³ (s + 2) Find the steady-state error of the system for each of the following inputs. = a) u(t) (t²+8t+5) 1(t) b) u(t) = 3t³ 1(t) c) u(t) (t+5t² - 1) 1(t) =

5. Consider following feedback system. R(s) + 100 S+4 +1 Find the steady-state error for (i) step input and (ii) ramp input.

29. The unity feedback system of Figure P7.1, where G(s) = K(s+a) s(s+ B) to Juqni ns Tol botoqxs 75 14. 9190 ST Jor Wa is to be designed to meet the following require- lo ments: The steady-state position error for a unit ramp input equals 1/10; the closed-loop poles will be located at -1 ± jl. Find K, a, and ß in order to meet Jinu onu O SIL 10 1 UST OB-DA the specifications. [Section: 7.4]

A unity feedback system with forward transfer function below G(s) = K/(s(s+6)).is operating with a closed-loop step response that has 15% overshoot. Please solve for the following:a. Evaluate the settling time. b. Evaluate the steady-state error for a unit ramp input. c. Design a lag-lead compensator to decrease the settling time by 2 times and decrease the steady-state error for a unit ramp input by 10 times. Place the lead zero at -3.