4) Consider industrial automatic controllers whose control actions are proportional, integral, proportional-plus-integral, proportional-plus-derivative and proportional-plus-integral-plus- derivative. The transfer functions of these controllers can be given, respectively, by: (U(S) = KP E(s) E(s) U(s) _K, U($) = K, (1 +I,s) E(s) E(s) s + 1+Is) E(s) Is Where U(s) is the Laplace transform of u(t), the controller output, and E(s) is the Laplace transform of e(t), the actuating error signal. Sketch u(t) versus t curves for each of the five types of controllers when the actuating error signal is (5pts. 0.5 pts each sketch. 10 sketches total): (a) e(t) = unit step function (b) e(t)= unit impulse function In sketching curves assume that the numerical values of Kp, Ki, Ti, and T. are given as: Kp = proportional gain = 2 Ki = integral gain = 4 Ti = integral time = 5 sec To = derivative time = 2 sec