3) Michael is hired by Collegiate Beverage Company to tune the controller on their new pasteurizer (installed to increase the shelf life of the product). The first-order temperature process has a time constant of 250 seconds is being controlled with PID controller with default integral and derivative gains set to Zero and a proportional gain of 1.0. At a time considered = 0, Michael changes the setpoint quickly from 70 to 80C. Determine the expected value of the controlled (temperature) variable after: a) 50 seconds b) 2 minutes c) 4 minutes d) 10 minutes 4) (continues from problem 3) Right at 20 minutes, Michael sets the proportional gain to Zero and the integral gain to 3 radians per minute, then: a) Determine the effective damping of this new controller setting on this feedback control system. b) Determine the period of any resulting oscillation of the pasteurizer's temperature of this controlled process. c) Determine the pasteurizer's temperature at time = 23.5 minutes.