Problem 1. (20 points) (a) Construct a Simulink model of the helicopter control system shown in the figure below. Controller3 1/K T Controller Scale Ty K a Integrator i == bu(t). Give Choose some reasonable parameters and plot the actual angular velocity as a function of time, assuming that the desired angular velocity is zero, (t) = 0, and that the top-rotor torque is non-zero, T+(t) your plot for three different values of K and discuss how the behavior varies with K. (b) Modify the model of part (a) to replace the Controller (the simple scale-by-K actor) with the alternative controller shown in the figure below. Controller i = 0 K This alternative controller is called a proportional-integrator (PI) controller. It has two parameter K and K2. Experiment with the values of these parameters, give some plots of the behavior with the same inputs as in part (a), and discuss the behavior of this controller in contrast to the one of part (a).