Using your favorite continuous-time modeling software (such as LabVIEW, Simulink, or Ptolemy II), construct a model of the helicopter control system shown in Figure 2.4. Choose some reasonable parameters and plot the actual angular velocity as a function of time, assuming that the desired angular veloc- ity is zero, (t) = 0, and that the top-rotor torque is non-zero, Tt(t) = bu(t). Give your plot for several values of K and discuss how the behavior varies with K.

Modify the model of part (a) to replace the Controller of Figure 2.4 (the sim- ple scale-by-K actor) with the alternative controller shown in Figure 2.6. This