Here is the helicopter with a compensator (which can be either a lead or a lag - you set the paramters) used as a controller.  The transfer function for the helicopter is given by:

        To design a controller for this system, Dr. Abner Mallity started with a Bode' plot for the helicopter.  That plot is shown below.

If we examine this plot, we can see that if we try to design for a reasonable phase margin - say 50^o - then, we would have to choose a gain that puts the zero db crossing at approximately .02 Hz.  That would be about a 50 second settling time.  If you simulate the system using the pre-loaded values you should find a settling time in that ball park.  Try that now.  (Note, that in the simulator the pre-loaded values have the compensator pole and zero at the same frequency, so that there is on compensator effect!)

Now, there are some questions raised by all of this, not the least of which is the question of what can be done to make the system respond more quickly without an excessive amount of overshoot.  (There is no SSE problem here because of the pole at the origin.

        Here is what you need to do.

• Add a lead compensator to the system, inserting a transfer function into the controller block instead of the proportional gain now there.  Keep the phase margin the same.
• The transfer function of the compensator is K(as +1)/(bs + 1).
• Dr. Abner Mallity believes that "a" should be in the vicinity of 20.  Using that value, adjust the value of b using the Bode' plot for the open loop transfer function.
• Using the Bode' plot, adjust the value of the gain, K, in the compensator to produce the highest frequency zero-db crossing (to maximize the closed loop bandwidth).
• Determine the settling time by simulating the system in Simulink.  How much improvement can you achieve?