Here is a system that presents some problems.  The control system should control the altitude of the helicopter.  However, the response is slower than desirable, and you need to design a system that will have a faster response.  You would like to have a settling time of 25 seconds or less.

        You can try the system with a number of gains.  You will probably find that the settling time is around 45 or 50 seconds, and that you can't make that measurement change much by varying the gain.

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.
• 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.