Our friend, Dr. Abner Mallity, has recently gotten some work from AAA. That's not the automobile club, it's the other AAA, the Antique Aircraft Association.
While AAA members like to keep their aircraft as close to original as possible, they also like to keep them together. AAA has contacted Dr. Mallity about designing a flight control system that will give some control of these aircraft as pilots do other things in their shows. He has decided to start by designing an altitude control system. Since the system will be used on a variety of old clunkers the system will have to work for a number of different aircraft - all with different dynamics. Mallity has made some paper airplanes and has come to the following conclusions.
Mallity needs your help. Actually, he needs any help he can get, not just technical help. However, for the moment he needs to predict performance for this system - assuming that his guess for the transfer functin is correct. One of his graduate students has written a simulation for this system, and that's shown below. You can experiment with this simulation - since you can change the gain to any value you want - to help your understanding of the system Mallity has proposed. The simulation has been written to reflect the environment where the president of AAA (Dr. Alex Blaine Layder, who teaches math at the local community college) lives, i.e. Worland, Wyoming. That's the Big Horn Mountains in the backdrop. Worland is just west of the Big Horns (Cloud Peak goes to 13,125 ft) and is at an elevation of about 4000 ft. The desired altitude of 7000 ft, used in the simulation, is a reasonable altitude for this area, except when flying near the Big Horn Mountains.
There are several questions that arise for this aircraft. Here are some links to those questions.