Control Systems Problem

A Proportional Control Problem
Problem PID1IP03

The old airplane company is at it again. They are not satisfied with the way they move the ailerons and other control surfaces (elevators and rudder) in their aircraft. They have been using mechanically connected wires and that seems to take enough pilot effort that they want to reduce the strength it takes to fly the plane. Now they want to use a hydraulic servo for every control surface, and they have been testing a few planes with those servos installed. The planes are similar in every regard to the ones you have already worked with, and they have two planes with servos installed - one of each variety that you have seen (two different kinds of control surfaces). Every servo is pretty much the same, and every one has a time constant of one second.

The addition of that one second time constant is the only real change in the system. The company figures that it won't change things much since that one second time constant is a lot faster than any of the other parts of the system's dynamics.

What they need from you is some analysis that will allow them to set the gain of the proportional controller for the plane. Willy Nilly and Millie Farad are back after being swindled on that "Island of Langerhans" thing and they are in no mood to give you any help. (Maybe you can figure out why it had to be a swindle and why they should have figured it out beforehand.) There is a simulator they wrote before they left that you can get to by clicking here.

Is the steady state error predictable?

SSE is a function of gain. Does the SSE behave the way you expect? You will need to check at least 3 (preferably more) values of gain, compute SSE and compare results with predictions.

Does the system behave as you expect? Evaluate the following.

Response in general.
Rise time.
Percent Overshoot.

Relate performance to pole location. In turn, pole location is a function of the proportional gain that you use. As you begin to study about the root locus you will find that pole location is a function of the loop gain, and that understanding how pole location affects performance, and how pole location changes as you change the gain are both important things for you to learn.

If you want a hard copy of the data after you run a simulation, highlight the simulator window by clicking in it, and then hit "Alt + Print Screen". That puts a copy of the picture on the clipboard, and you can paste that into any application that accepts pictorial data.