Control
System Design - Helicopter - Introductory Problem
Dr. Abner Mallity - engineer bon vivant - has taken on a consulting job
that involves designing a control system for a new sport helicopter.
(The sport might be riding in anything designed by Dr. Mallity.)
Dr. Mallity knows almost nothing about helicopter dynamics and is trying
to figure out what he needs to do. He has done the following.
He has gone to the plant
where they make the helicopters, and he has recorded the speed of the main
rotor when the commanded speed was given a step change. He figures
that the rotor/motor/drive system has a time constant of about one (1.0)
second.
He also figures that the
lift generated by the rotor is proportional to the speed of the rotor.
He has dug out his old
textbook on "Statics and Dynamics", and he figures that the lift applied
to the helicopter body will result in a vertical acceleration, so that
the vertical position can be computed by integrating the lift twice.
(One integration gets you vertical velocity, the second integration gets
you vertical position.)
In his efforts to understand the system, he has gone to his graduate students,
Willy Nilly and Millie Farad. They have some expertise in simulation,
and they have put together a simulation for him that is incorporated in
the simulator below.
The problem here is that Dr. Mallity has been having trouble with the design
of the system. He is using a proportional control system - as shown
in the simulator. The simulator also shows a very low gain for the
system. That's in the ballpark of what Mallity has been trying.
However, he has not been successful in creating a good system. Can
you help him out?
Determine the range of
gains for which this closed loop system is stable.
Enter the password here
and click the button to go on.