PendCon Advanced: The Rotary Pendulum Experiment
The Rotary Pendulum Experiment
Main characteristics
Perhaps the most famous experiment in control theory is the inverted pendulum experiment where the pendulum is mounted on a small carriage. This experiment has a rotary version: Then the pendulum is mounted on a horizontal rotating rod. The linearized dynamics for the inverted position has a double pole at the origin, one negative, and one positive pole (if friction is neglected). In this experiments, the students see perhaps for the first time that a PID controller is not adequate and that more refined controller design methods are required.
Some tasks for the students
The experiment should start with a careful analysis of the plant dynamics. Main topics are nonlinearity and instability and the students may be asked to adapt some parameters in the simulation model to bring the simulated quantities in accordance with the measured ones. Then, for the hanging pendulum, they may be asked to design a PID controller that places the horizontal bar in a desired position and, at the same time, is able to suppress the oscillations of the pendulum as good as possible. Then, in a second step, a better performance will be obtained when also the angular displacement of the pendulum is fed back, but this requires a more advanced design method. Much more exiting is of course the stabilization of the pendulum in its inverted position. Various tasks may be formulated and solved by different design methods. At the end of a lab session, the students could be asked to design intuitively a controller that swings-up the pendulum. The SW contains one proposal for such a controller.