Swinging up an inverted pendulum

The inverted pendulum (i.e., a pendulum standing upright instead of hanging down) is a classical benchmark system in control. Despite the stabilization of the system around the unstable upper equilibrium via suitalbe controllers, the swing-up of the pendulum is a challenging task. Various methods for this swing-up have been proposed in the literature. In the lab, energy-based, time optimal, data-driven approaches are investigated.

The lab starts with an introduction to the technical setup. The lab uses an inverted pendulum of the company Quanser (focussing on control education). The pendulum comes with a MATLAB/Simulink interface, which allows to easily apply and test controllers and swing-up procedures. Once the students are familiar with the setup, the lab first aims for an implementation of a stabilizing controller for the upper equilibrium. Then, three different swing-up strategies shall be investigated. First, an approach based on the maximization of the pendulum's (potential) energy is considered. Second, a time-optimal (bang-bang) actuation is computed. Third, a parameter identification is applied to improve the model-based swing-up. All approaches are applied to the actual system and compared with each other.

K. J. Aström and K. Furuta. Swinging up a pendulum by energy control, Automatica, vol. 36, pp. 287–295, 2000.

S. Mori, H. Nishihara and K. Furuta. Control of unstable mechanical system Control of pendulum, Intenational Journal of Control, pp. 673-692, 1976.