Robust control of the inverted pendulum

The inverted pendulum is a unstable non-minimum-phase plant, H
∞
output feedback control of the system is far less robust. The difficulties of control of such a plant are analysed from the viewpoint of system’s bandwidth: the bandwidth for control of a non-minimum-phase plant must be narrow, and the control of an unstable plant need a rather wider bandwidth. It is pointed out that a fast feedback loop must be designed first to stabilize the unstable dynamics. Then is the narrow bandwidth loop for the resulting non-minimum-phase but stable plant. Such an approach will give a robust design as illustrated by an example.