On the linear control of underactuated systems: The flywheel inverted pendulum

Underactuated systems are usually represented by nonlinear models and their control requires the design of nonlinear controllers. The flywheel inverted pendulum is a special case, also nonlinear, but admitting a linear approximation around the unstable equilibrium point in the upper position. In this paper, a linear controller is designed in two steps. First, the output is controlled with a simple PID controller, leading to an internally unstable plant. Then, a second linear controller in an outer loop provides the global stability, showing good regulation and disturbance rejection performance. Experimental results show the effectiveness of the design.