  Control of compliant mechanical systems is increasingly being researched for
several applications including flexible link robots and ultra-precision
positioning systems. The control problem in these systems is challenging,
especially with gravity coupling and large deformations, because of inherent
underactuation and the combination of lumped and distributed parameters of a
nonlinear system. In this paper we consider an ultra-flexible inverted pendulum
on a cart and propose a new nonlinear energy shaping controller to keep the
pendulum at the upward position with the cart stopped at a desired location.
The design is based on a model, obtained via the constrained Lagrange
formulation, which previously has been validated experimentally. The controller
design consists of a partial feedback linearization step followed by a standard
PID controller acting on two passive outputs. Boundedness of all signals and
(local) asymptotic stability of the desired equilibrium is theoretically
established. Simulations and experimental evidence assess the performance of
the proposed controller.
