Energy shaping control of an inverted flexible pendulum fixed to a cart

• A passivity-based controller (PBC) is proposed to stabilize an inverted flexible pendulum.
• The Euler–Lagrange model of the system takes into account a holonomic constraint and multiple equilibria.
• The PBC is designed without solving partial differential equations and consists in two main steps: a partial feedback linearization and an energy shaping feedback.
• Simulations and experiments results are presented.

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.