Energy Shaping Control of an Inverted Flexible Pendulum Fixed to a Cart

TL;DR

This paper introduces a nonlinear energy shaping control method for an ultra-flexible inverted pendulum on a cart, effectively stabilizing it despite complex nonlinear dynamics and gravity effects, with validation through simulations and experiments.

Contribution

A novel energy shaping control approach combining partial feedback linearization and PID control for ultra-flexible pendulums, validated experimentally.

Findings

Controller achieves local asymptotic stability.

All signals in the system are bounded.

Experimental results confirm effective stabilization.

Abstract

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.