Discrete-time Flatness-based Control of a Gantry Crane

TL;DR

This paper develops a discrete-time flatness-based control method for a gantry crane, demonstrating improved robustness and practical applicability through experimental results and comparison with continuous-time control.

Contribution

It introduces a novel discrete-time flatness-based control approach for gantry cranes that preserves system flatness and enhances robustness over traditional continuous-time methods.

Findings

Discrete-time controller is more robust for large sampling times.

The approach allows for easier design of optimal reference trajectories.

Experimental results validate the effectiveness of the discrete-time control.

Abstract

This article addresses the design of a discrete-time flatness-based tracking control for a gantry crane and demonstrates the practical applicability of the approach by measurement results. The required sampled-data model is derived by an Euler-discretization with a prior state transformation in such a way that the flatness of the continuous-time system is preserved. Like in the continuous-time case, the flatness-based controller design is performed in two steps. First, the sampled-data system is exactly linearized by a discrete-time quasi-static state feedback. Subsequently, a further feedback enforces a stable linear tracking error dynamics. To underline its practical relevance, the performance of the novel discrete-time tracking control is compared to the classical continuous-time approach by measurement results from a laboratory setup. In particular, it turns out that the discrete-time controller is significantly more robust with respect to large sampling times. Moreover, it is shown how the discrete-time approach facilitates the design of optimal reference trajectories, and further measurement results are presented.