Flatness Analysis for the Sampled-data Model of a Single Mast Stacker Crane

TL;DR

This paper demonstrates that the sampled-data model of a single mast stacker crane is flat by transforming a subsystem into a linear time-variant discrete-time form, enabling trajectory planning and control design.

Contribution

It introduces a novel flatness analysis for the sampled-data model of a crane, facilitating trajectory planning and control based on a new flat output construction.

Findings

The Euler-discretization of the crane model is flat.

A flat output involving backward-shifts is constructed.

Trajectory planning and feedforward control are enabled.

Abstract

We show that the Euler-discretization of the nonlinear continuous-time model of a single mast stacker crane is flat. The construction of the flat output is based on a transformation of a subsystem into the linear time-variant discrete-time controller canonical form. Based on the derived flat output, which is also a function of backward-shifts of the system variables, we discuss the planning of trajectories to achieve a transition between two rest positions and compute the corresponding discrete-time feedforward control.