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

Johannes Diwold, Bernd Kolar, Markus Schöberl

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.

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

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.
Paper Structure (12 sections, 55 equations, 3 figures)

This paper contains 12 sections, 55 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Model of a Single Mast Stacker Crane
  3. Derivation of the Continuous-time Model
  4. Flatness of the Continuous-time Model
  5. Motivation and Problem Statement
  6. Flatness of Time-variant Discrete-time Systems
  7. Flatness of Nonlinear Time-variant Systems
  8. Flatness of Linear Time-variant Single-input Systems
  9. Sampled-data Model of the Single Mast Stacker Crane
  10. Flatness of the Sampled-data Model
  11. Trajectory Planning and Feedforward Control
  12. Conclusion and Outlook

Figures (3)

  • Figure 1: Schematic of a single mast stacker crane.
  • Figure 2: Transition between two rest positions.
  • Figure 3: Feedforward control ($T_s=50\text{ms}$).