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Input-output linearization and decoupling of mechanical control systems

Marcin Nowicki, Witold Respondek

TL;DR

This work shows that the natural requirement of preserving mechanical structure of the system and of transformations imposes supplementary conditions when compared to the classical solution of the same problem for general control systems.

Abstract

In this work, we present a problem of simultaneous input-output feedback linearization and decoupling (non-interacting) for mechanical control systems with outputs. We show that the natural requirement of preserving mechanical structure of the system and of transformations imposes supplementary conditions when compared to the classical solution of the same problem for general control systems. These conditions can be expressed using objects on the configuration space only. We illustrate our results with several examples of mechanical control systems.

Input-output linearization and decoupling of mechanical control systems

TL;DR

This work shows that the natural requirement of preserving mechanical structure of the system and of transformations imposes supplementary conditions when compared to the classical solution of the same problem for general control systems.

Abstract

In this work, we present a problem of simultaneous input-output feedback linearization and decoupling (non-interacting) for mechanical control systems with outputs. We show that the natural requirement of preserving mechanical structure of the system and of transformations imposes supplementary conditions when compared to the classical solution of the same problem for general control systems. These conditions can be expressed using objects on the configuration space only. We illustrate our results with several examples of mechanical control systems.
Paper Structure (10 sections, 5 theorems, 52 equations, 3 figures)

This paper contains 10 sections, 5 theorems, 52 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Problem formulation
  3. Mechanical control systems
  4. Main result
  5. Examples
  6. The Inertia Wheel Pendulum
  7. TORA3
  8. Forced double pendulum on an oscillating base.
  9. Conclusions
  10. Appendix

Key Result

Theorem 1

For the mechanical control system eq:ms with outputs the MIOLD-problem is solvable, locally around $x_0\in Q$ and globally in $v\in \mathrm{T}_xQ$, if and only if the system eq:ms

Figures (3)

  • Figure 1: The Inertia Wheel Pendulum
  • Figure 2: The TORA3 system.
  • Figure 3: Forced double pendulum on an oscillating base

Theorems & Definitions (12)

  • Definition 1
  • Remark 1
  • Theorem 1
  • Remark 2
  • Remark 3
  • proof
  • Corollary 1
  • Corollary 2
  • Proposition 1
  • Remark 4
  • ...and 2 more