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Disturbance Decoupling Problem for $n$-link chain pendulum on a cart system

Sayar Das, Deepak Patil

Abstract

A disturbance decoupling problem for a $n$-link chain pendulum on a cart is considered. A model of the cart developed in a coordinate-free framework and the linearized equations of this system are considered from [1]. It is shown that it is possible to design a suitable state feedback such that the angular position or velocity of the $n^{th}$-link can always be decoupled from the disturbance coming at the cart.

Disturbance Decoupling Problem for $n$-link chain pendulum on a cart system

Abstract

A disturbance decoupling problem for a -link chain pendulum on a cart is considered. A model of the cart developed in a coordinate-free framework and the linearized equations of this system are considered from [1]. It is shown that it is possible to design a suitable state feedback such that the angular position or velocity of the -link can always be decoupled from the disturbance coming at the cart.
Paper Structure (10 sections, 2 theorems, 29 equations, 4 figures)

This paper contains 10 sections, 2 theorems, 29 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Problem Formulation
  4. Model of $n$-link chain pendulum on a cart
  5. Euler-Lagrange equations
  6. Equilibrium Configurations
  7. Linearized equations of motion
  8. Disturbance decoupling applied to the system
  9. Numerical Example
  10. Conclusion and Future Works

Key Result

Theorem 1

Let $\mathcal{V}$ be a controlled invariant subspace. Then the following statements are equivalent:

Figures (4)

  • Figure 1: Vibration Isolation in LIGO
  • Figure 2: $n$-link chain pendulum on a cart
  • Figure 3: Effect of disturbance decoupling
  • Figure :

Theorems & Definitions (3)

  • Theorem 1
  • Theorem 2
  • proof