Free collection of beautiful vector icons for your web pages.

Dynamic model of an inverted pendulum (part 1)

Introduction

This post presents the model of an inverted pendulum. This device is composed of an activated trolley and a pendulum which has its center of mass above its pivot point.

In this post, we will assume the following hypotheses:

$m_1$ is the mass of the trolley.
$m_2$ is the mass of the pendulum.
$I_1$ is the moment of inertia of the trolley.
$I_2$ is the moment of inertia of the pendulum.
$L$ is the distance between the pivot and the center of mass of the pendulum.
$\Theta$ is the angle of inclination of the pendulum.
$x_1$ and $y_1$ are the coordinates of the center of mass $C_1$ of the trolley .
$\Theta_1$ is the orientation of the trolley.
$x_2$ and $y_2$ are the coordinates of the center of mass $C_2$ of the pendulum.
$\Theta_2$ is the orientation of the pendulum.

The following notation will be used in this article to avoid too complex equations for the derivatives:

$$ \dfrac{d\Theta}{dt} = \dot{\Theta} $$

And for the second derivative:

$$ \dfrac{d^2\Theta}{dt^2} = \ddot{\Theta} $$

Part 2

Dynamic model of an inverted pendulum (part 1)

Introduction

See also