## Publication Date

Fall 12-3-2018

## Abstract

In this thesis the Double Pendulum Inverted on a Cart (DPIC) system is modeled using the Euler-Lagrange equation for the chosen Lagrangian, giving a second-order nonlinear system. This system can be approximated by a linear first-order system in which linear control theory can be used. The important definitions and theorems of linear control theory are stated and proved to allow them to be utilized on a linear version of the DPIC system. Controllability and eigenvalue placement for the linear system are shown using MATLAB. Linear Optimal control theory is likewise explained in this section and its uses are applied to the DPIC system to derive a Linear Quadratic Regulator (LQR). Two different LQR controllers are then applied to the full nonlinear DPIC system, which is concurrently modeled in MATLAB. Also, an in-depth look is taken at the Riccati equation and its solutions. Finally, results from various MATLAB simulations are shown.

## Degree Name

Mathematics

## Level of Degree

Masters

## Department Name

Mathematics & Statistics

## First Committee Member (Chair)

Jens Lorenz

## Second Committee Member

Monika Nitsche

## Third Committee Member

Stephen Lau

## Language

English

## Keywords

Control Optimal Riccati Double Pendulum Cart

## Document Type

Thesis

## Recommended Citation

Crowe-Wright, Ian J P. "Control Theory: The Double Pendulum Inverted on a Cart." (2018). https://digitalrepository.unm.edu/math_etds/132

#### Included in

Control Theory Commons, Dynamical Systems Commons, Dynamic Systems Commons, Non-linear Dynamics Commons