Feedback Stabilization of Inverted Pendulum Models

Many mechanical systems exhibit nonlinear movement and are subject to perturbations from a desired equilibrium state. These perturbations can greatly reduce the efficiency of the systems. It is therefore desirous to analyze the asymptotic stabilizability of an equilibrium solution of nonlinear systems; an excellent method of performing these analyses is through study of Jacobian linearization's and their properties. Two enlightening examples of nonlinear mechanical systems are the Simple Inverted Pendulum and the Inverted Pendulum on a Cart (PoC). These examples provide insight into both the feasibility and usability of Jacobian linearizations of nonlinear systems, as well as demonstrate the concepts of local stability, observability, controllability and detectability of linearized systems under varying parameters. Some examples of constant disturbances and effects are considered. The ultimate goal is to examine stabilizability, through both static and dynamic feedback controllers, of mechanical systems

Name thesis:degree_name

Master of Science

Level thesis:degree_level

Thesis

Discipline thesis:degree_discipline

Mathematical Sciences

Year dc:date.available

2005

Author dc:creator

• Cox, Bruce

• stability
• feedback
• inverted pendulum
• dynamic feedback controllers
• stabilization
• static feedback controllers
• Jacobian linearization
• Physical Sciences and Mathematics

Statement dc:rights

• © The Author

Identifier

https://scholarscompass.vcu.edu/etd/1174

OAI identifier oai:identifier

oai:scholarscompass.vcu.edu:etd-2173