andrew - Standup and Stabilization of the Inverted Pendulum...

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Standup and Stabilization of the Inverted Pendulum by Andrew K. Stimac Submitted to the Department of Mechanical Engineering in Partial Fulfillment of the Requirements for the Degree of Bachelor of Science at the Massachusetts Institute of Technology June 1999 © 1999 Andrew K. Stimac The author hereby grants permission to MIT to reproduce and distribute publicly paper and electronic copies of this thesis document in whole or in part. Signature of Author: ............................................................................................................ Department of Mechanical Engineering May 5, 1999 Certified by: ......................................................................................................................... David L. Trumper Associate Professor of Mechanical Engineering Thesis Supervisor Accepted by: ........................................................................................................................ Ernest G. Cravalho Chairman, Undergraduate Thesis Committee Department of Mechanical Engineering
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Standup and Stabilization of the Inverted Pendulum by Andrew K. Stimac Submitted to the Department of Mechanical Engineering on May 5, 1999, in Partial Fulfillment of the Requirements for the Degree of Bachelor of Science in Mechanical Engineering. Abstract The inverted pendulum is a common, interesting control problem that involves many basic elements of control theory. This thesis investigates the standup routine and stabilization at the inverted position of a pendulum-cart system. The standup routine uses strategic cart movements to add energy to the system. Stabilization at the inverted position is accomplished through linear state feedback. Methods are implemented using the Matlab Simulink environment, with a dSPACE DSP controller board for interaction with the physical system. Algorithms described in this report were successful and consistently produced the desired results. This report serves as a guide to the current working system and as background information on the inverted pendulum. Thesis Supervisor: David L. Trumper Title: Associate Professor of Mechanical Engineering 2
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Table of Contents Page 1. Introduction ....................................................................................................... 6 1.1 Purpose . ........................................................................................................ 6 1.2 Project Overview . ........................................................................................ 6 1.3 Organization . ................................................................................................ 7 1.4 Acknowledgements . ..................................................................................... 7 2. Pendulum Cart Modeling and Dynamics ........................................................ 8 2.1 Lagrangian Dynamic Analysis . .................................................................... 8 2.2 Linearization and Transfer Function Generation .
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andrew - Standup and Stabilization of the Inverted Pendulum...

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