Matlab and Ode Solvers

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Lab 0: MATLAB and ODE Solvers | ME 4173 Robot Kinematics

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Introduction

The following report will display the results and conclusions of an experiment to simulate the output of an inverse pendulum system in MATLAB. The objectives of this experiment were to review MATLAB programming and using MATLAB to simulate ODEs and systems.
Objectives

* Examine the basics of MATLAB

* Use MATLAB to simulate a system

* Use ODE solvers to numerically integrate the system over a set time period
Apparatus
The apparatus used in this experiment was MATLAB. It was used to provide a simulation environment to analyze the inverse pendulum’s motion.
Experiments and Results
There were six components of this experiment. This experiment was mostly familiarizing with MATLAB. All code used is illustrated in the Appendix – Code.

The first part consisted of learning commands within the MATLAB environment. It was a brief overview of how commands work in MATLAB. There was no code used in the part of the experiment.

The second part of the experiment examined how arrays were created and used in MATLAB. The first step was to create a matrix. This matrix was then subjected to various commands including eye( ), zeroes( ), and ones( ). Indexing was also used to access various parts of the matrix. Matrix operations such as transpose, inverse, size and length were also shown.

Part three of the experiment explained how a script was created and what it was used for. A script file was created and used for other parts of the lab.
Part four illustrated what a function was and how they are created. It explained how syntax was important in the naming and calling of the function. This allowed the user to write a function and save in within a directory. This function could be called by the function name and input variables and return an answer depending…...

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Matlab

...An Introduction to Matlab for Econometrics John C. Frain TEP Working Paper No. 0110 February 2010 Trinity Economics Papers Department of Economics Trinity College Dublin An Introduction to MATLAB for Econometrics John C. Frain. February 2010 ∗ Abstract This paper is an introduction to MATLAB for econometrics. It describes the MATLAB Desktop, contains a sample MATLAB session showing elementary MATLAB operations, gives details of data input/output, decision and loop structures, elementary plots, describes the LeSage econometrics toolbox and maximum likelihood using the LeSage toolbox. Various worked examples of the use of MATLAB in econometrics are also given. After reading this document the reader should be able to make better use of the MATLAB on-line help and manuals. Contents 1 Introduction 1.1 1.2 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The MATLAB Desktop . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.1 1.2.2 1.2.3 1.2.4 1.2.5 1.2.6 1.2.7 1.2.8 1.2.9 ∗ Comments 4 4 6 6 7 8 8 9 9 9 The Command Window . . . . . . . . . . . . . . . . . . . . . . . . The Command History Window . . . . . . . . . . . . . . . . . . . The Start Button . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Edit Debug window . . . . . . . . . . . . . . . . . . . . . . . . The Figure Windows . . . . . . . . . . . . . . . . . . . . . . . . . . The Workspace Browser . . . . . . . . . . . . . . . . . . . . . . . .......

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Ode to Autumn

...Conspiring with him how to load and bless With fruit the vines that round the thatch-eves run; * Ah, so now the sun and autumn are "conspiring," eh? Looks like we might have to separate the two of them. What are they whispering about over there? * OK, so not quite as thrilling as we thought. They are planning how to make fruit grow on the vines that curl around the roofs ("eves") of thatched cottages. * The image highlights the weight of the fruit as it "loads" down the vines. * Thatched cottages suggest a pastoral setting, characterized by shepherds, sheep, maidens, and agriculture. The "pastoral" as a literary genre was thought to originate in Ancient Greece, and the ode is a Greek form, so it is appropriate for this ode to include pastoral themes. Keats's other Great Odes, especially "Ode on a Grecian Urn," include similar imagery. Lines 5-6 To bend with apples the moss'd cottage-trees, And fill all fruit with ripeness to the core; * Keats is going nuts (pun!) with images of weight and ripeness. The richness here is like Willy Wonka's Chocolate Factory set in an orchard. * The apples "bend" down the branches of mossy trees with their weight. The trees belong not to some big farming cooperative, but to the simple cottages of country folk. * The ripeness penetrates deep to the very center of the fruit. They're not like those apples that look delicious until you take a bite and realize that the fruit is hard and sour. No, these babies are......

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