Lab Experiences for Teaching Undergraduate Dynamics by Katherine Ann Lilienkamp Abstract

464 Pages·2003·12.33 MB·English

Lab Experiences for Teaching Undergraduate Dynamics
by
Katherine Ann Lilienkamp
Submitted to the Department of Mechanical Engineering
February 19, 2003, in partial fulfillment of the
requirements for the degree of
Master of Science in Mechanical Engineering
Abstract
This thesis describes several projects developed to teach undergraduate dynamics
and controls. The materials were developed primarily for the class 2.003 Modeling
Dynamics and Control I. These include (1) a set of ActivLab modular experiments
that illustrate the dynamics of linear time-invariant (LTI) systems and (2) a two-
wheeled mobile inverted pendulum. The ActivLab equipment has been designed as
shareware, and plans for it are available on the web. The inverted pendulum robot
developed here is largely inspired by the iBOT and Segway transportation devices
invented by Dean Kamen.
Thesis Supervisor: David L. Trumper
Title: Associate Professor of Mechanical Engineering
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Acknowledgments
First, I’d like to thank Prof. David Trumper for his support and guidance throughout
this thesis. Prof. Trumper is an incredibly knowledgable resource, and he has given
me invaluable support and advice throughout the last several years: initially as an
undergraduate, then during the consulting and masters degree work I have done with
him. He is a gifted educator and genuinely motivated to teach students how to think.
This has been inspirational both in my own choice to work on this project to develop
educational tools and in getting through a masters thesis at all.
Joe Cattell and Andrew Wilson helped design and build the first generation of
ActivLab experiments during the summer of 2001. We could not have developed
an entire set of new laboratory experiments without their devotion to the project.
ThanksparticularlytoJoeforthelatenightsspentmachininginthegraduatemachine
shop and the missed vacation days that summer.
Joe and Andrew also worked with me as teaching assistants when the equipment
was first used (in the fall of 2001). They insured the lab sessions ran smoothly,
showing both the students and faculty how to operate the new equipment. Andrew
also put in a huge effort under the guidance of Prof. Samir Nayfeh to create the
laboratory write-ups. His patience going through multiple, last-minute iterations of
the pre-lab and lab assignment documentation was heroic, and I have included several
of his elegant pro-E drawings of the laboratory hardware in the pages of my thesis.
Willem Hijmans, an exchange student from Delft University in the Netherlands,
played a substantial role in insuring that the labs ran smoothly during this first term,
as well. He created our ActivLab website 1 and was always on hand to help set up
and calibrate equipment for class. Thanks also to Professor Jan van Eijk (also of
Delft) for arranging Mr. Hijmans internship with us at MIT and for his support and
advice throughout this project.
Special thanks to Prof. Ely Sachs for his suggestions and advice on hardware
design. Prof. Dave Gossard, Prof. Samir Nayfeh and Prof. Neville Hogan taught the
1http://web.mit.edu/2.003/www/activlab/activlab.html
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laboratory sessions in the fall of 2001, and they provided input into the development
of the equipment, as well. Their enthusiasm and attention to detail uncovered lots of
interesting physical phenomena in the hardware. The ActivLab hardware was greatly
enhanced by the effort they provided in enouraging the students to explore.
Thanks also for the efforts spent during the second running of the class in the
spring of 2002 in maintaining and refining the laboratory projects. Prof. Gossard
organized the class; Prof. Trumper ran the lab sessions; and Marten Byl took over
the work of the previous three T.A.’s to keep the class running smoothly. Marty
also gets my love and thanks for keeping me sane and happy outside lab during
the last few months spent finishing this thesis! In subsequent terms, Xiaodong Lu,
Vijay Shilpiekandula and Yi Xie have TA’d the course, and Prof. David Hardt will
be teaching the course with Prof. Trumper in the Fall of 2003.
This project could never have happened without the funding and support of the
Department of Mechanical Engineering and its benefactors. I’d particularly like to
acknowledge the efforts and encouragement of our department head, Prof. Rohan
Abeyaratne. ThanksaswelltoBritandAlexd’Arbelofffortheirfundingtocreatethe
d’Arbeloff Laboratory for Information Systems at MIT, where the 2.003 laboratory
resides. Maureen DeCourcey and Maggie Beucler graciously dealt with our constant
stream of purchase orders while building the lab equipment, always expediting our
efforts to obtain parts and materials. Thanks for putting up with so many “urgent”
requests!
WearegratefultoDrewDevittofNewWayMachineComponentsforprovidingair
bearings at a substantial discount. He also provided advice and enthusiastically sup-
ported our project, going so far as to deliver parts in person near the end of the term!
A few other sponsors are worth mentioning here as well. Tektronix and dSPACE each
provided equipment at a substantially discount, and the Intel Corporation donated
the computers used in the laboratory.
Finally, thanksverymuchtoMarkBelanger, GerryWentworthandDavidDowfor
their indispensible helpin the LMP (Laboratory for Manufacturingand Productivity)
machine shop and to Bob Nutall, Steve Haberek and Dick Fenner of the Pappalardo
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machine shop. Mark and Gerry in particular have taught me most of what I know
about getting around a machine shop. They have always been generous with their
time, and I modified several designs based on their advice. They often provided more
than a little “help” in actually manufacturing specific parts, too! I believe I’m typing
this now with all ten digits, thanks in no small part to their supervision and guidance.
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Contents
1 Introduction 25
1.1 Overview. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
1.2 General Motivations . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
1.3 Goals for the ActivLab Experiments . . . . . . . . . . . . . . . . . . 29
1.3.1 Motivation for Using Low-Friction Air Bearings . . . . . . . . 30
1.3.2 Presenting Non-Ideal Real World Behaviors . . . . . . . . . . 33
1.3.3 Transparent, Hands-on Operation . . . . . . . . . . . . . . . . 36
1.3.4 Ease of Assembly . . . . . . . . . . . . . . . . . . . . . . . . . 37
1.3.5 Cost Effectiveness . . . . . . . . . . . . . . . . . . . . . . . . . 42
1.4 Summary of the Inverted Pendulum Project . . . . . . . . . . . . . . 47
1.4.1 Ideal and Actual Hardware Implementation . . . . . . . . . . 50
1.4.2 Challenges and Control Strategy . . . . . . . . . . . . . . . . . 51
1.4.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
2 Survey of Related Projects 63
2.1 Inverted Pendulum Vehicles . . . . . . . . . . . . . . . . . . . . . . . 66
2.1.1 The iBOT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
2.1.2 Segway Human Transport . . . . . . . . . . . . . . . . . . . . 69
2.1.3 “Joe”: An Autonomous IP Robot . . . . . . . . . . . . . . . . 74
2.1.4 “nBot”: Segway-inspired IP Robot . . . . . . . . . . . . . . . 77
2.1.5 “LegWay”: Mindstorms Robot with Single-Sensor Balancing . 80
2.1.6 “GyroBot”: IP Robot with Integral Action . . . . . . . . . . . 82
2.1.7 Robotic Unicycles . . . . . . . . . . . . . . . . . . . . . . . . . 84
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2.2 Hands-On Experiences in Undergraduate System Dynamics . . . . . . 86
2.2.1 Literature on Learning and Teaching . . . . . . . . . . . . . . 88
2.2.2 Stanford Course ME161: Dynamic Systems . . . . . . . . . . . 103
2.3 Multi-Media Simulations of Dynamic Systems at MIT . . . . . . . . . 108
2.3.1 PiVOT/PT tutor for 8.01 Physics I . . . . . . . . . . . . . . . 108
2.3.2 TEAL/Studio Physics Project for 8.02 Physics II . . . . . . . 111
2.3.3 6.013 E & M Simulations and Movies . . . . . . . . . . . . . . 117
2.3.4 The OpenCourseWare Project . . . . . . . . . . . . . . . . . . 119
2.4 Robot Contests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
2.4.1 6.270 Lego Robots and the Handy Board at MIT . . . . . . . 120
2.4.2 The BASIC Stamp Robot Controller . . . . . . . . . . . . . . 124
2.4.3 Stanford SPDL March Madness duel . . . . . . . . . . . . . . 126
2.4.4 Micromouse Competition . . . . . . . . . . . . . . . . . . . . . 128
2.4.5 Intercollegiate NATCAR Competition . . . . . . . . . . . . . . 130
2.5 Laboratory Courses in Mechatronics . . . . . . . . . . . . . . . . . . 131
2.5.1 2.737 Mechatronics at MIT . . . . . . . . . . . . . . . . . . . 132
2.5.2 RPI Mechatronics Teaching Lab . . . . . . . . . . . . . . . . . 134
2.5.3 Other Programs of Note . . . . . . . . . . . . . . . . . . . . . 136
3 ActivLab Hardware 137
3.1 ActivLab Labware for Teaching Dynamics . . . . . . . . . . . . . . . 138
3.2 Philosophy for Designing Labs . . . . . . . . . . . . . . . . . . . . . . 138
3.3 1st-Order Spring-Damper Translational System . . . . . . . . . . . . 139
3.4 1st-Order Inertia-Damper Rotational System . . . . . . . . . . . . . . 161
3.5 2nd-Order Spring-Mass-Damper Translational System . . . . . . . . . 170
3.6 First- and Second-Order Electronic Circuits . . . . . . . . . . . . . . 179
3.7 Op-Amp Circuit Dynamics . . . . . . . . . . . . . . . . . . . . . . . . 180
3.8 Effects of Zeros in a Mechanical System . . . . . . . . . . . . . . . . . 181
3.8.1 Unmodeled System Dynamics . . . . . . . . . . . . . . . . . . 183
3.9 Introduction to Controls . . . . . . . . . . . . . . . . . . . . . . . . . 188
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3.9.1 Control of Translational Spring-Mass-Damper System . . . . . 188
3.9.2 Control of DC Motor System . . . . . . . . . . . . . . . . . . 190
3.10 Web Documentation of ActivLab Projects . . . . . . . . . . . . . . . 194
4 Other Project Suggestions in Dynamics 195
4.1 Possible ActivLab Additions . . . . . . . . . . . . . . . . . . . . . . . 195
4.1.1 2nd-Order Spring-Inertia-Damping Rotational System . . . . . 196
4.1.2 Whiskered Spring Cantilever . . . . . . . . . . . . . . . . . . . 198
4.1.3 MEMS Systems . . . . . . . . . . . . . . . . . . . . . . . . . . 200
4.2 In-Lab Demos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
4.2.1 Purpose of Hands-on Demonstration Hardware . . . . . . . . . 204
4.2.2 2nd-order Translational System with No Damping . . . . . . . 205
4.2.3 Rectangular Voice Coil . . . . . . . . . . . . . . . . . . . . . . 205
4.2.4 Eddy Current Demos . . . . . . . . . . . . . . . . . . . . . . . 209
4.2.5 Demo of How an LVDT Operates . . . . . . . . . . . . . . . . 211
4.2.6 Cantilever Spring Stiffening Demonstration . . . . . . . . . . . 214
4.2.7 Floppy Disk Drive Dissection . . . . . . . . . . . . . . . . . . 219
4.3 Lecture Demonstrations . . . . . . . . . . . . . . . . . . . . . . . . . 223
4.3.1 Low-Pass and High-Pass Audio Filtering . . . . . . . . . . . . 225
4.3.2 Camera Flash Charging Circuit . . . . . . . . . . . . . . . . . 225
4.3.3 MATLAB Tools . . . . . . . . . . . . . . . . . . . . . . . . . . 231
4.3.4 Real-World Dynamic Systems . . . . . . . . . . . . . . . . . . 235
5 Driven-Cart Inverted Pendulum 243
5.1 Cart IP Hardware . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245
5.2 Equations of Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . 247
5.3 Controller Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . 249
5.4 Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250
6 Tilt Sensing for Inverted Pendulum Robots 257
6.1 Tilt Sensing for Segway and iBOT . . . . . . . . . . . . . . . . . . . . 257
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6.1.1 A Brief Summary of the Use of Redundancy in FDI . . . . . . 258
6.1.2 Mathematics of FDI Using Geometric Redundancy . . . . . . 261
6.1.3 Linear Algebra for FDI . . . . . . . . . . . . . . . . . . . . . . 268
6.1.4 Advantages of Symmetry . . . . . . . . . . . . . . . . . . . . . 275
6.1.5 Suggested Geometries for Redundant Sensor Arrays . . . . . . 283
6.1.6 Redundant Gyro Sensing Array for the Segway . . . . . . . . 289
6.1.7 MEMS Gyros Used in the Segway . . . . . . . . . . . . . . . . 291
6.2 Complementary Filtering of Gyro and
Accelerometer Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . 295
6.2.1 Theory of Complementary Filtering . . . . . . . . . . . . . . . 297
6.2.2 Noise Characteristics of Accelerometer and Gyro . . . . . . . . 299
6.2.3 Selecting an Appropriate Time Constant . . . . . . . . . . . . 304
6.2.4 Performance of the Complementary Filters . . . . . . . . . . . 308
6.2.5 Minimizing the Effects of the DC Bias in the Gyro . . . . . . 312
6.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 316
7 Demo IP Robot (DIPR) 317
7.1 Robot Hardware . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322
7.1.1 Robot Chassis and Wheels . . . . . . . . . . . . . . . . . . . . 322
7.1.2 dSPACE/Simulink Control Environment . . . . . . . . . . . . 324
7.1.3 Motors and Power Amps . . . . . . . . . . . . . . . . . . . . . 324
7.1.4 Effects of Encoder Quantization and Backlash . . . . . . . . . 328
7.1.5 Single-Axis Gyroscope . . . . . . . . . . . . . . . . . . . . . . 342
7.1.6 2-Axis Accelerometer . . . . . . . . . . . . . . . . . . . . . . . 348
7.2 Lagrangian Derivation of the Equations of Motion . . . . . . . . . . . 353
7.3 Transfer Functions and Pole Plots for Plant . . . . . . . . . . . . . . 357
7.4 System Equations in State Space . . . . . . . . . . . . . . . . . . . . 362
7.5 Mechanical Design Issues and Simulation . . . . . . . . . . . . . . . . 367
7.5.1 State Space Control . . . . . . . . . . . . . . . . . . . . . . . . 367
7.5.2 Robot Moment of Inertia Estimations and Verification . . . . 370
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