- •1. INTRODUCTION
- •1.1 BASIC TERMINOLOGY
- •1.2 EXAMPLE SYSTEM
- •1.3 SUMMARY
- •1.4 PRACTICE PROBLEMS
- •2. TRANSLATION
- •2.1 INTRODUCTION
- •2.2 MODELING
- •2.2.1 Free Body Diagrams
- •2.2.2 Mass and Inertia
- •2.2.3 Gravity and Other Fields
- •2.2.4 Springs
- •2.2.5 Damping and Drag
- •2.2.6 Cables And Pulleys
- •2.2.7 Friction
- •2.2.8 Contact Points And Joints
- •2.3 SYSTEM EXAMPLES
- •2.4 OTHER TOPICS
- •2.5 SUMMARY
- •2.6 PRACTICE PROBLEMS
- •2.7 PRACTICE PROBLEM SOLUTIONS
- •2.8 ASSIGNMENT PROBLEMS
- •3. ANALYSIS OF DIFFERENTIAL EQUATIONS
- •3.1 INTRODUCTION
- •3.2 EXPLICIT SOLUTIONS
- •3.3 RESPONSES
- •3.3.1 First-order
- •3.3.2 Second-order
- •3.3.3 Other Responses
- •3.4 RESPONSE ANALYSIS
- •3.5 NON-LINEAR SYSTEMS
- •3.5.1 Non-Linear Differential Equations
- •3.5.2 Non-Linear Equation Terms
- •3.5.3 Changing Systems
- •3.6 CASE STUDY
- •3.7 SUMMARY
- •3.8 PRACTICE PROBLEMS
- •3.9 PRACTICE PROBLEM SOLUTIONS
- •3.10 ASSIGNMENT PROBLEMS
- •4. NUMERICAL ANALYSIS
- •4.1 INTRODUCTION
- •4.2 THE GENERAL METHOD
- •4.2.1 State Variable Form
- •4.3 NUMERICAL INTEGRATION
- •4.3.1 Numerical Integration With Tools
- •4.3.2 Numerical Integration
- •4.3.3 Taylor Series
- •4.3.4 Runge-Kutta Integration
- •4.4 SYSTEM RESPONSE
- •4.4.1 Steady-State Response
- •4.5 DIFFERENTIATION AND INTEGRATION OF EXPERIMENTAL DATA
- •4.6 ADVANCED TOPICS
- •4.6.1 Switching Functions
- •4.6.2 Interpolating Tabular Data
- •4.6.3 Modeling Functions with Splines
- •4.6.4 Non-Linear Elements
- •4.7 CASE STUDY
- •4.8 SUMMARY
- •4.9 PRACTICE PROBLEMS
- •4.10 PRACTICE PROBLEM SOLUTIONS
- •4.11 ASSIGNMENT PROBLEMS
- •5. ROTATION
- •5.1 INTRODUCTION
- •5.2 MODELING
- •5.2.1 Inertia
- •5.2.2 Springs
- •5.2.3 Damping
- •5.2.4 Levers
- •5.2.5 Gears and Belts
- •5.2.6 Friction
- •5.2.7 Permanent Magnet Electric Motors
- •5.3 OTHER TOPICS
- •5.4 DESIGN CASE
- •5.5 SUMMARY
- •5.6 PRACTICE PROBLEMS
- •5.7 PRACTICE PROBLEM SOLUTIONS
- •5.8 ASSIGNMENT PROBLEMS
- •6. INPUT-OUTPUT EQUATIONS
- •6.1 INTRODUCTION
- •6.2 THE DIFFERENTIAL OPERATOR
- •6.3 INPUT-OUTPUT EQUATIONS
- •6.3.1 Converting Input-Output Equations to State Equations
- •6.3.2 Integrating Input-Output Equations
- •6.4 DESIGN CASE
- •6.5 SUMMARY
- •6.6 PRACTICE PROBLEMS
- •6.7 PRACTICE PROBLEM SOLUTIONS
- •6.8 ASSGINMENT PROBLEMS
- •6.9 REFERENCES
- •7. ELECTRICAL SYSTEMS
- •7.1 INTRODUCTION
- •7.2 MODELING
- •7.2.1 Resistors
- •7.2.2 Voltage and Current Sources
- •7.2.3 Capacitors
- •7.2.4 Inductors
- •7.2.5 Op-Amps
- •7.3 IMPEDANCE
- •7.4 EXAMPLE SYSTEMS
- •7.5 ELECTROMECHANICAL SYSTEMS - MOTORS
- •7.5.1 Permanent Magnet DC Motors
- •7.5.2 Induction Motors
- •7.5.3 Brushless Servo Motors
- •7.6 FILTERS
- •7.7 OTHER TOPICS
- •7.8 SUMMARY
- •7.9 PRACTICE PROBLEMS
- •7.10 PRACTICE PROBLEM SOLUTIONS
- •7.11 ASSIGNMENT PROBLEMS
- •8. FEEDBACK CONTROL SYSTEMS
- •8.1 INTRODUCTION
- •8.2 TRANSFER FUNCTIONS
- •8.3 CONTROL SYSTEMS
- •8.3.1 PID Control Systems
- •8.3.2 Manipulating Block Diagrams
- •8.3.3 A Motor Control System Example
- •8.3.4 System Error
- •8.3.5 Controller Transfer Functions
- •8.3.6 Feedforward Controllers
- •8.3.7 State Equation Based Systems
- •8.3.8 Cascade Controllers
- •8.4 SUMMARY
- •8.5 PRACTICE PROBLEMS
- •8.6 PRACTICE PROBLEM SOLUTIONS
- •8.7 ASSIGNMENT PROBLEMS
- •9. PHASOR ANALYSIS
- •9.1 INTRODUCTION
- •9.2 PHASORS FOR STEADY-STATE ANALYSIS
- •9.3 VIBRATIONS
- •9.4 SUMMARY
- •9.5 PRACTICE PROBLEMS
- •9.6 PRACTICE PROBLEM SOLUTIONS
- •9.7 ASSIGNMENT PROBLEMS
- •10. BODE PLOTS
- •10.1 INTRODUCTION
- •10.2 BODE PLOTS
- •10.3 SIGNAL SPECTRUMS
- •10.4 SUMMARY
- •10.5 PRACTICE PROBLEMS
- •10.6 PRACTICE PROBLEM SOLUTIONS
- •10.7 ASSIGNMENT PROBLEMS
- •10.8 LOG SCALE GRAPH PAPER
- •11. ROOT LOCUS ANALYSIS
- •11.1 INTRODUCTION
- •11.2 ROOT-LOCUS ANALYSIS
- •11.3 SUMMARY
- •11.4 PRACTICE PROBLEMS
- •11.5 PRACTICE PROBLEM SOLUTIONS
- •11.6 ASSIGNMENT PROBLEMS
- •12. NONLINEAR SYSTEMS
- •12.1 INTRODUCTION
- •12.2 SOURCES OF NONLINEARITY
- •12.3.1 Time Variant
- •12.3.2 Switching
- •12.3.3 Deadband
- •12.3.4 Saturation and Clipping
- •12.3.5 Hysteresis and Slip
- •12.3.6 Delays and Lags
- •12.4 SUMMARY
- •12.5 PRACTICE PROBLEMS
- •12.6 PRACTICE PROBLEM SOLUTIONS
- •12.7 ASIGNMENT PROBLEMS
- •13. ANALOG INPUTS AND OUTPUTS
- •13.1 INTRODUCTION
- •13.2 ANALOG INPUTS
- •13.3 ANALOG OUTPUTS
- •13.4 NOISE REDUCTION
- •13.4.1 Shielding
- •13.4.2 Grounding
- •13.5 CASE STUDY
- •13.6 SUMMARY
- •13.7 PRACTICE PROBLEMS
- •13.8 PRACTICE PROBLEM SOLUTIONS
- •13.9 ASSIGNMENT PROBLEMS
- •14. CONTINUOUS SENSORS
- •14.1 INTRODUCTION
- •14.2 INDUSTRIAL SENSORS
- •14.2.1 Angular Displacement
- •14.2.1.1 - Potentiometers
- •14.2.2 Encoders
- •14.2.2.1 - Tachometers
- •14.2.3 Linear Position
- •14.2.3.1 - Potentiometers
- •14.2.3.2 - Linear Variable Differential Transformers (LVDT)
- •14.2.3.3 - Moire Fringes
- •14.2.3.4 - Accelerometers
- •14.2.4 Forces and Moments
- •14.2.4.1 - Strain Gages
- •14.2.4.2 - Piezoelectric
- •14.2.5 Liquids and Gases
- •14.2.5.1 - Pressure
- •14.2.5.2 - Venturi Valves
- •14.2.5.3 - Coriolis Flow Meter
- •14.2.5.4 - Magnetic Flow Meter
- •14.2.5.5 - Ultrasonic Flow Meter
- •14.2.5.6 - Vortex Flow Meter
- •14.2.5.7 - Positive Displacement Meters
- •14.2.5.8 - Pitot Tubes
- •14.2.6 Temperature
- •14.2.6.1 - Resistive Temperature Detectors (RTDs)
- •14.2.6.2 - Thermocouples
- •14.2.6.3 - Thermistors
- •14.2.6.4 - Other Sensors
- •14.2.7 Light
- •14.2.7.1 - Light Dependant Resistors (LDR)
- •14.2.8 Chemical
- •14.2.8.2 - Conductivity
- •14.2.9 Others
- •14.3 INPUT ISSUES
- •14.4 SENSOR GLOSSARY
- •14.5 SUMMARY
- •14.6 REFERENCES
- •14.7 PRACTICE PROBLEMS
- •14.8 PRACTICE PROBLEM SOLUTIONS
- •14.9 ASSIGNMENT PROBLEMS
- •15. CONTINUOUS ACTUATORS
- •15.1 INTRODUCTION
- •15.2 ELECTRIC MOTORS
- •15.2.1 Basic Brushed DC Motors
- •15.2.2 AC Motors
- •15.2.3 Brushless DC Motors
- •15.2.4 Stepper Motors
- •15.2.5 Wound Field Motors
- •15.3 HYDRAULICS
- •15.4 OTHER SYSTEMS
- •15.5 SUMMARY
- •15.6 PRACTICE PROBLEMS
- •15.7 PRACTICE PROBLEM SOLUTIONS
- •15.8 ASSIGNMENT PROBLEMS
- •16. MOTION CONTROL
- •16.1 INTRODUCTION
- •16.2 MOTION PROFILES
- •16.2.1 Velocity Profiles
- •16.2.2 Position Profiles
- •16.3 MULTI AXIS MOTION
- •16.3.1 Slew Motion
- •16.3.1.1 - Interpolated Motion
- •16.3.2 Motion Scheduling
- •16.4 PATH PLANNING
- •16.5 CASE STUDIES
- •16.6 SUMMARY
- •16.7 PRACTICE PROBLEMS
- •16.8 PRACTICE PROBLEM SOLUTIONS
- •16.9 ASSIGNMENT PROBLEMS
- •17. LAPLACE TRANSFORMS
- •17.1 INTRODUCTION
- •17.2 APPLYING LAPLACE TRANSFORMS
- •17.2.1 A Few Transform Tables
- •17.3 MODELING TRANSFER FUNCTIONS IN THE s-DOMAIN
- •17.4 FINDING OUTPUT EQUATIONS
- •17.5 INVERSE TRANSFORMS AND PARTIAL FRACTIONS
- •17.6 EXAMPLES
- •17.6.2 Circuits
- •17.7 ADVANCED TOPICS
- •17.7.1 Input Functions
- •17.7.2 Initial and Final Value Theorems
- •17.8 A MAP OF TECHNIQUES FOR LAPLACE ANALYSIS
- •17.9 SUMMARY
- •17.10 PRACTICE PROBLEMS
- •17.11 PRACTICE PROBLEM SOLUTIONS
- •17.12 ASSIGNMENT PROBLEMS
- •17.13 REFERENCES
- •18. CONTROL SYSTEM ANALYSIS
- •18.1 INTRODUCTION
- •18.2 CONTROL SYSTEMS
- •18.2.1 PID Control Systems
- •18.2.2 Analysis of PID Controlled Systems With Laplace Transforms
- •18.2.3 Finding The System Response To An Input
- •18.2.4 Controller Transfer Functions
- •18.3.1 Approximate Plotting Techniques
- •18.4 DESIGN OF CONTINUOUS CONTROLLERS
- •18.5 SUMMARY
- •18.6 PRACTICE PROBLEMS
- •18.7 PRACTICE PROBLEM SOLUTIONS
- •18.8 ASSIGNMENT PROBLEMS
- •19. CONVOLUTION
- •19.1 INTRODUCTION
- •19.2 UNIT IMPULSE FUNCTIONS
- •19.3 IMPULSE RESPONSE
- •19.4 CONVOLUTION
- •19.5 NUMERICAL CONVOLUTION
- •19.6 LAPLACE IMPULSE FUNCTIONS
- •19.7 SUMMARY
- •19.8 PRACTICE PROBLEMS
- •19.9 PRACTICE PROBLEM SOLUTIONS
- •19.10 ASSIGNMENT PROBLEMS
- •20. STATE SPACE ANALYSIS
- •20.1 INTRODUCTION
- •20.2 OBSERVABILITY
- •20.3 CONTROLLABILITY
- •20.4 OBSERVERS
- •20.5 SUMMARY
- •20.6 PRACTICE PROBLEMS
- •20.7 PRACTICE PROBLEM SOLUTIONS
- •20.8 ASSIGNMENT PROBLEMS
- •20.9 BIBLIOGRAPHY
- •21. STATE SPACE CONTROLLERS
- •21.1 INTRODUCTION
- •21.2 FULL STATE FEEDBACK
- •21.3 OBSERVERS
- •21.4 SUPPLEMENTAL OBSERVERS
- •21.5 REGULATED CONTROL WITH OBSERVERS
- •21.7 LINEAR QUADRATIC GAUSSIAN (LQG) COMPENSATORS
- •21.8 VERIFYING CONTROL SYSTEM STABILITY
- •21.8.1 Stability
- •21.8.2 Bounded Gain
- •21.9 ADAPTIVE CONTROLLERS
- •21.10 OTHER METHODS
- •21.10.1 Kalman Filtering
- •21.11 SUMMARY
- •21.12 PRACTICE PROBLEMS
- •21.13 PRACTICE PROBLEM SOLUTIONS
- •21.14 ASSIGNMENT PROBLEMS
- •22. SYSTEM IDENTIFICATION
- •22.1 INTRODUCTION
- •22.2 SUMMARY
- •22.3 PRACTICE PROBLEMS
- •22.4 PRACTICE PROBLEM SOLUTIONS
- •22.5 ASSIGNMENT PROBLEMS
- •23. ELECTROMECHANICAL SYSTEMS
- •23.1 INTRODUCTION
- •23.2 MATHEMATICAL PROPERTIES
- •23.2.1 Induction
- •23.3 EXAMPLE SYSTEMS
- •23.4 SUMMARY
- •23.5 PRACTICE PROBLEMS
- •23.6 PRACTICE PROBLEM SOLUTIONS
- •23.7 ASSIGNMENT PROBLEMS
- •24. FLUID SYSTEMS
- •24.1 SUMMARY
- •24.2 MATHEMATICAL PROPERTIES
- •24.2.1 Resistance
- •24.2.2 Capacitance
- •24.2.3 Power Sources
- •24.3 EXAMPLE SYSTEMS
- •24.4 SUMMARY
- •24.5 PRACTICE PROBLEMS
- •24.6 PRACTICE PROBLEMS SOLUTIONS
- •24.7 ASSIGNMENT PROBLEMS
- •25. THERMAL SYSTEMS
- •25.1 INTRODUCTION
- •25.2 MATHEMATICAL PROPERTIES
- •25.2.1 Resistance
- •25.2.2 Capacitance
- •25.2.3 Sources
- •25.3 EXAMPLE SYSTEMS
- •25.4 SUMMARY
- •25.5 PRACTICE PROBLEMS
- •25.6 PRACTICE PROBLEM SOLUTIONS
- •25.7 ASSIGNMENT PROBLEMS
- •26. OPTIMIZATION
- •26.1 INTRODUCTION
- •26.2 OBJECTIVES AND CONSTRAINTS
- •26.3 SEARCHING FOR THE OPTIMUM
- •26.4 OPTIMIZATION ALGORITHMS
- •26.4.1 Random Walk
- •26.4.2 Gradient Decent
- •26.4.3 Simplex
- •26.5 SUMMARY
- •26.6 PRACTICE PROBLEMS
- •26.7 PRACTICE PROBLEM SOLUTIONS
- •26.8 ASSIGNMENT PROBLEMS
- •27. FINITE ELEMENT ANALYSIS (FEA)
- •27.1 INTRODUCTION
- •27.2 FINITE ELEMENT MODELS
- •27.3 FINITE ELEMENT MODELS
- •27.4 SUMMARY
- •27.5 PRACTICE PROBLEMS
- •27.6 PRACTICE PROBLEM SOLUTIONS
- •27.7 ASSIGNMENT PROBLEMS
- •27.8 BIBLIOGRAPHY
- •28. FUZZY LOGIC
- •28.1 INTRODUCTION
- •28.2 COMMERCIAL CONTROLLERS
- •28.3 REFERENCES
- •28.4 SUMMARY
- •28.5 PRACTICE PROBLEMS
- •28.6 PRACTICE PROBLEM SOLUTIONS
- •28.7 ASSIGNMENT PROBLEMS
- •29. NEURAL NETWORKS
- •29.1 SUMMARY
- •29.2 PRACTICE PROBLEMS
- •29.3 PRACTICE PROBLEM SOLUTIONS
- •29.4 ASSIGNMENT PROBLEMS
- •29.5 REFERENCES
- •30. EMBEDDED CONTROL SYSTEM
- •30.1 INTRODUCTION
- •30.2 CASE STUDY
- •30.3 SUMMARY
- •30.4 PRACTICE PROBLEMS
- •30.5 PRACTICE PROBLEM SOLUTIONS
- •30.6 ASSIGNMENT PROBLEMS
- •31. WRITING
- •31.1 FORGET WHAT YOU WERE TAUGHT BEFORE
- •31.2 WHY WRITE REPORTS?
- •31.3 THE TECHNICAL DEPTH OF THE REPORT
- •31.4 TYPES OF REPORTS
- •31.5 LABORATORY REPORTS
- •31.5.0.1 - An Example First Draft of a Report
- •31.5.0.2 - An Example Final Draft of a Report
- •31.6 RESEARCH
- •31.7 DRAFT REPORTS
- •31.8 PROJECT REPORT
- •31.9 OTHER REPORT TYPES
- •31.9.1 Executive
- •31.9.2 Consulting
- •31.9.3 Memo(randum)
- •31.9.4 Interim
- •31.9.5 Poster
- •31.9.6 Progress Report
- •31.9.7 Oral
- •31.9.8 Patent
- •31.10 LAB BOOKS
- •31.11 REPORT ELEMENTS
- •31.11.1 Figures
- •31.11.2 Graphs
- •31.11.3 Tables
- •31.11.4 Equations
- •31.11.5 Experimental Data
- •31.11.6 Result Summary
- •31.11.7 References
- •31.11.8 Acknowledgments
- •31.11.9 Abstracts
- •31.11.10 Appendices
- •31.11.11 Page Numbering
- •31.11.12 Numbers and Units
- •31.11.13 Engineering Drawings
- •31.11.14 Discussions
- •31.11.15 Conclusions
- •31.11.16 Recomendations
- •31.11.17 Appendices
- •31.11.18 Units
- •31.12 GENERAL WRITING ISSUES
- •31.13 WRITERS BLOCK
- •31.14 TECHNICAL ENGLISH
- •31.15 EVALUATION FORMS
- •31.16 PATENTS
- •32. PROJECTS
- •32.2 OVERVIEW
- •32.2.1 The Objectives and Constraints
- •32.3 MANAGEMENT
- •32.3.1 Timeline - Tentative
- •32.3.2 Teams
- •32.4 DELIVERABLES
- •32.4.1 Conceptual Design
- •32.4.2 EGR 345/101 Contract
- •32.4.3 Progress Reports
- •32.4.4 Design Proposal
- •32.4.5 The Final Report
- •32.5 REPORT ELEMENTS
- •32.5.1 Gantt Charts
- •32.5.2 Drawings
- •32.5.3 Budgets and Bills of Material
- •32.5.4 Calculations
- •32.6 APPENDICES
- •32.6.1 Appendix A - Sample System
- •32.6.2 Appendix B - EGR 345/101 Contract
- •32.6.3 Appendix C - Forms
- •33. ENGINEERING PROBLEM SOLVING
- •33.1 BASIC RULES OF STYLE
- •33.2 EXPECTED ELEMENTS
- •33.3 SEPCIAL ELEMENTS
- •33.3.1 Graphs
- •33.3.2 EGR 345 Specific
- •33.4 SCILAB
- •33.5 TERMINOLOGY
- •34. MATHEMATICAL TOOLS
- •34.1 INTRODUCTION
- •34.1.1 Constants and Other Stuff
- •34.1.2 Basic Operations
- •34.1.2.1 - Factorial
- •34.1.3 Exponents and Logarithms
- •34.1.4 Polynomial Expansions
- •34.1.5 Practice Problems
- •34.2 FUNCTIONS
- •34.2.1 Discrete and Continuous Probability Distributions
- •34.2.2 Basic Polynomials
- •34.2.3 Partial Fractions
- •34.2.4 Summation and Series
- •34.2.5 Practice Problems
- •34.3 SPATIAL RELATIONSHIPS
- •34.3.1 Trigonometry
- •34.3.2 Hyperbolic Functions
- •34.3.2.1 - Practice Problems
- •34.3.3 Geometry
- •34.3.4 Planes, Lines, etc.
- •34.3.5 Practice Problems
- •34.4 COORDINATE SYSTEMS
- •34.4.1 Complex Numbers
- •34.4.2 Cylindrical Coordinates
- •34.4.3 Spherical Coordinates
- •34.4.4 Practice Problems
- •34.5 MATRICES AND VECTORS
- •34.5.1 Vectors
- •34.5.2 Dot (Scalar) Product
- •34.5.3 Cross Product
- •34.5.4 Triple Product
- •34.5.5 Matrices
- •34.5.6 Solving Linear Equations with Matrices
- •34.5.7 Practice Problems
- •34.6 CALCULUS
- •34.6.1 Single Variable Functions
- •34.6.1.1 - Differentiation
- •34.6.1.2 - Integration
- •34.6.2 Vector Calculus
- •34.6.3 Differential Equations
- •34.6.3.1.1 - Guessing
- •34.6.3.1.2 - Separable Equations
- •34.6.3.1.3 - Homogeneous Equations and Substitution
- •34.6.3.2.1 - Linear Homogeneous
- •34.6.3.2.2 - Nonhomogeneous Linear Equations
- •34.6.3.3 - Higher Order Differential Equations
- •34.6.3.4 - Partial Differential Equations
- •34.6.4 Other Calculus Stuff
- •34.6.5 Practice Problems
- •34.7 NUMERICAL METHODS
- •34.7.1 Approximation of Integrals and Derivatives from Sampled Data
- •34.7.3 Taylor Series Integration
- •34.8 LAPLACE TRANSFORMS
- •34.8.1 Laplace Transform Tables
- •34.9 z-TRANSFORMS
- •34.10 FOURIER SERIES
- •34.11 TOPICS NOT COVERED (YET)
- •34.12 REFERENCES/BIBLIOGRAPHY
- •35. A BASIC INTRODUCTION TO ‘C’
- •35.2 BACKGROUND
- •35.3 PROGRAM PARTS
- •35.4 HOW A ‘C’ COMPILER WORKS
- •35.5 STRUCTURED ‘C’ CODE
- •35.7 CREATING TOP DOWN PROGRAMS
- •35.8 HOW THE BEAMCAD PROGRAM WAS DESIGNED
- •35.8.1 Objectives:
- •35.8.2 Problem Definition:
- •35.8.3 User Interface:
- •35.8.3.1 - Screen Layout (also see figure):
- •35.8.3.2 - Input:
- •35.8.3.3 - Output:
- •35.8.3.4 - Help:
- •35.8.3.5 - Error Checking:
- •35.8.3.6 - Miscellaneous:
- •35.8.4 Flow Program:
- •35.8.5 Expand Program:
- •35.8.6 Testing and Debugging:
- •35.8.7 Documentation
- •35.8.7.1 - Users Manual:
- •35.8.7.2 - Programmers Manual:
- •35.8.8 Listing of BeamCAD Program.
- •35.9 PRACTICE PROBLEMS
- •36. UNITS AND CONVERSIONS
- •36.1 HOW TO USE UNITS
- •36.2 HOW TO USE SI UNITS
- •36.3 THE TABLE
- •36.4 ASCII, HEX, BINARY CONVERSION
- •36.5 G-CODES
- •37. ATOMIC MATERIAL DATA
- •37. MECHANICAL MATERIAL PROPERTIES
- •37.1 FORMULA SHEET
- •38. BIBLIOGRAPHY
- •38.1 TEXTBOOKS
- •38.1.1 Slotine and Li
- •38.1.2 VandeVegte
- •39. TOPICS IN DEVELOPMENT
- •39.1 UPDATED DC MOTOR MODEL
- •39.2 ANOTHER DC MOTOR MODEL
- •39.3 BLOCK DIAGRAMS AND UNITS
- •39.4 SIGNAL FLOW GRAPHS
- •39.5 ZERO ORDER HOLD
- •39.6 TORSIONAL DAMPERS
- •39.7 MISC
- •39.8 Nyquist Plot
- •39.9 NICHOLS CHART
- •39.10 BESSEL POLYNOMIALS
- •39.11 ITAE
- •39.12 ROOT LOCUS
- •39.13 LYAPUNOV’S LINEARIZATION METHOD
- •39.14 XXXXX
- •39.15 XXXXX
- •39.16 XXXXX
- •39.17 XXXXX
- •39.18 XXXXX
- •39.19 XXXXX
- •39.20 XXXXX
- •39.21 SUMMARY
- •39.22 PRACTICE PROBLEMS
- •39.23 PRACTICE PROBLEM SOLUTIONS
- •39.24 ASSGINMENT PROBLEMS
- •39.25 REFERENCES
- •39.26 BIBLIOGRAPHY
writing guide - 31.3
31.3 THE TECHNICAL DEPTH OF THE REPORT
Knowing the level of reader is very important when writing. Engineers often write reports for other engineers, or technically aware readers. As a result an engineer will often write at their own knowledge level. When necessary, appendices can be added to accommodate readers with variable backgrounds. The depth of detail is another common issue. The author should provide enough detail to allow others to follow and reproduce the results. The two questions below should form a good basis for evaluation.
“What happens if I am hit by a car; could somebody pick up my report and continue?” if the answer to this question is no the report requires more detail.
“Would I skip or skim this sentence/paragraph/section/report because it is so obvious?”. If the answer is yes section can be condensed, or moved to and appendix.
31.4 TYPES OF REPORTS
The list below shows many of the reports written by engineers. In general, reports give necessary background, discuss details and then draw conclusions from them. The credibility of a report is based upon the evidence it contains. These then support the conclusions drawn by the author.
Laboratory - Theses ‘Lab Reports’ describe one or more experiments, the results, and the conclusions drawn from them.
Consulting - A summary of details, test results, observations, and a set of conclusions. Typically they will also contain a recommendation.
Project - A description of work done in a project to inform other engineers who may be asked to take up further work on the project.
Research - A summary of current advances in a topic. This should end with some comparison of alternatives.
Interim - A report to apprise supervisors and others as to the progress of a project or other major undertaking.
Executive - A brief summary of the report, and any implications for decision making at the management levels.
Proposals - A technical document describing a project for the purposes of obtaining permission to proceed.
31.5LABORATORY REPORTS
•Purpose: These reports should outline your procedure and results in detail. They
writing guide - 31.4
should also contain the analysis and conclusions. The completeness of detail allows you (and others) to review these and verify the correctness of what has been done. These have been historically used for hundreds of years and are accepted as a form of scientific and legal evidence. It is completely unacceptable to make incorrect entries or leave out important steps or data.
• Standard Format:
1.Title, Author, Date - these make it clear what the labs contain, who did the work, and when it was done. If the report is done for a course it should also include the course name/number, the lab instructor and the lab section.
2.Purpose - a brief one line statement that allows a quick overview of what the experiment is about. This is best written in the form of a scientific goal using the scientific methods.
3.Theory - a review of applicable theory and calculations necessary. Any design work is done at this stage
4.Equipment - a list of the required equipment will help anybody trying to replicate the procedure. Specific identifying numbers should be listed when possible. If there are problems in the data, or an instrument is found to be out of calibration, we can track the problems to specific sets of data and equipment.
5.Procedure - these are sequential operations that describe what was done during the experiment. The level of detail should be enough that somebody else could replicate the procedure. We want to use this as a scientific protocol.
6.Results (Note: sometimes procedure and results are mixed) - the results are recorded in tables, graphs, etc. as appropriate. It will also be very helpful to note other events that occur (e.g. power loss, high humidity, etc.)
7.Discussion - At this stage the results are reviewed for trends and other observations. At this point we want to consider the scientific method.
8.Conclusions - To conclude we will summarize the significant results, and make general statements either upholding or rejecting our purpose.
•Style: These are meant to be written AS the work is done. As a result the work should be past tense
•Laboratory reports should have one or more hypotheses that are to be tested. If testing designs these are the specifications. Examples might be,
-what is the thermal capacity of a material?
-what is the bandwidth of an amplifier?
-will the counter increment/decrement between 0 to 9?
• NOTE: These reports are much easier to write if you prepare all of the calculations, graphs, etc. before you start to write. If you sit down and decide to do things as you
writing guide - 31.5
write it will take twice as long and get you half the marks...... believe me, I have written many in the past and I mark them now.
31.5.0.1 - An Example First Draft of a Report
Grand Valley State University
Padnos School of Engineering
EGR 345 Dynamics Systems Modeling and Control
Laboratory Exercise 7
Title: The Cooling of Coffee
Author: I. M. Wyred
Date: Dec., 23, 1998
Purpose: To derive a theoretical model of the rate at which coffee cools and experimentally verify the model and find coefficients.
Theory:
When coffee is heated kinetic energy is added, when coffee is cooled kinetic energy is removed. In a typical use, coffee cools as heat is lost through convection and conduction to the air and solids in contact. The factors involved in this convection/conduction can be difficult to measure directly, but we can approximate them with a simple thermal resistance. Consider the temperature difference between the coffee and the ambient temperature. The greater the temperature difference, the higher the rate of heat flow out of the coffee. This relationship can be seen formally in the equation below. We can also assume that the atmosphere is so large that the heat transfer will not change the temperature.
writing guide - 31.6
q = |
1 |
( θ |
|
– θ ) |
-- |
coffee |
|||
|
R |
|
air |
|
|
|
|
|
where,
q = heat flow rate from coffee to air (J/s)
R = thermal resistance between air and coffee
θ = temperatures in the coffee and air
We can also consider that coffee has a certain thermal capacity for the heat energy. As the amount of energy rises, there will be a corresponding temperature increase. This is known as the thermal capacitance, and this value is unique for every material. The basic relationships are given below. I will assume that the energy flow rate into the coffee is negligible.
∆θ |
coffee = |
1 |
– qout) |
= |
–1 |
dθ |
coffee |
= |
–1 |
---------------( qin |
---------------q |
------------------ |
---------------q |
||||||
|
|
Ccoffee |
|
|
Ccoffee |
|
dt |
|
Ccoffee |
where,
Ccoffee = thermal capacitance
Ccoffee = Mcoffee σ coffee
where,
Mcoffee = mass of thermal body
σ coffee = specific heat of material in mass
The temperatures can be found by consider that the energy flowing out of the cup, and into the atmosphere is governed by the resistance. And, the temperature in the coffee and air are governed by the two capacitances. We will make two assumptions, that the thermal capacitance of the atmosphere is infinite, and that there is no energy flowing into the coffee.
writing guide - 31.7
dθ coffee |
= |
|
–1 |
q |
|
|
|
|
|
|
|
|
|
|||
------------------ |
|
dt |
C---------------coffee |
|
|
|
|
|
|
|
|
|
||||
|
|
|
|
|
|
|
|
|
|
|
|
|
||||
|
|
dθ |
coffee |
|
|
–1 |
|
1 |
|
|
|
|
|
|
|
|
|
------------------ |
|
|
|
-------------------------------- |
-- |
|
|
– θ air) |
|
|
|
||||
|
|
dt |
|
= |
Mcoffeeσ |
coffee |
R( θ |
coffee |
|
|
|
|||||
|
|
dθ |
coffee |
|
|
1 |
|
|
|
|
|
1 |
|
|
||
|
|
------------------ |
|
|
|
------------------------------------ |
θ |
|
|
------------------------------------ |
θ air |
|||||
|
|
dt |
|
+ Mcoffeeσ |
coffeeR |
coffee |
= |
Mcoffee |
σ |
coffeeR |
This differential equation can then be solved to find the temperature as a function of time.
Guess |
|
|
θ |
|
|
|
|
|
|
Ct |
|
|
|
d |
θ |
|
|
Ct |
|
|
|
|
|
|
|
||
|
|
|
|
= A + Be |
|
|
|
|
---- |
= BCe |
|
|
|
|
|
|
|
|
|||||||||
|
|
|
|
|
|
|
|
dt |
|
|
|
|
|
|
|
|
|||||||||||
|
|
|
|
Ct |
|
|
|
|
|
1 |
|
|
|
Ct |
|
|
|
|
1 |
|
|
|
|
|
|||
|
BCe |
|
|
+ |
------------------------------------ |
|
|
|
|
( A + Be |
|
) |
------------------------------------ |
|
|
|
|||||||||||
|
|
|
Mcoffeeσ |
|
|
|
= |
Mcoffeeσ |
|
θ air |
|
|
|
||||||||||||||
|
|
|
|
|
|
|
|
coffee R |
|
|
|
|
|
coffeeR |
|
|
|
||||||||||
|
|
Ct |
|
|
|
|
|
|
|
B |
|
|
|
|
A |
|
|
|
|
|
–1 |
|
θ |
|
|||
|
|
BC + M------------------------------------coffee σ |
|
|
|
------------------------------------ |
|
|
------------------------------------ |
air = 0 |
|||||||||||||||||
e |
|
coffeeR + Mcoffee σ |
coffee R |
+ |
Mcoffeeσ |
coffeeR |
|||||||||||||||||||||
|
|
|
|
|
|
|
|
B |
coffeeR = 0 |
|
|
|
|
|
|
|
|
|
|
|
–1 |
|
|
||||
|
BC + |
|
M------------------------------------coffee σ |
|
|
|
|
|
|
|
|
|
C = M------------------------------------coffee σ |
coffee R |
|||||||||||||
|
|
|
|
|
A |
|
|
|
|
|
–1 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|||
|
------------------------------------ |
|
|
|
|
|
|
|
|
|
------------------------------------ |
θ |
air = 0 |
|
|
A = θ |
|
|
|
|
|||||||
|
Mcoffeeσ coffeeR + Mcoffee |
σ |
coffeeR |
|
|
air |
|
|
|
||||||||||||||||||
To find B, the initial temperature of the coffee should be used, |
|
|
|
|
|||||||||||||||||||||||
|
θ 0 |
= A + BeC( 0) = θ air + B |
|
|
|
|
|
|
|
B = θ |
0 – θ air |
|
|
|
|||||||||||||
The final equation is, |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
||||||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
–t |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
---------------------------------- |
|
|
|
|
|
|
|
|
|
|
|
|
|||
|
θ |
= θ |
air |
+ ( θ |
0 |
– θ |
) eMcoffee σ coffee R |
|
|
|
|
|
|
|
|
|
|
|
|
||||||||
|
|
|
|
|
|
|
|
|
air |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
The time constant of this problem can be taken from the differential equation
writing guide - 31.8
above.
τ = Mcoffeeσ coffeeR
Equipment:
1 ceramic coffee cup (14 oz.)
2 oz. ground coffee
1 coffee maker - Proctor Silex Model 1234A
1 thermocouple (gvsu #632357)
1 temperature meter (gvsu #234364)
1thermometer
2quarts of tap water
1 standard #2 coffee filter
1 clock with second hand
1 small scale (gvsu# 63424)
Procedure and Results:
1.The coffee pot was filled with water and this was put into the coffee maker. The coffee filter and grounds were put into the machine, and the machine was turned on. After five minutes approximately the coffee was done, and the pot was full.
2.The mass of the empty coffee cup was measured on the scale and found to be
214g.
3.The air temperature in the room was measured with the thermometer and found to be 24C. The temperature of the coffee in the pot was measured using the thermocouple and temperature meter and found to be 70C.
4.Coffee was poured into the cup and, after allowing 1 minute for the temperature to equalize, the temperature was measured again. The temperature was 65C. Readings of the coffee temperature were taken every 10 minutes for the next 60 minutes. These values were recorded in Table 1 below. During this period the cup was left on a table top and allowed to cool in the ambient air temperature. During this period the mass of the full coffee cup was measured and found to be 478g.
writing guide - 31.9
Table 1: Coffee temperatures at 10 minute intervals
time (min) |
temperature (deg C) |
|
|
0 |
65 |
10 |
53 |
20 |
43 |
30 |
35 |
40 |
30 |
50 |
28 |
60 |
26 |
|
|
Discussion:
The difference between the temperature of the coffee in the pot and in the cup was 5C. This indicates that some of the heat energy in the coffee was lost to heating the cup. This change is significant, but I will assume that the heating of the cup was complete within the first minute, and this will have no effect on the data collected afterwards.
The readings for temperature over time are graphed in Figure 1 below. These show the first-order response as expected, and from these we can graphically estimate the time constant at approximately 32 minutes.
temp |
|
|
|
|
|
(deg C) |
|
|
|
|
|
60 |
|
|
|
|
|
40 |
|
|
|
|
|
24 |
|
|
|
|
t (min) |
20 |
|
|
|
|
|
|
|
|
|
|
|
0 |
20 |
τ |
≈ |
32min 40 |
60 |
Figure 1 - A graph of coffee temperature measured at 10 minute intervals
writing guide - 31.10
We can compare the theoretical and experimental models by using plotting both on the same graph. The graph clearly shows that there is good agreement between the two curves, except for the point at 30 minutes, where there is a difference of 3.5 degrees C.
temp |
|
|
|
(deg C) |
|
|
|
60 |
|
|
experimental data |
|
|
mathematical model |
|
|
|
|
|
|
|
max. difference |
|
40 |
|
of 3.5 deg. C |
|
|
|
|
|
20 |
|
|
t (min) |
|
|
|
|
0 |
20 |
40 |
60 |
Figure 2 - Comparison of experimental and modelled curves
This gives an overall error of 8.5% between these two curves, compared to the total range of the data.
3.5
error = -----------------100 = 8.5% 65 – 24
Finally, the results can be used to calculate a thermal resistance. If we know the mass of the coffee and assume that the coffee has the same specific heat as water, and have the time constant, the thermal resistance is found to be 1731sC/J.
τ |
= Mcoffeeσ |
coffeeR |
|
Mcoffee |
= 478g – 214g = 0.264Kg |
||
|
|
|
|
|
σ |
|
C |
|
|
|
|
|
coffee |
= 4.2--------- |
|
R |
= |
τ |
|
= 1731sC |
|
|
KgJ |
|
τ |
|
|
||||
|
|
Mcoffeeσ |
coffee |
J |
= 32min = 1920s |