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Course Overview
Dynamic systems are systems that evolve with time. They occur all around us, throughout nature and the built environment, with
common examples including room thermostats, bicycles, electric power systems, species populations, human relationships, water
faucets, robot vacuum cleaners, automatic irrigation systems ... Understanding dynamic systems leads to the ability to control them,
so they behave according to the engineer's design.
This course introduces students to both linear dynamic system and modern control
theory, so that students will be able to analyze, design and begin to control simple dynamic systems.
EGR 326 Class and Assignment Schedule, Spring 2012
| Week
| Topic
| Reading
| HW due (Thursdays
by 4pm to FH 352)
|
Jan 27
(Fri) |
In which we are introduced to State-Space
Identifying dynamic systems all around us:
* Thermostats, Animal migration
* Power systems, Gossip, River flow
What do we need to know about a system in order to control its behavior?
* What do you already know?
* What do you need to learn?
|
+ Knowledge Building readings and the Eagle Challenge
Note green underlines in these readings
º Student Approach to Learning
º Knowledge Society
º Efficiency & Innovation
|
Both for MONDAY class:
º
Banana Disease?!, Science Friday podcast
º HWa - for Monday |
| Jan 30 |
Community Knowledge Building
º
Banana Disease?!, Science Friday podcast
--> Listen to before class, and propose answers to questions below
º Possible models? Dynamic elements?
º Purpose of the model?
º Expected outcomes and use?
A foray into State-Space: Dynamic system modeling
* Describing dynamics with difference and differential equations
* Brogan figure 1.5 and section 1.3
|
Luenberger Chapters 1 & 2 (Moodle)
Class Examples:
* First Order Systems
* ChainLetter.pdf
* RCckt.pdf
|
HW1 due
> Brogan reading (on Moodle)
|
| Feb 6 |
Launching into State-Space: Building the models
* Identifying state space and the elements in it
* State variables and state vectors
* Input, output, parameters (coupling coefficients)
* Mathematcial modeling:: x' = Ax + b; x[k+1] = Ax[k] + B
Modeling systems in Simulink (see links at bottom)
* Difference and differential equations models
Linear Algebra Review 1 - on own!, App'x A
| * Text Chapter 1: pp 1-13, section 1.6
* Text App'x A - review on your own (esp. inverse and transpose)
* Matlab tutorials (linked at bottom)
Wednesday Class Examples: Save with name shown to your directory, then open with Matlab:
* MassDamper.mdl
* RCckt.mdl
* MassSprDmpr.mdl
* RLCparallel.mdl
Friday Class Examples: Save with name shown to your directory, then open with Matlab:
* mass_spring.mdl
* mass_springSS.mdl
* mass_spring_script.m
* mass_spring_SSscript.m
|
HW2 due
HW2 soln
|
| Feb 13 |
Programming: Elements of Matlab scripts & Simulink diagrams
Trekking through state-space
Developing state-space models from anything
* Input/output equations (higher order diff eqs)
* Simulation diagrams
* Transfer functions
(Linear Algebra Review 2, begin on own, App'x B)
And always keep in mind... the Stages of Analysis:
* Create dynamic model
* Analyze system behavior
* Analyze structural relationships
* Modify or control system behavior
Matlab Slides
SS Model Development Slides
|
* Chapter 1 pp 14 to end (not section 1.4)
* Matlab tutorials, linked below
* Text App'x B
MODELS
* FerrisWheel.mdl
* FerrisWhl_detail.mdl
* FerrisWheel_script.m
* NatlEcon.mdl
|
HW3 due |
| Feb 20 |
Behaving in State Space: Generating solutions and analyzing behavior
* State and output equations
* Forced and natural response
* Initial conditions
and stored 'energy' |
Chapter 2
(Brogan Chapter 3 excerpts) |
HW4 due
|
| Feb 27 |
Exploring Stuctural Relationships in State-Space:
* Structural relationships over time and space
* In-class Matlab and Simulink practice
* Experimenting with magnetic levitation equipment
|
Simulink tutorials (at bottom)
MagLev documentation |
HW5 due |
| Mar 5 |
Characteristic Behavior based on System Structure:
* Linear algebra review 3
* Change of basis
* Eigenvalues and eigenvectors
* Modes of behavior (an ocean shore?)
* Romeo & Juliet Model
Romeo.m
* Left & right eigenvectors; Migration model
|
Luenberger Chapter 3 |
Midterm Exam |
| Mar 12 |
When can and can't we control things in state-space? (aka controllability)
Examples: Bus suspension system, National economy |
Text Chapter 3 |
HW7 due |
| Mar 19 |
A Break from State-Space |
|
|
| Mar 26 |
Class discussions and presentations of your own state-space models |
|
HW8 due: modeling analyses |
| Apr 2 |
When things hide in state-space (aka observability) |
Text Chapter 4 |
HW9 due
|
| Apr 9 |
Master trekking in state-space - advanced tools for controllability and observability (minimal realizations) |
Text Chapter 5 |
HW 10 due |
| Apr 16 |
When state variables & vectors try to escape -> Stabilizing our systems
* Cobweb.mdl
|
Text Chapter 6 |
HW 11 due |
| Apr 23 |
You are now in Control of State-Space -> Designing Control Laws
slides |
Text Chapter 7 |
HW 12 due |
| Apr 30 |
Class discussions and presentations -> Student control models and analysis |
Text Chapter 7 |
Presentations in class |
| |
Take Home Modeling Question for Final Exam |
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Course Objectives
Through homework assignments based
on Simulink, students gain experience in modeling dynamic systems, and designing a simple control input for the systems. The objective
of this course is to introduce students to the
analysis and design of dynamic systems. Through the
material presented in this course,
students will learn:
- The fundamentals of identifying and
characterizing linear dynamic systems, using both engineering theory and informed
observation of system
behavior,
- To model and analyze linear dynamic systems by
- Creating models using mathematical representations, and coding them in Matlab and Simulink,
- Generating solutions to these models, and plotting the results in ways that enhance understanding of system behavior,
- Exploring the structural relationships within systems, as represented by the mathematical models that are developed in class, and iterated
upon as necessary.
- To design simple control systems, to modify and control the behavior of linear dynamic systems,
- To improve oral, graphical and written communication skills,
- To evaluate her personal learning process and understanding of the concepts and skills from class.
Reading and Class Time
The syllabus lists the reading for each week.
Students are expected to do the reading before coming to
class, in order to be fully
prepared to solidify the
material in the class period.
Assignments
There will be weekly homework assignments. There may also be short reading and homework quizzes in class.
Homework format
All homework solutions must be written on standard
engineering paper (or typed and printed when appropriate,
e.g., Matlab code and computer plotted results). Students
are encouraged to work together to understand the concepts,
but each student must work out and hand in her own
solutions. All assignments are to be neatly written or
typed, and stapled, with your name and date. Note that
students are expected to follow the Honor Code for all work
in this course. Copying on homework, labs or quizzes/exams,
and other violations will be brought to the honor board.
The purpose of the homework is for you to have the
opportunity to practice - practice - practice the skills and
concepts from class. Since homework is the time to practice,
you are not expected to have perfects solutions at all
times. You are expected to do your best work for each
problem however. In recognition of these goals, each
homework problem will be evaluated on a 0-10 point scale as
follows:
- 0 No effort
- 2 Problem statement written out but not attempted
- 6 Incomplete attempt
- 9 Complete attempt, incorrect solution
- 10 Complete attempt, correct solution
A complete attempt includes identifying what is known,
articulating what you are solving, stating any assumptions,
properly labeling figures, including units and a reasonable
number of significant figures in your answer, and clearly
and neatly documenting your progression towards a final
result.
Quizzes and Exams
There may be weekly quizzes that are used to assess
progress and ensure students do not fall behind.
There will be one midterm exam and a final exam
, used to solidify concepts and assess the learning progress.
Project
Through a group or individual homework project, students will gain practical experience in designing and demonstrating a
dynamic system,
and a simple control input for the system.
Projects can include applications from any branch of
engineering science in which the students
identify a system
that evolves over time and can be controlled.
Class attendance
Students are required to attend class and participate in class discussions and problem solving exercises.
Grading
Grades in this course are designed to represent your achievement of the objectives
listed above. The course components that will make up your grade are listed below.
| ASSIGNMENT |
GRADE CONTRIBUTION
|
| Homework sets |
25%
|
| Knowledge Building |
25%
|
| Class particpation |
10%
|
| Midterm exam |
20%
|
| Final exam |
20%
|
Late Policy
All homework assignments must be turned in to room Ford Hall 352 (or prior to
that time, in class); late
assignments will be penalized at the rate of one point per
minute unless you have requested and received and extension
at least 24 hours before the deadline. However, each
student will have a total of 1 hour (60 minutes) grace time
to be used as desired by that student over the course of the
semester, such that you can have a semester total of 60
tardy minutes for homework and the project without penalty (note
that these minutes cannot be used for in-class reading
questions, μ-Quizzes or exams).
Honor Code
The weekly homework
assignments that you submit must be your own
work. You are encouraged to discuss the problems and
modeling issues with your classmates and work on them together,
but each student must work out her own solutions. It is not
okay to copy answers from another student's homework - doing
so is a violation of the Honor Code. Note that it is a
violation of the honor code to 1) use or copy another
student's work, and 2) provide another student with your
work. Projects will be done in small groups. Exams must be
exclusively each student's own work, following the
instructions provided with each exam. Do not hesitate to ask
any questions that you may have concerning the honor code.
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Matlab and Simulink Hints and Tutorials:
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