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 2019
Week
| Topic
| Reading
| HW due Tuesdays (at the start of class)
|
Jan 24 |
Introduction 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?
|
|
HW 1:
|
Jan 28 |
State-Space, dynamic system modeling
Launching into State-Space: Building the models
- Identifying the 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
- First and second order models
Linear Algebra Review 1 - on own!, App'x A
|
- Luenberger Chapters 1 & 2 (Moodle)
- Text Chapter 1: pp 1-13, section 1.6
- Text App'x A Linear Algebra - review on your own (esp. inverse and transpose)
Class Examples:
|
|
Feb 4 |
Modeling systems in Simulink (see links at bottom)
- 2nd Order System Models
- In-class practice on Thursday
|
- Matlab tutorials (linked at bottom of page)
Class Examples: Save with name shown to your directory, then open with Matlab:
|
HW2
HW2 Solutions
HW2_DetailModel_Soln
|
Feb 11 |
Trekking through state-space
Developing state-space models from anything
* Input/output equations (higher order diff eqs)
º Using Phase Variables
* Simulation diagrams
* Transfer functions
(Linear Algebra Review 2, begin on own, App'x B)
|
* Chapter 1 pp 14 to end (not section 1.4)
* Matlab tutorials, linked below
* Text App'x B
|
HW3
HW3 soln
|
Feb 18 |
Ferris Wheel Model
Begin system behavior and 'solution' form
And always keep in mind... the Stages of Analysis:
* Create dynamic model
* Analyze system behavior
* Analyze structural relationships
* Modify or control system behavior
|
Chapter 1 pp 14 to end (not section 1.4) |
HW4
HW4 Solution
|
Feb 25 |
System Behavior in State Space: Generating solutions and analyzing behavior
- The State Transition Matrix
- Forced and natural response
- Continuous Time Systems
|
Chapter 2: Understand the proofs in general, but focus on concepts and examples |
- HW5 due after break
- No Solutions
|
Mar 4 |
Thermal system modeling
- Dynamic equations for thermal systems
- Comparing different modeling options
- Investigating natural and forced response
|
|
Midterm Exam in Thursday Class
|
Mar 11 |
Spring Break |
|
|
Mar 18 |
Characteristic Behavior based on System Structure:
Transforming State-Space: Linear transformations
- Linear dependence and independence... on Moodle
- Change of basis
- Structural relationships
* Eigenvalues and eigenvectors
* Modes of behavior (an ocean shore?)
* Romeo & Juliet Model, part 2
(Romeo.m)
|
Appendix B, Sections 2.5 & 2.6 Luenberger Chapter 3 |
|
Mar 25 |
EigenAnalysis & Diagonalization
- State transition matrix with a diagonalized system
|
Luenberger Chapter 3
Text chapter 2, especially section 2.5 |
|
Apr 1 |
Eigenanalysis
- Modal analysis
- Diagonalization
|
Text Chapters 3 |
|
Apr 8 |
Controllability
- Migration example for eigenanalysis
|
Text Chapter 3, and some of 6 for HW |
|
Apr 15 |
Observability, Stability and Feedback Control
- Matlab practice in computer lab
- Observability
- Stability
|
Text Chapter 4, and 6 as needed |
Continue with homework 9
|
Apr 22 |
Designing Controllers
- Controllers
- Controllers in Matlab
|
Text Chapters 7 and 8, beginning |
|
Apr 29 |
Designing Controllers continued
- Controllers and Course Summary
- Meet in Ford Hall 2nd floor computer room
|
|
- HW 11
- HW 11 Solutions for review
|
|
Take Home Final Exam
|
Due Friday May 10 by 10:00am |
to Ford Hall 352 or EGR Main Office (1st floor) |
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.
ABET Outcomes for EGR 326
For students' Books of Evidence, the following ABET outcomes can be achieved by every student taking EGR 326.
Note that this is a shared responsibility between the course professor and each student. If you do not
understand how or when these outcomes are being addressed through the course material, be sure to come to
office hours (while there are still many weeks remaining in the semester). If populating your BoEs is left
until the end of the semester, it could be too late to achieve all you planned on.
- Student Outcome (a) APPLICATION: an ability to apply knowledge of mathematics, science, and engineering
- (a)1: The student solves engineering problems that require advanced math skills.
- (a)2: The student applies fundamental scientific and engineering principles in solving engineering problems.
- Student Outcome (c) DESIGN: an ability to design a system, component, or process to meet desired needs within realistic
constraints such as economic, environmental, social, political, ethical, health and safety, manufacturability, and sustainability
- (c)1: The student articulates stakeholder needs, realistic constraints, and relevant design requirements for a design problem.
- (c)2: The student generates, evaluates, and selects potential design concepts in response to stated design requirements.
- (c)3: The student develops, tests, and iteratively refines a design to meet desired needs and requirements.
- Student Outcome (e) PROBLEM FRAMING: an ability to identify, formulate, and solve engineering problems
- (e)1: The student identifies an engineering problem and articulates relevant big ideas.
- (e)2: The student transforms a complex problem statement into a simplified model.
- (e)3: The student solves an engineering problem and articulates the impact of simplifying assumptions.
- Student Outcome (g) COMMUNICATION: an ability to communicate effectively
- (g)1: The student’s writing utilizes appropriate grammar and format, effectively articulates ideas, and demonstrates appropriate style for the audience.
- (g)3: The student presents engineering concepts utilizing a graphical representation.
- Student Outcome (h) CONTEXT: the broad education necessary to understand the impact of engineering solutions in a global, economic, environmental, and societal context.
- (h)1: The student identifies the global and societal contexts within their engineering work.
- (h)3: The student evaluates the economics of an engineering solution.
- Student Outcome (i) LIFE-LONG LEARNING: a recognition of the need for, and ability to engage in life-long learning
- (i)1: The student is able to articulate gaps in their knowledge.
- Student Outcome (k) MODERN TOOLS: an ability to use the techniques, skills, and modern engineering tools necessary for engineering practice
- (k)3: The student demonstrates an ability to use modern tools for mathematical modeling or data analysis.
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.
Exams
There will be one midterm exam and a final exam
used to solidify concepts and assess the learning progress.
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 |
20%
|
Class particpation |
15%
|
Midterm exam |
25%
|
Final exam |
40%
|
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.
Matlab and Simulink Hints and Tutorials:
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