EGR 326, Spring 2019
Dynamic Systems and Introduction to Control Theory

Professor: Judith Cardell; Room 352 Ford Hall
Office hours: TBD

Class Time: Tu/Th Seelye 311

Pre-requisites:
 * EGR 220 - for mathematical background (326 is a general engineering course)
 * CSC 111 - for some programming experience

Text: Linear State-Space Control Systems, by Williams and Lawrence, Wiley, 2007.
optional reference: Introduction to Dynamic Systems, David Luenberger, Wiley & Sons, 1979.  


   

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:

  1. The fundamentals of identifying and characterizing linear dynamic systems, using both engineering theory and informed observation of system behavior,
  2. To model and analyze linear dynamic systems by
    1. Creating models using mathematical representations, and coding them in Matlab and Simulink,
    2. Generating solutions to these models, and plotting the results in ways that enhance understanding of system behavior,
    3. Exploring the structural relationships within systems, as represented by the mathematical models that are developed in class, and iterated upon as necessary.
  3. To design simple control systems, to modify and control the behavior of linear dynamic systems,
  4. To improve oral, graphical and written communication skills,
  5. 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: