# Mdl Eg Ehomework

**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 2017**

Week | Topic | Reading | HW due (the next Fridayat the start of class) |

Jan 27 | 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 30 | State-Space, dynamic system modeling - Describing dynamics with difference and differential equations
- Class Examples
- 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:
| HW2 HW2 Solutions |

Feb 6 | Modeling systems in Simulink (see links at bottom) - Difference and differential equations models
- Programming Review: Elements of Matlab scripts & Simulink diagrams
- In-class practice on Friday
| - Matlab tutorials (linked at bottom of page)
Class Examples: Save with name shown to your directory, then open with Matlab: | HW3 HW3 Solutions |

Feb 13 | Trekking through state-spaceDeveloping 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 | HW4 HW4 soln |

Feb 20 | Review of State Space ModelsBegin system behavior and 'solution' formAnd always keep in mind... the Stages of Analysis: | Chapter 1 pp 14 to end (not section 1.4) | HW5 HW5 Solutions - none posted this week as everyone's model will be wildly different |

Feb 27 | System Behavior in State Space: Generating solutions and analyzing behavior **The State Transition Matrix**- Forced and natural response
- Continuous Time Systems
- Thermal system modeling
- Dynamic equations for thermal systems
- Comparing different modeling options
- Investigating natural and forced response
- In-class Matlab and Simulink practice on Friday
| Chapter 2: Understand the proofs in general, but focus on concepts and examples | |

Mar 6 |
- Linear dependence and independence
- Change of basis
- Structural relationships
| Appendix B, Sections 2.5 & 2.6 | |

Mar 13 | Spring Break | ||

Mar 20 | Characteristic Behavior based on System Structure:* Eigenvalues and eigenvectors * Modes of behavior (an ocean shore?) * Romeo & Juliet Model, part 2 (Romeo.m) | Luenberger Chapter 3 | |

Mar 27 | EigenAnalysis & Diagonalization- State transition matrix with a diagonalized system
- Left & right eigenvectors; Migration model
| Luenberger Chapter 3 Text chapter 2, especially section 2.5 | |

Apr 3 | When (aka controllability & observability) can and can't we control and find things in state-space? | Text Chapters 3 & 4 | |

Apr 10 | Stability Analysis- Equilibrium and stable equilibrium points
- Phase portrait
- Dominant eigenvalue and reduced order models
- HW analysis: Controllability & Observability
- Introduction to feedback control
| Text Chapter 6 | |

Apr 17 | Closed-loop Feedback Control | Text Chapter 7 | |

Apr 24 | Designing Observers (state estimators) | Text Chapters 7 and 8, beginning | |

May 1 | |||

Take Home Final Exam |

**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

**Exams **

There will be one midterm exam and a final exam , used to solidify concepts and assess the learning progress.

**Project **

There will be a small group project in which students will be able to demonstrate their knowledge building from the semester. Intermediate stages of the project (topic selection, bibliography...) will be handed in with homework assignments during the semester.

**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 |

Homework sets |

System Analysis Project |

Class particpation |

Midterm exam |

Final exam |

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