Session Overview
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In this session, we'll learn about poles: what they are, how to find them, and what they tell us about the long-term behavior of an LTI system. The overview handout provides a more detailed introduction, including the big ideas of the session, key vocabulary, what you should understand (theory) and be able to do (practice) after completing this session, and additional resources. |
Session Content
Readings
Read sections 5.4-5.7 of the course notes.
Lecture Video
Watch the lecture video. The handout and slides present the same material, but the slides include answers to the in-class questions.
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Lecture 5: Characterizing System Performance (01:18:31)
Lecture 5: Characterizing System Performance
> Download from iTunes U (MP4 - 188MB)
> Download from Internet Archive (MP4 - 188MB)
About this Video
Introduction to poles, which provide a way to characterize the behavior of a system in terms of a mathematical description as a system function.
Recitation Video
These videos have been developed for OCW Scholar, and are designed to supplement the lecture videos.
Session Activities
The problems in the tables below are taken from the 6.01 Online Tutor, an interactive environment that is not available on OCW. Do not try to answer these questions in the PDF files; answers will not be checked, and cannot be submitted.
Software Lab
- Software Lab 5: System Functions (PDF)
- Code for Software Lab 5 (ZIP) (This ZIP file contains: 2 .py files.)
| PROBLEM # | QUESTIONS |
|---|---|
| 5.1.1 | System function class (PDF) |
| 5.1.2 | Cascading systems (PDF) |
| 5.1.3 | Cascade of system functions (PDF) |
| 5.1.4 | Feedback subtract expression (PDF) |
| 5.1.5 | FeedbackSubtract code (PDF) |
Design Lab
- Design Lab 5: Staggering Proportions (PDF)
- Code for Design Lab 5 (ZIP) (This ZIP file contains: 2 .py files.)
Do problem 5.2.1 before the design lab.
| PROBLEM # | QUESTIONS |
|---|---|
| 5.2.1 | Wall finder system function (PDF) |
| 5.3.2 | Wall follower system function (PDF) |
| 5.3.4 | Wall follower model (PDF) |
Additional Exercises
| PROBLEM # | QUESTIONS |
|---|---|
| 5.4.1 | System behavior (PDF) |
Check Yourself
Nano-Quiz
Nano-quiz problems and solutions are taken from a previous version of the 6.01 Online Tutor. Do not try to answer these questions in the PDF files; answers will not be checked, and cannot be submitted.
Homework
- Homework 2: Heads Up! (PDF)
- Code for Homework 2 (ZIP) (This ZIP file contains: 1 .py file.)
| PROBLEM # | QUESTIONS |
|---|---|
| 5.5.1 | Modeling the controller/sensor (PDF) |
| 5.5.2 | Modeling the plant (PDF) |
| 5.5.3 | Putting it together (PDF) |
| 5.5.4 | Analyzing the system (PDF) |