Overview
Week 11 at a Glance
Differential equation modelsLaplace transform propertiesTransfer functionsBlock diagram algebraPoles and zerosSystem analogy method
Why it matters in practice. Transfer functions are the universal language of control systems. Every topic in Weeks 12-15 — step response, Bode plots, root locus, PID design — is built on the transfer function framework you establish this week.
Objectives
What You Will Be Able to Do
Course objectives (CO) define program-level skills. Module objectives (MO) define specific weekly targets that build toward them.
Course Objectives (CO)
CO7: Derive transfer functions from differential equation models; characterize first- and second-order systems from step response and Bode plot data.
Module Objectives (MO) — Week 11
Apply Newton's law, KVL, energy balance, and mass balance to derive differential equations for mechanical, electrical, thermal, and fluid systems.
CO7
CO7
Apply the Laplace transform to convert a linear ODE (with zero initial conditions) to a transfer function G(s).
CO7
CO7
Manipulate block diagrams using series, parallel, and feedback reduction rules to obtain a single closed-loop transfer function.
CO7
CO7
Locate poles and zeros of a transfer function and describe their effect on system behavior.
CO7
CO7
Review these objectives before you start each assignment. They map directly to what is assessed on the quiz, homework, and exams.
Suggested Learning Path
How to Work Through This Week
Follow this sequence. Each step prepares you for the next. Do not attempt graded work before completing the instructional material it depends on.
1
Read Alciatore Ch. 7 (dynamics and Laplace sections)
The Laplace table on the first page is essential — keep it open throughout the week. Work through the spring-mass-damper derivation example completely before lecture.
2
Attend Lecture
Lecture 1 covers system modeling and Laplace transform properties. Lecture 2 covers transfer functions, block diagrams, and pole-zero analysis. The problem session derives a complete second-order transfer function.
3
Begin Module 5 Homework
Module 5 Homework (Weeks 11-13) is due at the end of Week 13. The differential equation modeling and Laplace transform problems map directly to this week's content.
Instructional Material
Required Readings, Videos, and Resources
Complete all required items before moving to graded activities. The Aligns to column maps each resource to the module objectives it directly supports.
| Resource | What You Will Gain | Aligns to | Est. Time |
|---|---|---|---|
| Read Alciatore Ch. 7 — Dynamic System Modeling (Laplace sections) |
System analogy method, Laplace transform table, transfer function derivation, block diagram manipulation, and partial fraction expansion for inverse transforms. | MO1-MO4 | 75 min |
| Watch Micro-lecture: Block Diagram Reduction in 4 Steps |
Concise visual walkthrough of series, parallel, and feedback reduction with a worked multi-loop example. | MO3 | 4 min |
| Explore MATLAB Control System Toolbox: tf() and bode() tutorial |
Learn to enter transfer functions in MATLAB and generate Bode plots — tools you will use extensively in Weeks 12-13. | MO4 | 20 min |
Graded Learning Activities
Assignments and Due Dates
All graded work is submitted through Canvas. Complete the listed prerequisites before attempting each assignment.
| Assignment | Prerequisites | What Is Assessed | Aligns to | Points |
|---|---|---|---|---|
| Module 5 Homework: Dynamic Systems End of Week 13 |
Complete Ch. 7 reading and attend Week 11 lectures before starting modeling and Laplace problems. | System differential equation derivation, Laplace transform, transfer function, block diagram reduction, and pole-zero identification. | MO1-MO4 | 50 pts |
Academic integrity. Dynamic systems homework problems must be worked individually. You may discuss concepts with classmates, but all written derivations, transfer functions, and final answers must be your own work.