Overview
Week 13 at a Glance
Bode magnitude plotBode phase plotGain marginPhase marginFrequency sweepExperimental system ID
Why it matters in practice. The Bode plot is the primary tool for controller design and stability analysis in industry. Gain and phase margins are reported in every control system specification. Experimental frequency response is how you identify a system when you do not have a physics model.
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: Characterize systems from Bode plot data.
CO8: Assess closed-loop stability using gain and phase margins; interpret system behavior in the frequency domain.
Module Objectives (MO) — Week 13
Construct the asymptotic Bode magnitude and phase plots for a transfer function containing poles, zeros, and a gain factor.
CO7
CO7
Identify gain margin and phase margin from a Bode plot and interpret their significance for stability robustness.
CO8
CO8
Measure the frequency response of a physical system by sweeping sinusoidal inputs and recording magnitude and phase at each frequency.
CO7
CO7
Fit a first- or second-order transfer function to measured frequency response data.
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. 9 (Bode sections)
The asymptotic construction rules for poles and zeros are the key skill — practice constructing three Bode plots by hand before lecture. Speed on this improves with repetition.
2
Attend Lecture
Lecture 1 covers Bode plot construction and frequency response interpretation. Lecture 2 covers gain/phase margins and experimental system identification. Problem session includes a full Bode plot construction and margin calculation.
3
Lab: Experimental Frequency Response on Arduino
Drive a first-order RC circuit with a sine wave at multiple frequencies using Arduino DAC output. Record amplitude and phase lag at each frequency. Fit a transfer function to the data.
4
Submit Module 5 Homework — due this week
Module 5 Homework covers Weeks 11-13. All problems must be submitted by the Canvas deadline. Begin your Midterm 2 review immediately after submitting.
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. 9 — Frequency Response (Bode sections) |
Asymptotic magnitude and phase rules for poles and zeros, gain crossover frequency, phase crossover frequency, gain margin, phase margin, and experimental frequency sweep procedure. | MO1-MO4 | 60 min |
| Lab Lab: Experimental Bode Plot with Arduino |
Frequency sweep experiment, amplitude and phase measurement, Bode plot construction from data, and first-order TF fitting. | MO3, MO4 | ~2 hr lab |
| Explore Study Guide: Midterm 2 Exam Prep |
Practice problems and conceptual review for Module 3 content (Weeks 11-13). Begin review immediately this week. | All | 2-3 hr review |
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 all Week 11-13 readings and labs before finalizing Bode plot and system identification problems. | Transfer function derivation, step response analysis, Routh-Hurwitz, Bode plot construction, gain/phase margins, and experimental TF fitting. | MO1-MO4 | 50 pts |
Academic integrity. Your experimental Bode plot must be measured from your own hardware at the specified frequencies. The amplitude and phase data you report must come from your own Arduino measurements, not from simulation.