Concepts and Content Students Learn
Students learn the foundational concepts of transfer functions, including how physical laws governing motion can be translated into mathematical models suitable for analysis. They develop the ability to analyze the dynamical behavior of physical systems—specifically vehicle cruise‑control dynamics and a two‑mass suspension model—and understand how system parameters influence stability, responsiveness, and comfort. A key conceptual takeaway is recognizing that control design is an iterative process, where parameter tuning requires experimentation, evaluation, and justification.

How MATLAB Supports Learning
MATLAB serves as the primary computational environment for modeling and simulation. Students use MATLAB (and optionally Simulink) to:
> Derive and implement transfer functions from differential equations
> Simulate system responses to step inputs
> Visualize dynamical behavior through plots and time‑response curves
> Experiment with controller gains and damping parameters

MATLAB acts as a bridge between mathematical formulation and visual interpretation, enabling students to see how changes in equations directly affect system performance. This visualization significantly improves comprehension of abstract control concepts.

Higher‑Order Thinking Skills Developed
This activity strengthens several higher‑order skills:
> Critical thinking: Students must evaluate how parameter choices affect system behavior and justify their selections.
> Computation and data analysis: They compute transfer functions, generate simulations, and interpret response curves.
> Model development and refinement: Students iteratively adjust controller gains or damping coefficients to achieve desired performance.
> Synthesis of ideas: They connect physics, differential equations, and control theory to build coherent models of real‑world systems.

Additional Skills Developed
Students also practice:
> Technical writing: Communicating their reasoning, simulation results, and design choices clearly in a MATLAB Live Script.
> Presentation of ideas: Organizing plots, explanations, and conclusions in a professional format suitable for engineering documentation.
> Engineering judgment: Making informed decisions about "preferred" parameter values based on comfort, stability, or responsiveness.

This activity is designed for junior‑level undergraduate students in a 4‑year engineering program, typically in courses covering control systems or dynamic system modeling. It fits well in classes with 50–90 students, where MATLAB‑based homework assignments are standard and students have already encountered introductory examples during lecture. The assignment functions as a short, simulation‑based homework activity rather than a lab or long project. Students generally spend 1–2 hours completing the tasks, which include deriving a transfer function, simulating system responses, and performing basic control design through trial‑and‑error parameter tuning.

Student Preparation and Required Skills:
Students should already have:
> Basic proficiency with MATLAB scripting and familiarity with the Control System Toolbox
> Ability to define and manipulate transfer functions
> Experience running linear system simulations

Optional but helpful skills:
> building simple Simulink models from differential equations
> Foundational knowledge of differential equations,
> introductory physics, and the connection between mathematical models and real‑world driving systems

Course Placement:
This activity is assigned after classroom coverage of:
> Principles of vehicle cruise control
> Fundamentals of vehicle suspension systems
> Demonstrated examples of similar MATLAB/Simulink workflows
> Distribution of sample code to support student learning

Because students have already seen related demonstrations, this homework reinforces conceptual understanding while giving them hands‑on experience with simulation and controller tuning.

Adaptability:
The activity is easy to adapt for other courses or institutions. It can be used in:
> Smaller or larger classes
> Lab‑supported courses
> Introductory control courses at other universities
> Any setting where students have basic MATLAB familiarity and exposure to dynamic systems

Its modular nature, cruise control modeling, suspension modeling, and proportional control tuning, makes it flexible for instructors who want to emphasize modeling, simulation, or introductory controller design.

This homework activity is implemented after in‑class lectures and demonstrations on transfer functions, dynamical system modeling, and MATLAB/Simulink simulation. Students apply these concepts by revising equations of motion, deriving transfer functions, and simulating system responses for both a cruise‑control model and a two‑mass suspension model.

How the Activity Works
Students complete the assignment using a MATLAB Live Script, which allows them to:
> Define system parameters and construct transfer functions
> Simulate closed‑loop responses using MATLAB commands or Simulink models
> Visualize system behavior through plots generated directly in the Live Script
> Experiment with controller gains to observe changes in system performance

The assignment is designed to be completed in 1–2 hours, functioning as a short, focused homework activity rather than a lab or multi‑week project.

Materials Needed
Faculty implementing this activity typically provide:
> Assignment template (PDF exported from MATLAB Live Script)
> Sample MATLAB code demonstrating transfer‑function creation and simulation
> Lecture slides covering cruise control, suspension systems, and introductory control design
> Textbook references for dynamic systems and control fundamentals

Optional Simulink model snapshots for students who choose to use Simulink

Each item plays a specific role:
> Assignment template: Guides students through required tasks and expected outputs
> Sample code: Reduces overhead and helps students focus on conceptual understanding
> Lecture slides: Provide theoretical background and worked examples
> Textbook references: Reinforce foundational concepts and offer additional practice problems
> Simulink snapshots: Help students visualize block‑diagram modeling if they choose that route

Use of MATLAB (and Alternatives)
MATLAB is used because it provides:
> A straightforward interface for transfer‑function manipulation
> Built‑in tools for linear system simulation
> High‑quality visualization with minimal setup

Easy integration of Simulink for students who prefer block‑diagram modeling

Other software—such as Mathematica, Python with control libraries, or Octave—could theoretically be used. However, MATLAB is chosen because:
> It is widely adopted in engineering curricula
> Its Control System Toolbox simplifies the workflow
> Simulink offers an intuitive visual modeling environment
> Students can produce polished, reproducible results directly in a Live Script

External Materials and URLs
If you host materials externally (e.g., on a departmental site, GitHub, or LMS), you can include:
> Full URLs to assignment templates
> Links to MATLAB documentation or tutorials
> Links to course repositories containing sample code
(You can provide these URLs and I will integrate them into the final version.)

File Format Recommendations
> Editable materials (instructions, starter code): Word, plain text, or MATLAB .m files
> Read‑only materials (final assignment, reference sheets): PDF
> Simulink models: .slx files
> Figures or diagrams: PNG or PDF

All uploaded materials should be freely redistributable under your institution's guidelines.

Lecture Slides (Acrobat (PDF) 1.2MB Aug19 26)
Sample MATLAB and Simulink Code (Zip Archive 122kB Aug19 26)
Student Template Files for Assignment (MATLAB Live Script 5kB Aug19 26)

Instructors using this activity may find it helpful to frame the assignment as an intuitive introduction to control systems and dynamic system behavior rather than a formal control‑design exercise. Students often assume they need to apply rigorous performance specifications (rise time, overshoot, settling time, etc.), but this activity is intentionally designed to build intuition using everyday physical reasoning.

Helping Students Use MATLAB and Simulink
Students typically succeed when they begin with the MATLAB transfer‑function workflow before attempting Simulink.

Encourage them to use built‑in functions such as tf, step, and lsim to visualize system behavior.

For students who choose Simulink, remind them that simple block diagrams are sufficient and no advanced modeling is required.

Provide or demonstrate a minimal working example so students can focus on interpreting results rather than debugging syntax.

Common Areas of Confusion
Over‑formalizing the task: Students may think they must evaluate the system using classical control metrics. Reinforce that this assignment is about physical intuition, not formal specifications.

Interpreting system response plots: Some students struggle to connect plots to real‑world behavior. Encourage them to think in terms of acceleration, speed, and how a car feels when responding to throttle or suspension disturbances.

Parameter tuning: Students may expect a single "correct" value of
K or b. Clarify that the goal is to explore how parameters influence behavior, not to meet a strict design target.

Concepts That Need Reinforcement
Emphasize that proportional control is simply a way of adjusting engine force based on speed error. Students should relate this to how they press the gas pedal while driving.

For the suspension model, remind students that damping affects how "smooth" or "bouncy" the ride feels. Connecting this to daily driving experience helps them choose a reasonable value of
b.

Reinforce the relationship between differential equations and physical systems, especially how mass, damping, and stiffness shape motion.

Pedagogical Tips
Encourage students to describe system behavior in plain language before using technical terms.

Ask them to compare the simulated response to what they would expect in a real car. This builds intuition and confidence.

Suggest that students annotate their MATLAB Live Script with short reflections on why certain parameter values "feel" better.

Safety and Practical Considerations
No physical lab work is required, but instructors should remind students that high‑voltage or automotive systems in real life require strict safety protocols.

When discussing cruise control or suspension systems, emphasize that these simulations are simplified models.

Making the Best Use of the Activity
This assignment works well immediately after lectures on cruise control and suspension systems, when students have fresh conceptual grounding.

It is highly adaptable: instructors can scale it up by adding more complex inputs or scale it down by providing more starter code.

The activity is effective in large classes (50–90 students) because MATLAB Live Scripts allow students to produce clean, self‑contained submissions.

Student performance in this activity is evaluated based on their ability to demonstrate conceptual understanding and correct use of MATLAB tools rather than formal control‑system specifications. Instructors can determine whether students have met the learning goals through three key outcomes:

> Successful derivation of the transfer function
Students should correctly revise the equations of motion, identify the input–output relationship, and construct the appropriate transfer function using their knowledge of dynamics and basic modeling principles.

> Accurate simulation of system behavior
Students must use MATLAB or Simulink to generate system responses for both the cruise‑control and suspension models. This includes proper use of functions such as tf, step, or lsim, or equivalent Simulink block diagrams.

> Clear reasoning based on physical intuition
Rather than relying on formal control‑performance specifications, students should interpret the simulated responses using everyday physics (acceleration, speed, damping), and how a car behaves in real driving situations. Their explanations should show they can connect plots to real‑world behavior and justify their chosen values of K or b using intuitive, experience‑based reasoning.

Together, these elements demonstrate that students can model a dynamical system, simulate its behavior, and evaluate performance using practical, physically grounded insight.

The primary resource supporting this activity is the freely available online textbook authored by the instructor. It provides foundational explanations of transfer functions, dynamic system modeling, and introductory control design, all of which directly align with the concepts used in this assignment.

Online Resource
Textbook: Introduction to Control Engineering
URL: https://repository.lsu.edu/cgi/viewcontent.cgi?params=/context/etext/article/1000/&path_info=Introduction_to_Control_Engineering.pdf
Description: This freely accessible textbook, written by the instructor, offers a clear and practical introduction to control engineering. It includes chapters on modeling physical systems, deriving transfer functions, and simulating dynamical behavior using MATLAB. The text is highly relevant to this activity because it provides the theoretical background students need before completing the homework and includes examples similar to the cruise‑control and suspension models used in the assignment.

Why This Resource Is Relevant
> Supports students in understanding the mathematical foundations behind the assignment.

> Provides step‑by‑step examples of MATLAB‑based simulation workflows.

> Reinforces intuitive, physics‑based reasoning about system behavior—an essential part of this activity.

> Freely available, making it accessible to faculty and students at any institution.

Additional Materials (Optional Uploads)
If uploaded, the following materials can be embedded directly into the activity page:

> Assignment Template (PDF or Live Script): The exact homework instructions students follow.

> Sample MATLAB Code (.m or Live Script): Starter scripts demonstrating transfer‑function creation and simulation.

> Lecture Slides (PDF or PPTX): Slides covering cruise control, suspension systems, and introductory control concepts.

Each of these materials supports faculty in implementing the activity and helps students complete the assignment efficiently.