Project 4: Simulating a Bouncing Ball with Simulink

Build a Simulink model of a bouncing ball and compare it to an analytic solution.

Project Overview

Attribute Value
Difficulty Level 2: Intermediate
Time Estimate Weekend
Main Language MATLAB + Simulink
Alternative Languages Python (SimPy), Modelica
Knowledge Area Simulation and dynamics
Tools Simulink
Main Book “System Dynamics” by Katsuhiko Ogata

What you’ll build: A Simulink model that simulates a ball falling and bouncing with a restitution coefficient.

Why it teaches MATLAB: Simulink teaches block-diagram modeling and continuous-time systems.

Core challenges you’ll face:

  • Building integrator chains
  • Implementing collision detection and bounce
  • Comparing numeric vs analytic results

Real World Outcome

You will run the simulation and see the ball’s height over time with decreasing bounce heights.

Example Output:

Simulation time: 10 s
Bounces detected: 6
Saved plot: bounce_height.png

Verification steps:

  • Compare bounce heights against expected restitution ratio
  • Validate free-fall segments against analytic curves

The Core Question You’re Answering

“How do continuous-time equations become a block simulation?”

This is the essence of Simulink modeling.

Concepts You Must Understand First

Stop and research these before coding:

  1. Second-order motion
    • How do acceleration, velocity, and position relate?
    • Book Reference: “System Dynamics” by Katsuhiko Ogata, Ch. 2
  2. Restitution coefficient
    • How does it control bounce height?
    • Book Reference: “Classical Mechanics” by John Taylor, Ch. 4
  3. Event handling
    • How do you detect ground contact in a simulation?
    • Book Reference: “System Dynamics” by Katsuhiko Ogata, Ch. 4

Questions to Guide Your Design

  1. Model structure
    • How will you chain integrators for velocity and position?
    • Where will you insert the bounce logic?
  2. Validation
    • How will you compare to analytic free-fall equations?
    • How will you test different restitution values?

Thinking Exercise

Bounce Ratio

If a ball drops from 10 meters and restitution is 0.8, what height should the first bounce reach?

Questions while working:

  • How does energy relate to height?
  • Why does the bounce ratio square the restitution coefficient?

The Interview Questions They’ll Ask

Prepare to answer these:

  1. “What is a restitution coefficient?”
  2. “How do you model continuous-time systems in Simulink?”
  3. “Why do you need event detection in simulations?”
  4. “How do integrators represent physics?”
  5. “How do you validate a simulation model?”

Hints in Layers

Hint 1: Starting Point Start with a simple free-fall model without bouncing.

Hint 2: Next Level Add a condition to reverse velocity at ground contact.

Hint 3: Technical Details Use a saturation or relational operator to detect collisions.

Hint 4: Tools/Debugging Plot height and velocity to confirm physics.

Books That Will Help

Topic Book Chapter
Motion equations “System Dynamics” by Katsuhiko Ogata Ch. 2
Restitution “Classical Mechanics” by John Taylor Ch. 4
Event handling “System Dynamics” by Katsuhiko Ogata Ch. 4

Implementation Hints

  • Keep block layout readable with clear labels.
  • Start with fixed time step to simplify debugging.
  • Log signals for analysis outside Simulink.

Learning Milestones

  1. First milestone: You can simulate free fall in Simulink.
  2. Second milestone: You can implement bounce behavior.
  3. Final milestone: You can validate the model against analytic physics.