Ball-and-Beam Control Energy Comparison

ISEF Category: Engineering Technology: Statics and Dynamics

Subcategory: Control Theory  ·  Difficulty: Advanced  ·  Setup: University Lab  ·  Time: Full Year

The Hook

A control system can waste more energy than it needs, even when it looks smooth. That matters for drones, robots, and factory machines that run all day. Your project asks a sharp question, can a smarter controller stabilize a ball with less energy than a classic one?

What Is It?

A ball-and-beam system is a classic control problem. A ball sits on a beam, and the controller changes the beam angle so the ball moves to a target spot. Your version uses an air jet from a centrifugal fan, which makes the ball-and-beam motion easier to build and measure.

Think of the controller like a careful driver. PID, which stands for proportional-integral-derivative, reacts to error using three terms. Model predictive control, or MPC, tries to predict future motion and choose the next move with that future in mind. Event-triggered MPC adds one more twist, it only updates when the system crosses a chosen condition, so it may save energy by skipping unnecessary corrections.

Why This Is a Good Topic

This topic works well because you can measure real numbers, not just guess which controller feels better. You can compare settling time, overshoot, tracking error, and energy use on the same physical rig. That makes the project testable and fair. It also connects to real systems that care about battery life, heat, and actuator wear, which gives you a strong engineering story.

Research Questions

• How does event-triggered MPC change energy per stabilization compared with classical PID?
• What is the effect of random reference step size on settling time for each controller?
• To what extent does event threshold choice change tracking error and actuator use?
• Which controller keeps overshoot lower when the ball starts far from the target?
• How does fan power draw correlate with control effort under repeated target changes?
• What is the effect of sensor noise on the stability of PID versus event-triggered MPC?

Basic Materials

• Ball-and-beam test rig with a centrifugal fan or air jet source.
• Small lightweight ball or puck that the beam can support.
• Microcontroller board such as Arduino or Raspberry Pi Pico.
• Motor driver or fan control module matched to the fan.
• Angle sensor or IMU for beam position.
• Position sensor for the ball, such as a camera, ultrasonic sensor, or linear sensor.
• Bench power supply or battery pack with known output.
• Digital multimeter for voltage and current checks.
• Ruler or measuring tape for calibration.
• Laptop for logging and analysis.

Advanced Materials

• High-frame-rate camera for motion tracking.
• Load cell or inline power meter for fan energy measurements.
• Precision encoder for beam angle feedback.
• Data acquisition interface for synchronized logging.
• Programmable centrifugal fan or blower with controllable speed.
• Optical tracking markers for ball position extraction.
• Vibration isolation base for cleaner control tests.
• MATLAB, Python, or similar environment for controller simulation and comparison.
• Calibration targets for camera and geometry correction.
• Safety enclosure or barrier for the moving ball and fan.

Software & Tools

• Python: Runs simulations, processes logs, and calculates settling time, overshoot, and energy metrics.
• OpenCV: Tracks the ball position from video frames if you use camera-based measurement.
• ImageJ: Measures motion in recorded clips and helps with quick calibration checks.
• GNU Octave: Lets you prototype control models and compare PID and MPC without paid software.
• Jupyter Notebook: Keeps code, plots, and notes together for cleaner analysis.

Experiment Steps

1. Define the performance metrics you will compare, especially settling time, tracking error, overshoot, and energy per trial.
2. Build a simplified model of the ball, beam, and fan so you can simulate controller behavior before hardware testing.
3. Choose one baseline controller, then design the event-trigger rule for the MPC version so the comparison stays fair.
4. Plan your sensing method and calibration steps so ball position, beam angle, and fan output all use the same reference frame.
5. Design a test matrix with random reference steps, repeated trials, and controlled starting positions.
6. Plan your analysis workflow so you can compare controller performance with the same statistical test and the same energy calculation method.

Common Pitfalls

• Mixing simulation assumptions with hardware results, which makes the control comparison look better on paper than in real life.
• Measuring energy only from command signal size, which ignores actual fan power draw and weakens the conclusion.
• Letting camera angle drift or sensor calibration shift, which changes ball position estimates between trials.
• Comparing controllers with different tuning quality, which makes the test about tuning skill instead of control strategy.
• Using random step inputs without enough repeats, which leaves you with noisy data and no clear trend.

What Makes This Competitive

A strong version of this project goes beyond a simple controller bake-off. You would build a careful energy metric, match the controllers as fairly as possible, and explain why one saves power without losing stability. Better still, you would test how the result changes with different reference patterns, sensor noise, or fan nonlinearities. That gives you a deeper control story, not just a demo.

Project Variations

• Test the same controller comparison on different ball masses or ball sizes to see how inertia changes efficiency.
• Replace the camera with a non-vision sensor and compare whether measurement noise changes the PID and MPC gap.
• Compare event-triggered MPC against gain-scheduled PID instead of fixed-gain PID to see whether adaptation narrows the energy difference.

Learn More

• MIT OpenCourseWare: Search for control systems lectures and model predictive control notes in mechanical engineering courses.
• NPTEL: Search for free university-level control systems courses with MPC and PID units.
• PubMed: Search for review articles on event-triggered control and energy-aware robotics.
• IEEE Xplore abstracts: Search for papers on ball-and-beam control, then read abstracts and figures when full text is limited.
• NASA: Search for guidance, navigation, and control resources that explain feedback, stability, and actuator limits.