Week 9 · Learn: Error closes the loop

Session 1 of 4 · Close the loop · Phase 3

Plan about 15 minutes for explanation, 30 minutes for practical work and 10–15 minutes for documentation. A longer build may continue into the next session: stop safely, commit the current state and record the next check. Desktop simulations count as software evidence; label them clearly and record physical validation separately.

Engineering challenge

Can measuring the result reject a disturbance that a timed command cannot notice? This session focuses on error closes the loop.

Before you start

The previous week’s recorded baseline and Week 8, Improve. For later sessions this week, retain the preceding session’s files and predictions.

Equipment: Desktop Python, editor, paper and ruler; for physical work, the configured 3pi+ 2040, clear floor mat and hardware checklist. Week 3 additionally uses the separate low-voltage LED circuit described in its procedure.

For any motion, verify the stop button, short time limit and clear floor area first. Keep the wheels raised for a new device program until its commands and stop behaviour are checked. A hazard or uncertain input is a reason to stop and document, not to force the trial to finish.

Theory and mathematics

Error closes the loop

A reference is the desired measured quantity, such as wheel speed in m/s. A measurement estimates the actual quantity. Error is reference minus measurement. A controller converts error to a motor command; the motor and wheel are the plant. Negative feedback means acting to reduce error, not using a negative numeric command in every case. If a slow wheel causes a larger forward drive, the correction has the right sign. If it causes still less drive, the loop reinforces its error and can become unstable.

Worked example — illustrative values

If k = 0.0001 m/count, ΔN = 100 and Δt = 0.1 s, measured speed is 0.10 m/s. A reference of 0.12 m/s gives error +0.02 m/s. With gain 1000 command units per m/s, the proportional correction is +20 command units.

Write the calculation in your notebook before running code. State which values you measured, which you assumed and which the program calculates. A correct numerical calculation cannot rescue an incorrect physical assumption.

Run and explain the model

The following is desktop Python, not a ready-to-run motor program. Download this week’s example, save it in your student repository and run python3 code/w09.py from the repository root. The same small model is reused across the week so you can learn it, build with it, test it and revise it.

# Desktop Python teaching example. Numerical inputs are illustrative.
reference = 0.12
speed = 0.0
for step in range(40):
    disturbance = 0.7 if step >= 20 else 1.0
    error = reference - speed
    command = max(0.0, min(1.0, 0.4 + 2.0 * error))
    speed += 0.2 * (0.3 * command * disturbance - speed)
    print(step, round(speed, 4), round(error, 4), round(command, 4))

Predict the example’s output by hand. Mark the inputs, units and assumptions; explain where this model could fail. If an exception appears, read its final line, identify the input or assumption that caused it and make the smallest explained correction. Do not delete validation merely to obtain output.

Understanding the model and its limits

The command includes an illustrative feedforward value 0.4 plus proportional correction. The plant moves 20% of the way toward its new steady speed each step, representing lag. After step 20, multiplying the plant speed by 0.7 introduces a load-like disturbance. The error printed for each row uses the speed before that update, while the printed speed is after the update; label this timing if you plot both. Compare with a fixed-command run using the same plant and disturbance. This normalized command model is not Pololu’s ±6000 device-unit interface.

Practical instructions

1. Draw reference, comparison, controller, motor and encoder in a feedback diagram.
2. Calculate error for below-target, on-target and above-target speeds.
3. Trace the sign of each correction without a powered robot.
4. Choose wheel speed as the controlled quantity and ruler distance as an independent check.

Experiment

Calculate error and the sign of drive correction for three speeds. Deliberately reverse the correction on paper and explain the runaway direction.

Before testing, record your prediction, changed factor, measured response, fixed conditions and stopping rule. Save every attempted run, including failures, with a condition and source version. If hardware is unavailable, use an explicitly labelled synthetic/replay dataset and list the physical question it cannot answer. Do not invent completed trials.

Deliverable

A complete feedback diagram, correct correction signs and unit-consistent speed/error calculations.

Save notebook/w09-s1.md, the relevant code revision, raw CSV or test-case records, and one labelled diagram/plot/table. Link the files relatively from your notebook. Use the entry template and report guide.

Completion criteria

• Explain error closes the loop in your own words using this session’s example and its units/assumptions.
• Produce the specific evidence above: A complete feedback diagram, correct correction signs and unit-consistent speed/error calculations.
• Keep predictions and raw outcomes, distinguish observations from interpretation, and explain one limitation or unresolved failure.
• Review the Git diff, commit the session’s intended files and state the next experiment or safe continuation point.

A documented failed prediction can meet the learning criteria. A missing physical trial must remain marked untested; software success alone does not validate the robot.

Reading and video

• Focused reading: MathWorks: Understanding PID, Part 1. Study task: Identify setpoint, measured output, error and disturbance in the feedback diagram.
• Video/lecture option: MathWorks: What is PID control?. Study task: Draw the closed-loop signal path and label the measured quantity. Watch a relevant 5–10 minute excerpt or use the linked notes if video is inaccessible. This is supporting conceptual material; hardware in a demonstration may differ from yours.
• Practical reference: Engineering handbook and hardware setup. Manufacturer/API references and video metadata were checked on 2026-10-09; recheck the actual firmware before transferring code.

Reflection and next step

Which assumption most affected your result? Point to one observation that supports your explanation and one alternative explanation the evidence has not ruled out. Write a specific next test with a changed factor and measurable outcome, then proceed through the week’s Learn → Build → Experiment → Improve cycle.