Week 11 · Improve: Tune terms separately

Session 4 of 4 · Integral and derivative · 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

When does remembering error help, and when does it create a problem? This session focuses on tune terms separately.

Before you start

The previous week’s recorded baseline and Week 10, 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

Tune terms separately

Start from a stable P baseline, add a small integral term only if steady offset matters, then consider derivative only for a measured damping/noise problem. Changing all three gains at once conceals causes. Log the P, I and D contributions alongside raw and clipped output. Compare a P, PI and PID controller on the same scenario, including unreachable targets and noisy measurements. If PID performs no better than PI, choose the simpler controller and explain why. A sophisticated label is not a requirement.

Worked example — illustrative values

At error 0.02 m/s for 0.1 s, accumulated error increases by 0.002 m. A speed measurement jump from 0.08 to 0.10 m/s over 0.1 s has slope 0.2 m/s². With measurement derivative gain 0.1, its damping contribution is −0.02 normalized output 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/w11.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.
target, speed, integral, previous = 0.1, 0.0, 0.0, None
dt, kp, ki, kd = 0.1, 3.0, 2.0, 0.05
for step in range(80):
    error = target - speed
    integral = max(-0.2, min(0.2, integral + error * dt))
    derivative = 0.0 if previous is None else -(speed - previous) / dt
    raw = kp * error + ki * integral + kd * derivative
    command = max(0.0, min(1.0, raw))
    previous = speed
    speed += 0.2 * (0.3 * command - speed)
    print(step, speed, integral, raw, command)

Compare the unchanged baseline and your proposed change on the same inputs. Keep the original files so another reader can reproduce the comparison. 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 integral accumulator adds error times 0.1 s and is clipped to ±0.2 in the model’s accumulated-error units. The derivative uses the negative change in measured speed, so a sudden target change does not directly create a derivative kick. previous starts as None, making the first derivative zero rather than dividing an undefined change. Output is then limited to 0–1. Integral clipping limits accumulation but is not a perfect anti-windup design for every actuator. Compare P, PI and PID using the same disturbance/noise traces, and reset accumulator/history whenever the experiment restarts.

Practical instructions

1. Choose P, PI or PID based on error, overshoot, noise and recovery data.
2. Test a target step and an emergency reset without altering gains.
3. Remove any unused derivative path if PI is the supported design.
4. Document gains, state bounds, reset policy, dt and the next validation case.

Experiment

Freeze one controller and test fresh-start, target-step and reset scenarios. State which acceptance metric decides whether derivative is retained.

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 justified simplest-sufficient controller with all state and timing settings recorded.

Save notebook/w11-s4.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 tune terms separately in your own words using this session’s example and its units/assumptions.
• Produce the specific evidence above: A justified simplest-sufficient controller with all state and timing settings recorded.
• 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: Sketch a constant error and predict what its accumulated integral will do.
• 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.