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Lesson / authored

Week 10 · Improve: Choose a gain, not a favourite plot

Session 4 of 4 · Proportional control · 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

How much correction is helpful before lag and noise make the controller worse? This session focuses on choose a gain, not a favourite plot.

Before you start

The previous week’s recorded baseline and Week 9, 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

Choose a gain, not a favourite plot

A tuning decision trades response speed against overshoot, effort and sensitivity to noise. Use a small, planned gain sweep and choose a gain satisfying all declared requirements. Validate it on a different reference or disturbance without retuning. A zero steady-state error in a simplified simulation is not evidence of exact physical motion. If several gains work, a less aggressive one with margin can be preferable to a fastest-looking trace. Document output caps and sample interval alongside Kp because they are part of the controller.

Worked example — illustrative values

For reference 0.10 and measured 0.08 m/s, e = 0.02 m/s. Kp = 2 gives correction 0.04 in a normalized command scale; Kp = 6 gives 0.12. At reference = measured the proportional correction is zero, so a motor with drag may need feedforward or an integral term to maintain speed.

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/w10.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.
def run(kp):
    speed = 0.0
    trace = []
    for step in range(60):
        command = max(0.0, min(1.0, kp * (0.1 - speed)))
        speed += 0.25 * (0.3 * command - speed)
        trace.append(speed)
    return trace

for kp in [1.0, 3.0, 8.0]:
    values = run(kp)
    print(kp, "final_m_s", values[-1], "peak_m_s", max(values))

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

This experiment starts with pure proportional control and no feedforward. At steady state the illustrative model satisfies speed = 0.3 Kp (0.1−speed), so speed = 0.03 Kp/(1+0.3 Kp). Finite proportional gain leaves an offset in this model. Larger gain reduces that offset but can produce an aggressive response when lag, sampling or saturation matters. The printed peak and final speed are only two summary features; keep the full trace for settling and oscillation analysis. Do not copy these dimensionless gains into a real motor loop with different output units.

Practical instructions

  1. Choose a gain under stated overshoot/error/effort requirements.
  2. Validate at a second reference without changing the gain.
  3. Inspect source for unit names, caps and dt rather than only the plot.
  4. Write a tradeoff statement and preserve both training and validation traces.

Experiment

Hold the selected gain fixed at two reference speeds. Test whether your original requirements still hold in the second case.

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 chosen gain justified by metrics and tested on an unseen reference.

Save notebook/w10-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

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

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.

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