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Lesson / authored

Week 10 · Build: Lag and overshoot

Session 2 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 lag and overshoot.

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

Lag and overshoot

Overshoot occurs when the measured variable crosses beyond the reference after a change. A motor keeps responding to earlier drive while a new correction is being calculated. At high gain the controller can alternate large corrections and create oscillation. A controller that starts from rest is a different experiment from one already near its target. Keep initial state fixed. To observe oscillation safely, use the desktop lag model, not escalating wheel power until a robot shakes. Hardware gains remain bounded by an independently verified motion envelope.

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))

Run the example on desktop Python before adapting it. Change one valid input and check the result; keep device-only calls in a separate adapter. 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. Save run(kp) and make it return speed, error and command for every step.
  2. Define sample interval as 0.1 s for plotting and retain that value with each trace.
  3. Implement a tolerance-band check that requires all remaining samples to be inside the band.
  4. Test the metric with a hand-written trace that enters and then leaves the band.

Experiment

Test the settling function with one always-inside, one briefly-inside and one never-inside trace. Require honest not-settled results.

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 bounded P model with correctly defined settling behaviour and retained time axis.

Save notebook/w10-s2.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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