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Lesson / authored

Week 10 · Experiment: Metrics describe a response

Session 3 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 metrics describe a response.

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

Metrics describe a response

Rise time describes how quickly a response reaches a selected fraction of its final/reference level. Settling time is the first time after which all later samples stay inside a stated tolerance band. It is not the first time the trace merely touches that band. Steady-state error is the remaining error after transients have died away. Maximum command and overshoot are useful guardrails. State metric definitions and observation duration; if a trace never settles during the run, report not settled rather than inventing a settling time.

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))

Use your own recorded data or named test fixtures instead of the illustrative inputs. Save expected and actual values side by side. 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. Run gains 1, 3 and 8 at identical reference, initial state and caps.
  2. Plot each trace on the same axes; calculate final error, peak and maximum command.
  3. Add the same small alternating measurement noise to each run and repeat.
  4. Keep unstable or poorly performing traces and explain clipping rather than deleting them.

Experiment

Change only Kp in the three-gain sweep and compare clean/noisy cases using the same noise sequence.

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

Three complete gain traces with documented noise and saturation tradeoffs.

Save notebook/w10-s3.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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