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Week 9 · Build: Sampling and estimating speed

Session 2 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 sampling and estimating speed.

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

Sampling and estimating speed

An encoder supplies count increments over an elapsed interval. With scale k, measured wheel speed is k ΔN/Δt. Δt must be positive and measured; assuming every loop takes exactly the requested sleep duration ignores computation and scheduling. A short interval responds quickly but contains few counts, so quantization is more visible. A long interval averages more counts but delays correction. Start at a modest fixed interval in simulation and record timing before hardware use. A zero increment can mean stopped, stale input or a disconnected sensor; context matters.

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))

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

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. Run the lag-model example and save the printed trace as simulated data.
  2. Change the code to record time_s,reference_m_s,speed_m_s,error_m_s,command.
  3. Build an open-loop version using constant command 0.4 and the same lag/disturbance.
  4. Plot the two speeds against sample time with a reference line.

Experiment

Compare open-loop/feedback simulated traces from identical starting states; preserve model parameters with the result.

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

Two labelled simulated traces with the same conditions and reference.

Save notebook/w09-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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