PYTHON · NUMPY

The Improvement Loop: Measure → Tune → Re-Sim

Your device overshoots at 18 percent against a 5 percent limit. You raise the actuator proportional gain. What happens?

Diagnose a failing device from sim telemetry and adjust the correct parameter(s) in the correct direction to bring it to spec, and prove the change was driven by the measured data, not by guessing.

01Challenge

The Bench opens with the latch-arm-v1 rig (a clean single-DOF tuning device, NOT the M4 slider-crank) already loaded, assembled, actuated, and already failing its spec. A red OUT OF SPEC chip sits top-right; a telemetry strip live-plots theta(t), theta_dot(t), and tau_act(t). The pinned spec card: S1 settle_time ≤ 0.80 s, S2 overshoot ≤ 5.0 %, S3 steady_error ≤ 1.0 deg, S4 hold_under_load (0.15 N·m disturbance at t=2.0s, |Δθ| ≤ 3°), S5 |tau_act| < 2.0 N·m for ≥95% of the run. First run: settle_time 2.26s (S1 FAIL), overshoot 66.5% (S2 FAIL), saturation 8% (S5 FAIL); steady_error 0.89° and hold_under_load 2.73° pass. VERDICT OUT OF SPEC. Editable params: arm_len, arm_thick, spring_k, actuator_kp, actuator_kv, stop_angle. Your goal, BEFORE watching anything: edit the panel, hit Re-Sim, and get all five checks to PASS. You are NOT told which knob to turn. Most learners' first instinct is to crank actuator_kp to 'get there faster', and the telemetry is engineered so that makes overshoot WORSE. That productive failure sets up the Model.

Predict firstYour device overshoots at 18 percent against a 5 percent limit. You raise the actuator proportional gain. What happens?

02Model

Your device just failed. A worse engineer guesses; a better one reads. Telemetry isn't decoration. It's a confession. This curve overshoots the target by twenty-three percent, then takes more than a second to settle. Overshoot has a meaning: the push driving the arm is winning against whatever should be slowing it down. Too much go, not enough whoa. Cranking the gain to 'get there faster' (the obvious move) makes overshoot worse. The fix is the other dial: damping. More whoa, not more go. This is the loop: measure the gap, form ONE hypothesis about ONE parameter, change only that one, re-simulate. If you change three knobs at once and it passes, you've learned nothing: you can't repeat it. One change, driven by the data, re-sim. That's not luck; that's engineering you can defend. Now go close the loop on yours.

Measure → tune → re-sim until in spec.

03Guided practice

Step A (fully scaffolded worked example): the Bench shows a filled-in diagnosis table, every number read off the rollout you just ran at actuator_kv = 0.15: overshoot 66.5% (S2 FAIL) MEANS push >> damping → candidate knob actuator_kv → INCREASE; settle_time 2.26s (S1 FAIL) MEANS oscillating before resting → actuator_kv (same) → INCREASE; saturation 8% (S5 FAIL) MEANS commanding more torque than the actuator can deliver → actuator_kv again → INCREASE; steady_error 0.89° (PASS, the limit is 1.0°) MEANS the aim is already fine → leave actuator_kp → HOLD. Takeaway: three failing checks point at the SAME knob: actuator_kv (damping) is too low; raise it; do NOT touch kp, because touching it would risk the one thing that already works. Step B (partial scaffold, predict-then-run): the panel locks all but one parameter to enforce 'change ONE.' The learner types a prediction ('raising kv should ____ overshoot and ____ settle_time' → 'decrease / decrease'), makes exactly one edit (raise actuator_kv), and Re-Sims. Expected result at kv≈0.8: settle_time passes at 0.47s and overshoot falls from 66.5% to 6.7%, but S2 still fails by a little. Scaffold prompt: 'Your hypothesis held; you're close but S2 still fails by a little. Nudge the SAME knob a little further, don't jump to a new one.' Step C (scaffold removed): the full panel unlocks, no table, no prediction field, just the spec card, telemetry, and Re-Sim. The learner converges (e.g. actuator_kv ≈ 1.0, where settle_time is 0.33s and overshoot 1.2%) until all five pass. The window is not one-sided: below about 0.83 the arm rings, above about 1.92 it is over-damped and settle_time fails again, so 'more damping' stops being the answer at some point and the telemetry says where. A change-log auto-records every edit plus the resulting metrics; this log is graded by Gate G.

04Feedback

PASS WHEN All five spec checks PASS at seed 0xD2C1 (settle_time ≤ 0.80s, overshoot ≤ 5.0%, steady_error ≤ 1.0°, hold_under_load ≤ 3°, saturation < 5%), AND Gate G holds: the change-log's decisive edit was on a telemetry-implicated parameter moved in the implicated direction (raising actuator_kv). Passing the spec by brute-forcing every knob does NOT pass G.

If your run fails, check:

S2 overshoot 18% (limit 5%). You raised actuator_kp, which adds PUSH and grows overshoot. The telemetry shows too little damping: raise actuator_kv instead.
S2 overshoot 6.2%, close, limit is 5.0%. Same knob, same direction: nudge actuator_kv up ~0.05 more and re-sim.
Spec met, but the change isn't defensible: you moved 4 parameters at once, so the fix can't be attributed to the data. Reset, change ONE implicated knob, and re-sim. A fix you can't explain isn't a fix.
S5 saturation: tau hit 2.0 N·m for 11% of the run. You're commanding more torque than the actuator can deliver. Lower actuator_kp or raise actuator_kv to ask for less force.
PASS: settle, overshoot, steady-error, hold, and saturation all in spec. One change, driven by the data, re-simulated. That's engineering you can defend.

05Retrieve & space

(M2, constraints/ranges) Before you push actuator_kp higher: the M2 guard says arm_thick ≥ 0.006. If raising kp led you to thin the arm to drop inertia, which guard would you violate? Type the failing constraint. Reconnects tuning to the valid design envelope.
(M3, DOF) How many degrees of freedom does this latch arm have, and about which axis does theta measure? Answer: 1 DOF, revolute about hinge z. Keeps the kinematic model alive under the physics.
(M4, metric definition) overshoot is computed relative to travel, not to stop_angle. If stop_angle were 70° instead of 35°, would the same absolute peak give a larger or smaller overshoot %? Answer: smaller (larger travel denominator). Reinforces that a metric is a definition, not a vibe.

06Mastery & project

To unlock 5.2, demonstrate IN SIM: (1) bring latch-arm-v1 from OUT OF SPEC to all five checks PASS at seed 0xD2C1; (2) pass Gate G, where the change-log shows the decisive edit was on a telemetry-implicated parameter in the implicated direction (evidence-driven, not brute-forced); and (3) pass a transfer probe, a second, unseen failing instance (seed 0xD2C1 with spring_k perturbed so the device now under-shoots and lands with steady_error ≈ 4.2°). Recognize the symptom changed (steady-state error, not overshoot) and pick the now-correct knob (actuator_kp↑ or spring_k↓), proving you're reading data, not pattern-matching last time's answer. Passing all three demonstrates the L2 competency: diagnose from telemetry and correct on evidence.

This lesson IS the engine of the capstone. The diagnose→hypothesize→change-one→re-sim loop you just proved is exactly the optimization phase you run in 5.2, except there, no one hands you the failing instance or the parameter panel: you define the spec, you build the model, and you drive it past target.

GO FURTHER · THE LIVE PLAYGROUND

Iterate a design in Forge ↗ · describe → simulate → tune the loop, end to end.

← Reading the Verdict: Did It Settle?Capstone: Design, Simulate, Validate & Optimize a Device →

PYTHON · NUMPY

The Improvement Loop: Measure → Tune → Re-Sim

latch-arm-v1: a single-DOF revolute hinge driven by a torsion-spring + position actuator, modelled parametrically in numpy (in the full Bench this is CadQuery geometry + MuJoCo-WASM dynamics). Deterministic seed 0xD2C1, 3.0s rollout. Tune ONE knob, actuator_kv (damping), and Re-Sim until all five spec checks PASS. Cranking actuator_kp makes overshoot worse; the data points at kv.

You read

the arrays and values already in scope

You change

the code you write in each cell

Fixed

the dataset and the checks that grade you