Results and Design Guidance

This chapter collects what the models say about the 17HS19-2004S1 on the B-G431B-ESC1 at 24 V, and turns it into guidance for configuring the library and the board. All values come from the tests in the Test Catalogue; the assumptions behind them (datasheet motor parameters, detent and friction values, board passives) are listed in Motor Model and Power Stage Model.

Current loop

Quantity	Value	Test
Bandwidth (design)	1 kHz	—
Step 0 → 2 A: overshoot / rise (90 %) / settling (2 %)	1.12 % / 0.35 ms / 0.40 ms	T04
Same with R ×0.9 … 1.3, L ×0.8 … 1.2	overshoot ≤ 5.2 %, settling ≤ 1.6 ms	T08
Phase lag at 1 rev/s	about 4°	T03, T05
Current ripple at 2 A, locked (20 kHz, 3 mH)	23 mA p-p	T10

The pole-zero cancellation keeps the loop well damped for the whole tolerance range of the datasheet; a hot winding (R +30 %) with a low inductance slows the last 2 % of the step to 1.6 ms but does not destabilise it. Guidance: 1 kHz bandwidth at 20 kHz PWM is a safe default; do not exceed fast_loop_hz / 4 (enforced by sstep_init()).

Voltage limit and speed

Speed	Two H-bridges: current, scale, load angle	Shared leg (ESC1): current, scale, load angle
2 rev/s	2.00 A, 1.00, 6°	2.00 A, 1.00, 6°
4 rev/s	1.97 A, 1.00, 12°	1.97 A, 1.00, 12°
6 rev/s	1.93 A, 1.00, 18°	1.90 A, 0.81, 19–20°
8 rev/s	1.86 A, 0.97, 24°	1.56 A, 0.51, 36–39°
9 rev/s	1.73 A, 0.83, 31°	1.27 A, 0.46, 48–50°
10 rev/s	1.46 A, 0.71, 42°	1.02 A, 0.41, 51–63° (oscillating)
12 rev/s	limit cycle, 16–95°	limit cycle, 3–134°

(Unloaded rotor, 2 A reference, back-EMF feed-forward on; scale is the smallest factor the power stage applied to the requested voltage, 1 = not limited.)

With three legs the largest circular voltage is Vbus/√2: the ESC1 reaches the voltage limit at about 6 rev/s at 24 V, two H-bridges at about 8 rev/s. Beyond the limit the current — and the torque — drops with speed, and the load angle grows even without load.

Guidance: at 24 V on the ESC1 plan for at most 8 rev/s with useful torque reserve; the torque available at speed n is roughly K_t · I(n), minus the angle already used for acceleration. A higher bus voltage moves every speed in the table up proportionally (the ESC1 accepts up to 6S LiPo voltages).

Rotor resonance

Low-speed resonance. The rotor on the current vector is a spring-mass system with f_n = √(p K_t I / J) / 2π = 254 Hz at 2 A (248 Hz with the current loop). Any torque ripple at that frequency excites it. The detent torque has four periods per electrical period, so it excites the rotor at 4 p n = f_n, i.e. about 1.25 rev/s with the rotor alone: with an assumed detent torque of 0.02 N·m the oscillation reaches ±14° there against ±3–5° elsewhere. A load inertia lowers f_n (∝ 1/√J) and with it the resonant speed.

Mid-band instability. As long as the current loop controls the current, it damps the rotor: no oscillation at 5 rev/s. Once the bridge limits the voltage, the drive behaves like a voltage source and the back-EMF coupling undamps the rotor: ±1.3° at 8 rev/s, a limit cycle of ±48° at 11 rev/s on the ESC1 (from about 12 rev/s with two H-bridges).

Guidance:

• Do not run continuously at the low-speed resonance; accelerate through it. Microstepping (M ≥ 16) already removes the full-step excitation; the detent torque remains.
• Keep the operating speed below the voltage limit (previous section) — that is also the region where the rotor is damped.
• Measure f_n on the real motor (a small angle step, as in T11a) and the detent torque; the resonant speed depends on both.
• Active damping in the library (from the back-EMF estimate) is a possible extension.

Robustness

Variation	Effect	Test
R ×0.9 … 1.3, L ×0.8 … 1.2 in the plant, nominal controller	current loop stable, settling ≤ 1.6 ms	T08
5× load inertia	synchronous at 4 rev/s, 50 rev/s², load angle 13°	T08
5× inertia + 0.15 N·m load + R ×1.3, L ×0.8	synchronous, load angle 46°	T08
Load 0.25 N·m at 1 rev/s (below K_t I = 0.417 N·m)	synchronous, load angle 37.2° = asin(T/(K_t I))	T06
Load 0.5 N·m (above K_t I)	loss of synchronism after 152 ms	T06

Guidance: keep the static load below about 60 % of K_t I (0.25 N·m at 2 A) to leave angle for acceleration; the load angle in the SIL diagram shows the reserve directly.

Power stage

Quantity	Value	Consequence
Effective dead time (timer 500 ns)	133 ns	phase voltage error ±0.135 V; distortion near the current zero crossing
Dead time margin	154 ns	do not set the timer dead time below about 350 ns without measuring
Gate bump of the off switch	3.7 V with 10 Ω (assumed)	check the real gate resistors / turn-off diodes
Shunt valid	345 ns after the low-side command	sample centred; leg duty ≤ 0.956
Current peak at 4 rev/s incl. ripple	2.03 A	trip at 3.5 A leaves margin

Open points

Topic	Status	Where
Measure R, L, K_t, detent torque, f_n of the real motor	to do (P3)	Hardware Bring-up
Board passives (Rg, shunt, amplifier gain) from the schematic	to do	Power Stage Model
Dead time compensation in the library	planned; value and error table available	dead_time_ns, leg_error_table
Delay compensation (angle advance)	planned	Control Algorithms
Limit of the leg duty for valid shunt samples	planned	0.956 from SP03
ADC zero auto-calibration at enable	planned	—
Fast loop execution time on the STM32G431	to measure (P3)	—
Scilab run of T08, T10–T12, X04, S01, S04	pending	Test Catalogue