Motor Control

Loss flow — Electrical input splits into mechanical output plus copper and iron losses. The copper share grows with current, so peak efficiency sits at a load where fixed losses and I²R balance.

T–ω line — The motor drops from no-load speed rpm0 at zero torque to stall at Ts. With a constant load torque the steady speed is where the two lines cross — higher load, lower speed.

Trapezoidal ramp — A point-to-point move accelerates at a set rate α = Δω/Δt to cruise speed, holds it, then decelerates to a stop. While accelerating, the drive must add torque enough to overcome inertia J·α on top of the load; set α too high and the motor stalls or the driver trips.

Three-phase inverter — Six switches in three half-bridge legs drive the three phase coils of a BLDC or PMSM; one PWM per leg synthesizes the rotating field from the DC bus. Never turn on both switches of a leg at once — add dead time between commutations, and never let the inductive phase currents open-switch without a freewheel path.

Low-side switch — A single N-FET switches the motor to GND. When it turns off, the motor's inductive energy would spike the drain — the flyback diode clamps it back to the rail.

H-bridge — Four switches let you drive the motor in both directions. Turning on Q1+Q4 runs it forward, Q2+Q3 reverses. Never turn on both sides of a leg (shoot-through) — add dead time.

Inductive clamp — The diode across the coil provides a freewheel path when the switch opens, so the flyback current decays instead of forcing a high spike. Pick a diode fast enough for the switching frequency.

Stepper drive — Each coil is driven by its own H-bridge; a sense resistor feeds current back so the driver chops the PWM to hold the target microstep current. This prevents over-heating at low speed.

DC motor equivalent circuit — The armature is a winding resistance, a series inductance and a back-EMF source proportional to speed. At steady state, applied voltage splits between the I·R drop and the back-EMF, linking voltage, speed, current and torque together.

Torque–speed & acceleration — A permanent-magnet DC motor delivers maximum torque at stall and drops to zero at no-load speed. The operating point sits where the motor line meets the load; the excess torque above the load drives acceleration.

Gear reduction — Meshing a small gear on the motor into a larger one slows the shaft but multiplies torque by the ratio (times the gearbox efficiency). A high ratio slashes the load inertia seen by the motor by the square of the ratio.

4-quadrant operation — The torque–speed plane splits into four operating regions. Forward motoring is +τ,+ω; reverse motoring −τ,−ω. The other two are braking: with the load back-driving the shaft, torque opposes speed (regenerative), returning energy to the bus for a four-quadrant drive that must sink current when decelerating.

Hobby servo PWM — A hobby servo is commanded by a pulse repeated every ~ 20 ms (50 Hz). A 1 ms pulse holds one end stop, 1.5 ms centers on 90°, and 2 ms reaches the other stop — the width sets the target angle, roughly 1 ms per 180°. Keep the frame period fixed; only the on-time moves the arm.