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DC motor speed control — the three knobs

V_t below base speed, field weakening above base speed, armature resistance for starting. Modern 4Q drives integrate all three.

Freshman ~8 min

Step 1 — The speed equation: N = (V_t − I_a·R_a) / (K_a·Φ)

Animation speed 0.55×

N — T — P —

Reference notes

Use Next → on the narrator above to step through the three classical knobs for DC motor speed control, and the modern power-electronic implementation that combines them all.

The speed equation — three knobs in one formula

From the equivalent circuit of a DC motor: V_t = E_a + I_a·R_a, and E_a = K_a·Φ·ω. Rearranging gives the central control equation:

N ∝ (V_t − I_a · R_a) / (K_a · Φ)

Three quantities the operator can change at runtime:

V_t — armature terminal voltage (in the numerator).
Φ — main-pole flux, set by the field current (in the denominator).
R_a-effective — by inserting series resistance in the armature circuit (subtracted in the numerator).

1. Armature voltage control — speed BELOW base speed

Reduce V_t below rated → numerator shrinks → N drops proportionally.
Φ stays at rated, so K_a·Φ stays at rated → torque capability T = K_a·Φ·I_a stays at rated.
Constant-torque region: full rated torque available at any speed from 0 to base.
Historical method: Ward-Leonard — a separate DC generator drove the motor with adjustable V_t.
Modern method: a thyristor or IGBT-based 4-quadrant converter directly controls V_t with PWM. Standard for variable-speed DC drives.

2. Field-weakening (flux) control — speed ABOVE base speed

Reduce Φ below rated → denominator shrinks → N rises.
You cannot increase Φ above rated — the iron is already at the saturation knee, so more field current barely adds flux.
At reduced Φ, the torque capability T = K_a·Φ·I_a drops (I_a,rated can't change, Φ has dropped).
Constant-power region: V·I stays at rated, T·ω stays at rated, but T drops as ω rises. This is the field-weakening region above base speed.
Field weakening is bounded — you can typically reach 2–3 × base speed, beyond which mechanical stresses and commutation problems take over.

3. Armature-circuit resistance control — wasteful, mostly historical

Insert external resistance R_ext in series with the armature → numerator term (V_t − I_a·(R_a + R_ext)) shrinks → speed drops.
Inefficient: I_a² · R_ext is dissipated as heat in the external resistor.
Useful for starting (limit inrush current) and for very limited speed adjustment in small drives. Largely obsolete for variable-speed control.

The constant-torque + constant-power picture

Plot torque vs speed for a complete drive. From 0 to base speed (V_t controls speed, Φ at rated): horizontal "constant torque" line at T_rated. Above base speed (Φ weakening, V_t at rated): curve T ∝ 1/N at constant P_rated. This two-region capability map is exactly what motor selection charts show.

Modern implementation

A modern variable-speed DC drive integrates everything: a 4-quadrant power-electronic converter on the armature for V_t control (smooth from 0 to rated), and a smaller converter on the field for Φ control (full at low speed, weakening above base speed). Closed-loop controllers handle armature current limiting (also handles starting), regenerative braking, and torque regulation. The operator just sets a speed setpoint.

Take-away. Three knobs in the speed equation, two operating regions (constant-torque below base, constant-power above), one integrated power-electronic controller. The DC machine's clean linearity is exactly what makes high-performance servo and traction control work.

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