A brushed DC motor converts electrical power into rotational mechanical power by carrying current through an armature that sits in a magnetic field. The useful engineering question is not only “how does it spin?” but “which electrical variables determine its speed and torque, and which of those variables can be manipulated safely?”
Four variables are especially important for speed control: field flux, armature resistance, armature voltage, and armature current. The relationships between them explain the traditional control methods and the modern use of PWM.
Motor construction and commutation
In a conventional brushed DC motor, the stationary magnetic system is the stator and the rotating winding is the armature or rotor. The magnetic field may come from permanent magnets or field windings. Brushes make electrical contact with the rotating commutator, which reverses current in the appropriate armature conductors as the rotor turns.
That switching keeps electromagnetic torque acting in a useful rotational direction. In a very simple one-loop motor, the armature would otherwise rotate toward magnetic alignment and stop. The commutator continuously changes the electrical connection so the torque is renewed each half-turn.
Back EMF, torque, and speed
When the armature rotates through the magnetic field it generates a voltage that opposes the applied supply. This is the motor back electromotive force, or back EMF.
Ea = ke Φ ωHere, Ea is back EMF, Φ is field flux, ω is angular speed, and ke is a motor constant. The armature voltage equation is approximately:
Va = Ea + Ia RaCombining the two gives the familiar speed relationship:
ω ≈ (Va − Ia Ra) / (ke Φ)This equation explains the key speed-control variables. Speed increases when effective armature voltage increases. Increasing armature current under load increases the IaRa voltage drop and therefore tends to reduce speed. Reducing field flux can increase speed, although it also changes torque capability and is not applicable in the same way to every small permanent-magnet motor.
Electromagnetic torque is approximately:
T = kt Φ IaSo armature current is strongly tied to load torque and is primarily a consequence of load rather than the main open-loop speed-control variable.
The three classic speed-control methods
1. Field-flux control
In shunt- or compound-wound motors, the field current can be changed by adjusting resistance or by using an electronic field supply. Reducing field current reduces flux. From the speed relation above, lower flux can raise speed for a given armature voltage.
This method is traditionally associated with operation above base speed, but field weakening reduces available torque per ampere and must respect commutation and mechanical speed limits. It is not the usual approach for the permanent-magnet DC fan used in the aeroponic project because its magnetic field is not controlled by a separate field winding.
2. Armature-resistance control
A variable resistor can be placed in series with the armature. As series resistance increases, more voltage is lost before reaching the motor, so speed falls.
The method is simple but inefficient. The added resistor dissipates power as heat, and speed regulation worsens because the voltage drop depends on load current. It was historically useful for some series-motor applications but is rarely the preferred electronic method for a small modern control system.
3. Armature-voltage control
Changing the voltage applied to the armature changes speed directly while leaving the magnetic field essentially unchanged. Before inexpensive semiconductor power electronics, adjustable DC supplies for larger motors were costly, so systems such as Ward–Leonard motor-generator sets were used. Today, switching converters and transistor drivers make electronic armature-voltage control straightforward.
| Method | Main manipulated quantity | Advantage | Limitation |
|---|---|---|---|
| Field-flux control | Φ | Can extend speed above base speed in wound-field machines | Reduced torque capability; not available on ordinary PM motors |
| Armature resistance | Series R | Simple | Inefficient and load dependent |
| Armature voltage | Va | Efficient and direct with power electronics | Requires a suitable driver and supply |
PWM as practical armature-voltage control
For a small DC motor, the supply is often switched on and off rapidly with a transistor or H-bridge. The ratio of ON time to the total switching period is the PWM duty cycle. The motor winding inductance, electrical time constant, and rotor inertia prevent the mechanical system from following every switching edge.
At a simplified level, a 50% duty cycle from a fixed DC bus produces a lower effective armature voltage than a 90% duty cycle. The motor therefore settles at a lower operating speed for the same load.
However, duty cycle is not the same as speed. A command of 60% does not imply 60% of rated RPM. The final speed depends on supply voltage, motor constants, load torque, driver losses, friction, airflow load for a fan, and the minimum duty cycle required to overcome static friction.
A microcontroller output pin should provide the control signal, not the motor power. The driver must carry motor current, handle switching losses, and protect the controller from inductive voltage transients. A freewheel path is essential when switching an inductive load.
Connecting motor control to the aeroponic fan
In the humidity-control project, the DC motor was part of a fan. The plant being controlled was therefore not “motor speed” alone. PWM changed motor voltage, motor speed changed fan airflow, airflow changed the transport rate of humid mist, and the chamber humidity responded after transport and mixing delay.
This chain means a humidity controller can experience nonlinearity even if the motor itself is predictable. Fan airflow often scales approximately with rotational speed, while fan pressure and power follow different relationships. Chamber restriction, mist loading, and changing root geometry can alter the operating point.
Open-loop duty cycle versus closed-loop speed
If accurate motor speed is required, the system needs speed feedback from an encoder, Hall sensor, tachometer, or another measurement. The controller then adjusts duty cycle to correct for changing load.
The aeroponic project did not need fan RPM as its controlled variable. Humidity was the feedback variable, so the fan could be treated as an actuator inside the larger environmental loop. That is an important system-design distinction: the most useful feedback variable is the one tied to the actual process objective.