DC Motors: Principles and Control
DC motors are the workhorse of robotics, converting electrical energy into rotary mechanical motion via the Lorentz force — the force on a current-carrying conductor in a magnetic field. The motor armature (rotor) carries windings that interact with the stator's permanent magnets or field windings to produce torque.
Brushed DC motors use carbon brushes contacting a commutator to switch current direction as the rotor turns, maintaining continuous torque. They are simple and cheap but the brushes wear, generating electromagnetic noise and limiting maximum speed. Brushless DC (BLDC) motors replace mechanical commutation with electronic commutation via a motor controller that switches three-phase currents based on rotor position feedback (Hall sensors or encoders). BLDC motors achieve higher efficiency, higher speed, longer life, and greater power density at the cost of a more complex controller.
The steady-state electrical equation of a DC motor is:
V = Ke · ω + I · R
where V is terminal voltage, Ke is the back-EMF constant, ω is angular velocity, I is armature current, and R is armature resistance. At stall (ω = 0), all voltage drops across R, giving maximum current and maximum torque. At no-load (I ≈ 0), back-EMF equals supply voltage. PWM (Pulse Width Modulation) varies the effective supply voltage by switching at high frequency (typically 20–100 kHz), allowing smooth speed control without dissipative resistors.
DC Motor Fundamental Equations
Steady-state torque-speed relationship and power for a DC motor
τ = Kt · I V = Ke · ω + I · R (steady state) P_mechanical = τ · ω τ_stall = Kt · V / R ω_no_load = V / Ke
Kt = torque constant (N·m/A), Ke = back-EMF constant (V·rad⁻¹·s), I = armature current (A), R = armature resistance (Ω), ω = angular velocity (rad/s), V = terminal voltage (V)
In SI units Kt = Ke numerically. The torque-speed curve is linear between stall torque (ω = 0) and no-load speed (τ = 0). Peak efficiency occurs near 1/3 of stall torque.
Servo Motors: Closed-Loop Position and Torque Control
A servo motor is not a distinct motor type per se, but rather an electric motor (typically BLDC or AC synchronous) integrated with a position or velocity encoder and operated inside a closed-loop control system — the servo drive. The drive continuously compares the commanded state to the measured state and applies corrective voltages via a PID (Proportional-Integral-Derivative) or cascade control law.
RC servos (hobby servos) integrate a small DC motor, plastic gearbox, potentiometer, and a simple PWM decoder into a compact package. Position is commanded by the duty cycle of a 50 Hz PWM pulse (1 ms = full CCW, 2 ms = full CW). They are low-cost and widely used in legged robots, pan-tilt mechanisms, and educational platforms, but offer limited torque and no current feedback.
Industrial servo systems consist of a high-performance motor (often with rare-earth permanent magnets), a multi-turn absolute encoder (17–23 bit resolution), and a digital servo drive with field-oriented control (FOC). FOC decouples the torque-producing (q-axis) and flux-producing (d-axis) current components, enabling precise torque control at all speeds including zero. Modern industrial servos achieve position repeatability of ±1 arc-second and bandwidth exceeding 1 kHz.
Frameless motor kits (rotor-stator sets without bearings or housing) are increasingly popular for robot joint design: they mount directly around the joint axis, giving compact, hollow-shaft configurations used in collaborative robots and humanoid limbs.
Stepper Motors: Open-Loop Discrete Positioning
Stepper motors move in discrete angular increments (steps) by energising different combinations of stator windings in sequence. A standard 2-phase hybrid stepper has 50 rotor teeth and 2 phases, giving 1.8° per full step (200 steps/revolution). Each step is commanded digitally — no position feedback is required for operation — making stepper drives simple and low-cost.
Microstepping drives interpolate between full steps by simultaneously energising two phases with sinusoidally varying currents, reducing vibration and improving resolution by factors of 8, 16, or 32. However, positional accuracy does not improve proportionally because the motor's magnetic detent forces and load torque cause actual position to deviate from the ideal microstep angle.
Key stepper characteristics include:
- Holding torque — torque developed when phases are energised and shaft is stationary; resists position disturbances
- Pull-out torque — maximum load torque at a given step rate before the motor loses synchronisation (loses steps)
- Resonance — at certain step rates, mechanical resonance degrades torque and causes missed steps; dampening or microstepping mitigates this
- Open-loop operation means lost steps are undetected; encoder feedback is added when reliability is critical (closed-loop stepper or servo mode)
Stepper Motor Step Angle
Full step angle from motor geometry; microstepping divides this further
θ_step = 360° / (N_rotor_teeth × N_phases) θ_microstep = θ_step / M
N_rotor_teeth = number of rotor teeth (typically 50), N_phases = number of electrical phases (typically 2), M = microstepping divisor (e.g. 8, 16, 32)
For a standard 50-tooth, 2-phase hybrid stepper: θ_step = 360° / (50 × 2) = 3.6° per electrical step, but the mechanical step is 1.8° due to bipolar winding configuration.
Electric Motor Technology Comparison
| Type | Control Mode | Position Accuracy | Torque at Low Speed | Typical Application | Driver Complexity |
|---|---|---|---|---|---|
| Brushed DC | Open/closed loop, PWM | Low (needs encoder) | Good (drops with speed) | Toys, low-cost wheels, hobby robots | Low |
| BLDC | Closed loop (FOC) | High (with encoder) | Excellent (full torque at 0 rpm) | Drones, e-bikes, collaborative robots | Medium–High |
| RC Servo | Closed loop (PWM angle) | Medium (potentiometer) | Medium | Hobby robots, pan-tilt heads, education | Very Low |
| Industrial Servo | Cascade PID / FOC | Very high (17–23 bit encoder) | Excellent | CNC machines, robot arms, precision assembly | High |
| Stepper | Open loop (step/dir pulses) | Medium (1.8° per step) | Good at low speed, drops at high speed | 3D printers, CNC routers, camera sliders | Low–Medium |