Stepper motors and servo motors

VR, PM and hybrid steppers, step angle, pulse-rate speed and drive modes, and DC and AC servo motors with the armature-controlled DC servo transfer function.

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Why it matters

Stepper and servo motors are the actuators of instrumentation and automation: chart recorders, valve positioners, dosing pumps, 3D printers, CNC axes, robot joints, camera gimbals and antenna drives. An instrumentation engineer must be able to pick between open-loop stepping and closed-loop servo control, compute resolution and speed from pulse rates, and write the transfer function of a servo motor for a control loop.

Key ideas

Stepper motors convert each input pulse into a fixed angular step, so position = number of pulses × step angle and speed = pulse rate × step angle. No feedback is needed as long as the motor does not lose steps (open-loop control).

  • Variable-reluctance (VR): soft-iron toothed rotor, no magnet. The rotor moves to the position of minimum reluctance for the energised phase. Step angle depends on the difference between stator and rotor tooth numbers. Small steps, low torque, no detent torque.
  • Permanent-magnet (PM): magnetised rotor; larger step angles (7.5°–90°); has detent torque (holds position with no current).
  • Hybrid: a magnetised, toothed rotor (two toothed caps with an axial magnet); fine steps (typically 1.8° or 0.9°), highest torque; most common in industry.
  • Drive modes: one-phase-on full stepping; two-phase-on (more torque, same step); half stepping (alternating one and two phases, half the step angle); microstepping (sinusoidally shaped phase currents, many sub-steps, smoother motion, less resonance — but the extra positions are less accurate and torque per microstep is small).
  • Torque terms: holding torque (energised, at rest), detent torque (unenergised, PM/hybrid only), pull-in torque/rate (can start and stop without losing steps) and pull-out torque/rate (can run once accelerated). Torque falls as stepping rate rises because winding inductance limits current build-up; chopper (constant-current) drives with higher supply voltage extend the speed range.
  • Problems: missed steps under overload or too-fast acceleration (position error goes undetected in open loop), mid-range resonance, and current drawn even at standstill.

Servo motors are motors designed for closed-loop position or speed control: low inertia, linear torque–speed characteristics, fast response, with a feedback sensor (encoder, resolver, tachogenerator or potentiometer) and a servo drive.

  • DC servo motor (armature-controlled): separately excited or PM field, so flux is constant. Torque T = Kt·Ia and back EMF Eb = Kb·ω, with Kt = Kb numerically in SI units. With armature inductance neglected and viscous friction B, the speed transfer function is first order: ω(s)/Va(s) = K/(1 + τm·s), with K = Kt/(Ra·B + Kt·Kb) and τm = Ra·J/(Ra·B + Kt·Kb). Integrating gives the familiar type-1 position transfer function θ(s)/Va(s) = K/[s·(1 + τm·s)].
  • Field-controlled DC servo: constant armature current, field voltage varied; slower (field time constant), used for small powers.
  • AC servo motor (two-phase induction): a reference winding on fixed voltage and a control winding fed 90° shifted, of variable amplitude. The rotor has a high R/X ratio so that the torque–speed curve is nearly linear with a negative slope over the whole speed range — giving stable, damped behaviour and no single-phasing run-on when the control voltage is removed. Used in low-power instrument servos.
  • Brushless (PMSM/BLDC) servos with encoder feedback are the modern industrial standard.

Stepper versus servo. Steppers: cheap, simple, open loop, high holding torque at low speed, but lose steps under overload and lose torque at high speed. Servos: need feedback and tuning, but give high speed, high peak torque, and correct for disturbances.

Formulas

  • θs = 360° / (m·Nr) — VR motor full-step angle (degrees) for m phases and Nr rotor teeth.
  • θs = 360° / (2·m·Nr) — hybrid motor full-step angle (each phase is driven with both polarities, giving 2m steps per tooth pitch); e.g. 2 phases, 50 teeth → 1.8°.
  • θs = 360°·(Ns − Nr) / (Ns·Nr) — VR motor step angle from stator teeth Ns and rotor teeth Nr.
  • Steps per revolution = 360° / θs ; resolution = θs.
  • n = f·θs / 360° (rev/s) ; N = 60·f·θs / 360° (rpm) — speed for pulse rate f (pulses/s).
  • T = Kt·Ia ; Eb = Kb·ω — DC servo torque (N·m) and back EMF (V); Kt in N·m/A, Kb in V·s/rad.
  • ω(s)/Va(s) = K / (1 + τm·s) ; K = Kt/(Ra·B + Kt·Kb) ; τm = Ra·J/(Ra·B + Kt·Kb) — armature-controlled DC servo, La neglected; J in kg·m², B in N·m·s/rad.
  • T_stall = Kt·Va / Ra — stall torque (N·m); ω_no-load = Va / Kb (B = 0).

Worked examples

Example 1 (standard): VR stepper. Given: 3-phase VR stepper, 12 stator teeth, 8 rotor teeth, driven at 400 pulses/s in full-step mode.

  1. θs = 360°·(Ns − Nr)/(Ns·Nr) = 360 × 4/96 = 15° (check: 360/(m·Nr) = 360/(3 × 8) = 15°).
  2. Steps per revolution = 360/15 = 24.
  3. Speed = 400 × 15/360 = 16.67 rev/s = 1000 rpm.
  4. To move 135°, the controller sends 135/15 = 9 pulses.

Example 2 (GATE level): DC servo transfer function. Given: armature-controlled PM DC servo, Kt = 0.05 N·m/A, Kb = 0.05 V·s/rad, Ra = 2 Ω, rotor + load inertia J = 1 × 10⁻⁴ kg·m², friction and La negligible. Supply 12 V.

  1. Gain: K = Kt/(Ra·B + Kt·Kb) = 0.05/(0 + 0.0025) = 20 rad/s per volt (= 1/Kb when B = 0).
  2. Mechanical time constant: τm = Ra·J/(Kt·Kb) = 2 × 10⁻⁴/0.0025 = 0.08 s.
  3. Transfer function: ω(s)/Va(s) = 20/(1 + 0.08·s).
  4. No-load speed at 12 V: ω = 12/0.05 = 240 rad/s = 2292 rpm, reached to 98 % in about 4τm = 0.32 s.
  5. Stall torque: T_stall = Kt·Va/Ra = 0.05 × 12/2 = 0.30 N·m.

Common mistakes

  • Using stator pole count instead of rotor teeth in θs = 360°/(m·Nr), or forgetting the extra factor 2 for a hybrid motor.
  • Forgetting the factor 60 when converting rev/s to rpm.
  • Assuming a stepper "knows" its position after an overload — it does not, unless an encoder is added.
  • Treating microstepping as adding true accuracy; it adds resolution and smoothness, not stiffness or accuracy.
  • Mixing Kt (N·m/A) and Kb (V·s/rad) units or using Kb in V/rpm without conversion.
  • Designing an AC servo rotor with low resistance like a normal induction motor — it needs high R/X for a linear, negative-slope characteristic.

For GATE IN

Typical questions: step angle and steps per revolution for VR and hybrid motors, speed from pulse rate, the number of pulses to move a given angle, the effect of half stepping, and the transfer function, gain and time constant of an armature-controlled DC servo used inside a position-control loop. Conceptual MCQs ask why an AC servo rotor has high resistance and what detent torque is.

Quick check

  1. A 2-phase hybrid stepper has 50 rotor teeth. What is the full-step angle?
  2. A 1.8° stepper receives 1000 pulses/s. What is its speed in rpm?
  3. What does half stepping do to the step angle?
  4. Why does an AC servo motor have a high-resistance rotor?

Answers: 1. 360/(2 × 2 × 50) = 1.8° (200 steps per revolution). 2. 300 rpm. 3. Halves it. 4. To make the torque–speed curve linear with a negative slope (stable, damped) and to stop the motor when the control voltage is removed.

Interview questions

All Electrical Machines interview questions

Try answering each one aloud before you open it.

  1. 1.What is a stepper motor and how does it work?Concept

    A stepper motor is an electromechanical device that converts electrical pulses into discrete mechanical movements. The motor's rotation is divided into a number of steps, allowing precise control of angular position. It works by energizing coils in a sequence, creating a magnetic field that interacts with the rotor's permanent magnets or soft iron core, causing it to move in steps.

  2. 2.Explain the working principle of a servo motor.Concept

    A servo motor is a rotary actuator that allows for precise control of angular position, velocity, and acceleration. It consists of a motor coupled to a sensor for position feedback. A control circuit uses this feedback to adjust the motor's position by comparing the desired position with the actual position and minimizing the error through a control loop, often a PID controller.

  3. 3.What are the main differences between stepper motors and servo motors?Concept

    A stepper moves a fixed angle per input pulse, so it is positioned open loop by counting pulses; it is cheap, has high holding torque at low speed, but loses torque at high speed and can miss steps under overload without anyone knowing. A servo motor runs in a closed loop with an encoder, resolver or tachogenerator, so the drive corrects any error; it gives higher speed, higher peak torque and good dynamic response, at the cost of feedback hardware and loop tuning.

  4. 4.Why are stepper motors commonly used in 3D printers?Application

    Stepper motors are used in 3D printers because they provide precise control over position and speed, which is essential for accurate layer deposition. Their ability to move in discrete steps allows for fine control over the print head's movement, ensuring high-quality prints. Additionally, they are cost-effective and relatively simple to control compared to servo motors.

  5. 5.What happens if a stepper motor is overloaded?Application

    If a stepper motor is overloaded, it may lose steps, meaning it will not reach the intended position. This can lead to inaccuracies in applications requiring precise positioning. Overloading can also cause excessive heat generation, potentially damaging the motor or reducing its lifespan.

  6. 6.In what applications would you prefer a servo motor over a stepper motor?Application

    Servo motors are preferred in applications requiring high speed, high torque, and precise control over position and velocity. Examples include robotics, CNC machinery, and conveyor systems where dynamic response and feedback control are crucial. Their ability to provide continuous rotation and handle varying loads makes them suitable for these applications.

  7. 7.How does the feedback mechanism in a servo motor improve its performance?Concept

    The feedback mechanism in a servo motor continuously monitors the motor's position and compares it with the desired position. This allows the control system to adjust the motor's operation to minimize any error. The feedback loop, often implemented with a PID controller, ensures high precision, stability, and responsiveness, improving the motor's performance in dynamic applications.

  8. 8.Calculate the step angle of a stepper motor with 200 steps per revolution.Numerical

    The step angle of a stepper motor is calculated by dividing 360 degrees by the number of steps per revolution. For a motor with 200 steps per revolution, the step angle is 360° / 200 = 1.8°.

  9. 9.A servo motor rotates at 3000 RPM. How many degrees does it rotate in one second?Numerical

    To find the degrees rotated in one second, first convert RPM to revolutions per second: 3000 RPM / 60 = 50 revolutions per second. Since one revolution is 360 degrees, the motor rotates 50 * 360 = 18000 degrees in one second.

  10. 10.What are the advantages of using a microstepping driver with a stepper motor?Application

    Microstepping drivers allow stepper motors to move in smaller increments than their natural step angle, providing smoother motion and reducing resonance and vibration. This results in quieter operation and improved precision. Microstepping also helps in achieving finer resolution and better control over the motor's speed and position.

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