Servo Motors and Linear Induction Motors

A servo motor is the actuator in a closed-loop position or speed control system. It is judged not by its efficiency at one operating point but by how quickly and accurately it follows a command.

• Low inertia — long, slender rotor (or ironless/disc armature) for high acceleration \(T/J\).

• Linear torque–speed and torque–voltage characteristics over the whole range, including reversal.

• High torque at zero and low speed, with no tendency to run on (single-phasing) when the control signal is removed.

• Smooth torque, fast electrical time constant, and a built-in feedback device (encoder, resolver or tachogenerator).

A DC servo is a separately excited or PM DC motor with low armature inertia. In armature control (the usual method) the field is constant and the armature voltage is the control input:

The torque–speed curves are parallel straight lines, one for each control voltage — ideal for linear control design. Field control is possible but slower, because the field time constant is large.

The classic AC servo is a two-phase induction motor. The reference (main) winding is fed with a fixed voltage; the control winding, in space quadrature, receives a variable voltage 90° phase-shifted from it. The magnitude of the control voltage sets the torque, and its phase (leading or lagging) sets the direction.

Thin drag-cup (non-magnetic aluminium cup) rotors give very low inertia for small instrument servos. Modern industrial "AC servos", however, are almost always PMSMs (Chapter 90) under field-oriented control with high-resolution encoders.

Imagine cutting a cage induction motor along a radius and unrolling it flat. The stator becomes the primary — a flat three-phase winding producing a travelling field instead of a rotating one. The rotor becomes the secondary — usually an aluminium or copper sheet, often backed by steel. The force produced is linear thrust.

\(\tau\) is the pole pitch in metres. Note that \(v_s\) does not depend on the number of poles — only on the pole pitch and frequency. As in the rotary motor, \(P_\text{mech} = (1 - s)P_\text{ag}\) and secondary copper loss \(= sP_\text{ag}\).

• Single-sided LIMs have one primary and a steel-backed secondary; double-sided LIMs have primaries on both sides of a thin conducting plate.

• Either the primary or the secondary can be the moving member (short-primary or short-secondary designs).

• End effects: the primary has a beginning and an end. Secondary material entering the field resists the build-up of flux; material leaving it carries trailing currents. Both reduce thrust and efficiency, especially at high speed.

• Large air gap: mechanical clearance plus the non-magnetic secondary sheet gives high magnetising current and low power factor.

• Normal force: single-sided LIMs produce a large attractive force between primary and steel-backed secondary, which the structure must resist (or exploit for levitation).

• Servo motors need low inertia, linear characteristics and stability over the whole speed range.

• Two-phase AC servo: control voltage in quadrature; high \(R_2/X_2\) gives a negative-slope characteristic.

• LIM: \(v_s = 2\tau f\); thrust \(= P_\text{ag}/v_s\); end effects and large gap reduce performance.

1. P92.1 A LIM with a pole pitch of 0.3 m is supplied at 40 Hz and runs at 20 m/s. Find \(v_s\) and the slip.

   Show answer

   \(v_s = 2(0.3)(40) = 24\) m/s; \(s = 4/24 = 0.167\).

2. P92.2 The LIM of P92.1 develops 1.5 kN of thrust. Find the air-gap power, mechanical power and secondary loss.

   Show answer

   \(P_\text{ag} = 1500 \times 24 = 36\) kW; \(P_\text{mech} = 1500 \times 20 = 30\) kW; loss \(= 6\) kW.