Back emf is directly proportional to rotational speed of shaft:

Where:

e = back emf

= rotational speed of stator

= constant

From Kirchhoff’s voltage law:

The directed sum of the potential differences (voltages) around any closed loopis zero.

Therefore:

3.2 Mechanical

Torque is directly proportional to current and electric field strength:

Assuming armature controlled motor therefore electric field strength is constant

Where:

T = torque

i = current

= constant

From Newton’s Second Law for Rotation:

If more than one torque acts on a rigid body about a fixed axis, then the sum of the torques equals the moment of inertia times the angular acceleration

Therefore:

4 Transfer function

In SI units, the motor torque and back emf constants are equal

Laplace transform equation:

General Laplace transforms:

4.1 Electrical

Assuming i(0) = 0

4.2 Mechanical

Assuming

Open loop transfer function given input is voltage and output is rotational speed: