Mathematical Approach
Among many ways of defining the characteristic of a system, obtaining a transfer characteristic is one of the most commonly used methods. Below are the steps to obtain the transfer function, eq 4.
Before going into the equations, first conventions should be set up, which will follow the convention data used. The first subscripts 'g' and 'm' each represents generator and motor. The superscripts 'f', 'r',and 'a', correspond to field, rotor, and armature.
= plant state vector = gain = time constant = polar moment of inertia = angular viscous friction = rotational inductance constant = Laplace operator
eq 1: The generator field equation
eq 2: The equation of electrical equilibrium in the armature circuit
eq 3: Motor torque equation
With total impedance, neglected, the transfer function can be obtained by solving eq 3 .
eq 4: Transfer function
with the constants defined as below:
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