Snapshot of the front panel of the simulator:
DC-motors are used in many servo mechanisms. Compared to other electric motors, DC-motors are easy to model mathematically.
The DC-motor simulated is the Electro-Craft S-19-3AT which is an armature controlled DC-motor. The motor parameters are given on the front panel of the simulator.
In the expressions below the following quantities are used: S is rotational speed. va is armature voltage. ia is armature current. Tf is friction torque. TL is load torque. J is the sum of the intertias of the motor and the load, i.e. J = Jmotor + Jload. B is the sum of the damping coefficients of motor and load. La is the armature inductance. Ra is the armature resistance. Ke is the voltage constant (the so called back-emf constant). KT is the torque constant.
Dynamic model (differential equation)
A mathematical model of the motor can be found from the Kirchhoff's voltage law on the armature circuit and the torque balance of the mechanical rotation:
Kirchhoffs voltage law yields
Torque balance yields
Transfer function model
By taking the Laplace transform of the model above we will find the following transfer function from armature voltage va to speed S:
where the parameters are as follows:
Relative damping factor:
Undamped resonance frequency:
By setting the derivatives in (1) and (2) equal to zero and eliminating ia, we get the following static model (all variables are assumed to have constant values):