Equation of PMDC

Electrical Part

The voltage equations of PMDC are as follows.  

where,  is the input armature voltage,  is the armature resistance,  is the armature inductance,  is the armature current, and  is the back electromotive force.

The armature winding is connected to the outside terminal. This block is very similar to a shunt connected DC motor. A back electromotive force (BEMF) by magnet, which is generated between the armature terminals, is proportional to the machine speed. 

where,  is the voltage (BEMF) constant,  is the mechanical angular speed.

The electrical torque, which is developed by PMDC motor, is proportional to the armature current .

The torque constant  is equal to the voltage (BEMF) constant .

When the machine is in generator mode, the sign of torque is positive. In motor mode, the sign of torque is negative.

Mechanical Part

•     Exclude Rotor

The driving torque  subtracts the viscous friction of rotor from the electrical torque .

where,  is the viscous friction gain and is the viscous friction offset.  

•     Include Rotor

The mechanical dynamics of the rotor is governed by the equation 

where,  is the inertia of rotor,  is the viscous friction gain,  is the viscous friction offset, and  is the load torque.