Dynamic equation

In motor technology, the dynamic equation refers to the differential equation that governs the various aspects of motion associated with motor behavior, i.e., start-up, acceleration, slew, deceleration, and also vibrations. The dynamic equation for a DC motor can be obtained by combining the kinetic equation governing mechanical parts and voltage equation governing voltage-current relations as follows. The equation below is the equation of angular speed ω of the motor. The rotor angle θ is computed as the integration of ω.

where _τM is a system parameter known as the mechanical time constant and defined by

while _τE is the electrical time constant given by