DC Motor Model

Motor Slides

Here's a really nice set of slides from Kurt Heinzman that explain all the motor equations, constants and give lots of plots: Intro Motor Slides

Electrical Model

Electrically, a DC motor can be modelled as the RL circuit shown above. The additional element is a depiction of the armature showing torque generation and the back-emf caused by the rotating magnetic field. The electrical dynamics are described by $e_s = \frac{di}{dt}L + iR + \omega k_e$, where $k_e$ is the back-emf constant of the motor. The torque produced by the motor is proportional to current according to $T = i k_t$.

Steady State

The system is in steady state when $\frac{di}{dt} = 0$ and $\frac{d\omega}{dt} = 0$. If a plot of all possible torque vs. rotational velocity points were made for the steady state, they would form a straight line according to the equation $T = \frac{-k_e k_t}{R}\omega + \frac{e_s k_t}{R}$. Attached to this page is a matlab script to generate the torque-speed curves for a motor based on the motor constants, resistance, and a vector of supply voltages.

External Links

• Useful motor primer at MIT