# Messuring DC-Motor parameters

I have to describe methods how one can determine the parameters of a DC-Motor by meassuring them. In my problem, I have to actually to determine the parameters for two motors, that is why everything is bold (I only need to know the method for one motor). I know that one could try to use parameter identification by comparing simulation data to measurements, but I have to do it experimentally.

The model that I have is the following:

$$\boldsymbol{u}_{\text{a}}=\boldsymbol{R}_{\text{a}}\boldsymbol{i}_{\text{a}}+\boldsymbol{L}_{\text{a}}\dfrac{d \boldsymbol{i}_{\text{a}}}{dt}+\boldsymbol{K}_{\text{e}}\boldsymbol{\omega}$$

$$\boldsymbol{M}_{\text{e}}=\boldsymbol{K}_{\text{m}}\boldsymbol{i}_{\text{a}}=\boldsymbol{J}_{\text{m}}\dot{\boldsymbol{\omega}}+\boldsymbol{i}^{-1}_{\text{G}}\left[\boldsymbol{\tau}_q+\boldsymbol{B}_v\dot{\boldsymbol{\alpha}}+\boldsymbol{B}_c\operatorname{sgn} \dot{\boldsymbol{\alpha}} \right]$$

$$\boldsymbol{\omega}=\boldsymbol{i}_{\text{G}}\dot{\boldsymbol{\alpha}}$$

$\boldsymbol{u}_a$ is the input voltage, $\boldsymbol{i}_{\text{a}}$ is the current of the motor, $\boldsymbol{\omega}$ is the angular velocity of the DC-Motor, $\dot{\boldsymbol{\alpha}}$ is the angular velocity of the transmission output shaft, $\boldsymbol{i}_{\text{G}}$ is the known grear ratio of the DC-Motor, $\boldsymbol{\tau}_{\text{q}}$ is the motor torque, $\boldsymbol{L}_{\text{a}}$ is the inductance, $\boldsymbol{K}_{\text{e}}$ and $\boldsymbol{K}_{\text{m}}$ are modor constants, $\boldsymbol{J}_{\text{m}}$ is the inertia of the motor.

I need to determine the resistance, inductance, the motor constants and the inertia of the motor.

I have almost no practical experience in measuring electrical parameters. So the following ideas are just from a layman's perspective :D. I thought that I could maybe drive the motor with constant current and stop the motor from rotating by holding the output shaft. Then by $u_a/i_a$ I could determine the resistance. Then I would try the same but now with linearly increasing current again holding the output shaft. That would make it possible to determine $L_a$. Then I would again use constant current but now I would let the motor rotate such that I can determine $K_e$ by using the gear ratio and the angular velocity of the output shaft.

In order to determine $K_m$ I would use different currents to obtain multiple equations such that I can determine the unknowns $K_m$, $J$ and $\tau_{\text{q}}$.

Are the methods that I described in any way applicable? What is the easiest way to determine the parameters?

• +1:How do I obtain the Inductance from the phase angle? Could I also use $\text{const.}=u_a=L_a \left.\dfrac{di_a}{dt}\right|_{t=0}$ to determine the Inductance? And why are $K_m$ and $K_e$ the same? – MrYouMath Oct 22 '17 at 14:06