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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?

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  1. Use ohmmeter to determine the resistance. Or lock the rotor, apply certain voltage level and measure the current.
  2. With AC voltage you can measure phase angle between current and voltage, thus determine the inductance.
  3. Spin the motor with some auxiliary motor coupled to a shaft, measure the speed and the induced voltage. Determine Ke.
  4. Derive the Km from Ke. If they are in SI units [Vs/rad],[Nm/A], then they are the same value.
  5. You'd need to know the torque and acceleration to derive the moment of inertia. Or you can wind a tiny rope on the shaft and apply a mass, then measure the time and speed to determine the acceleration - the torque is T=mgR .
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  • \$\begingroup\$ +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? \$\endgroup\$ – MrYouMath Oct 22 '17 at 14:06
  • \$\begingroup\$ They are the same value because Power = I*V = torque * speed so they are two ways of saying the same thing. \$\endgroup\$ – user_1818839 Oct 22 '17 at 15:57

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