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?
