Extracting the phase resistance from the measured data required only the application of Ohm’s law (\(R = V/I\)) using the steady-state values for voltage and current. For the PMSM we calculated the resistance as 23.26 volts / 2.01 amps = 11.60 ohms. By subtracting 10 ohms (the value of the current limiting resistor), and dividing the result by 2 to account for the two-phase resistances in series, we calculated the motor phase resistance to be 0.8 ohms.

Characterizing the inductance required a more sophisticated approach. At first glance, it looks as if we could have used curve fitting, as we did when characterizing the rotor inertia. However, due to the internal resistance of the DC supply, the measured DC voltage decays from an initial value of 24 volts at the start of the test, when the current into the circuit is 0, to a steady-state value of 23.26 volts after the current is flowing in the circuit. Because the input voltage is not a pure step signal, the results from curve fitting the solution to the series RL circuit equation would not be accurate.

To overcome this difficulty we opted for a more robust approach using parameter estimation and Simulink Design Optimization™. The advantage of this approach is that it requires neither a pure step input nor curve fitting.

We modeled the motor’s equivalent series RL circuit with Simulink and Simscape™ (Figure 7). Simulink Design Optimization applied the measured voltage as an input to the model, and with the value of the limiting resistor (R_limit) and the motor phase resistance (R_hat) already known, estimated the value of the inductance (L_hat) to make the current predicted by the model match the measured current data as closely as possible.