Embedded Motor Control

Characterization for electric motor needs to be done in order to obtain machine parameters, which will be used for:

• Optimize current command for different operation conditions.
• Calculate feedforward term for Current Regulars.

Using synchronous motor as an example, following are the equations for machine modeling:

φ_d and φ_q are the flux on d and q axis. R_s is the stator resistance. Notice that comparing the equations that shown in the FOC Overview, φ_d and φ_q are used instead of L_d, L_q, and φ_pm. This allows us to work on only two parameters, instead of three. All of these parameters can be impacted by temperature. And φ_d and φ_q are also impacted by current on both d and q axis, since they get saturated as current increases. While R_s can be measured simply by using a multimeter, flux values are more difficult to obtain. Following explains one of the possible procedures:

• Spin motor at a median speed while it is high enough, so the voltage drop on the stator resistance is small comparing with the cross coupling term. But it shall also not too high to cause difficulties on current regulation.
• Command different i_d and i_q commands.
• Record u_d and u_q commands when different i_d i_q combinations are achieved.
• Calculate φ_d and φ_q based on voltage equation. Since all data are measured during steady state, di_d/dt and di_q/dt in the voltage equations can be assumed to be 0.

During the measurement, notice that:

• id and iq cannot be measured directly, so it has to either:
  • Measure the 3-phase current, and also the rotor position, then calculate the i_d and i_q offline. This sometimes can be difficult, since rotor position may not be easily recorded using data accusation device. OR
  • Trust the i_d and i_q feedback that is shown by control software. This requires the control software has proper current and position feedback mechanism, which is usually the case, but needs to be carefully verified.
• u_d and u_q commands cannot measured directly either. Similar two current measurements, there are two possibilites:
  • Measure the 3-phase voltage, and also the rotor position, then calculate the u_d and u_q offline. Besides the difficulties of obtaining position signal, phase voltage measurement is also tricky since these are PWM square waveforms. A software or hardware low pass filter needs to be implemented. OR
  • Trust the u_d and u_q commands that is shown by control software. PWM algorithm needs to be tested first to make sure whatever the voltage commanded by the software matches real achieved value.

Future Reference

K.M. Rahman, etc., “Identification of machine parameters of a synchronous motor“, IEEE Transition on Industry Application, vol. 41, pp. 557 – 565, Mar. – Apr. 2005. is a good reference paper with hands-on step by step explanation that how the machine parameters are measured.