Sensorless Estimation with the Coordinate SMO

The SMO estimation precision and dynamics have the highest impact on the sensorless vector control application’s overall performance. This section describes the measurements and the measurement results of the system’s static and dynamic responses. Each measurement includes some graphs with concentration on the estimation angle and estimation speed error. The measurements were provided using the default SW parameter settings.

NOTE

The default SW parameters settings are a trade-off between constant speed and dynamic performance. The SMO feedback, regulators, and speed ramps can be set for lower errors at constant speed/torque or at dynamic transients.

7.3.1 Required Speed Step Transient – Coordinate SMO

This section presents measurements with a required speed step transient. The speed step is defined in the required speed column of Table 7-5.

The recorder pictures are sensed using the FreeMASTER project

PMSM_Sinusodial_Sensorless_Tuning.pmp with its recorder observer error tuning/performance measurement/speed error curr beta cosine-angle error recorder. The variable transients are displayed in Figure 7-9 and Figure 7-10. The results are displayed in Table 7-5. The variables are described after Figure 7-10.

Table 7-5. Required Speed Transient

Required Speed Load Torque Sampling Period

Figure

Position Error Speed Error

rpm Nm ms Degree rpm

500 to 3000 0 2.625 Figure 7-9 4.0 to 1.0 ±45

500 to 3000 0.4 2.625 — 4.0 to 1.0 ±45

3000 to 500 0 2.625 — 3.0 to 3.0 ±45

3000 to 500 0.4 2.625 Figure 7-10 3.0 to 3.0 ±50

Figure 7-9. Acceleration Measurement, Speed 500 to 3000 rpm, Load 0 Nm

Figure 7-10. Deceleration Measurement, Speed 3000 to 500 rpm, Load 0.4 Nm

The figures display the following variables:

speedMotorSens rotor speed sensed by the encoder

speedMotorEstim rotor speed estimated by the SMO

speedMotorErr difference between estimated and measured rotor speed speedMotorEstim – speedMotorSens

smoBemfStruct.curr.beta.F16.H estimated current – beta component

sinCosEst.cos estimated rotor position cosine

sinCosSens.cos sensed rotor position cosine

sinCosElScalarErr rotor electrical angle estimation error according to equation Equation 7-5

7.3.2 Load Torque Step Transient – Coordinate SMO

This section presents measurements with a constant required speed and load torque step transient at a defined speed range. The load torque step is defined in the table column load torque.

The recorder pictures are sensed using the FreeMASTER project

PMSM_Sinusodial_Sensorless_Tuning.pmp with its recorder observer error tuning/performance measurement/speed error curr beta cosine-angle error recorder. The variable transients are displayed in Figure 7-11 and Figure 7-12. The results are displayed in Table 7-6. The variables are described in Section 7.3.1, “Required Speed Step Transient – a,b Coordinate SMO”.

Table 7-6. Load Torque Transient

Required

Speed Load Torque

Recorder Name

Sampling Period

Figure

Position Error Speed Error

rpm Nm ms Degree rpm

3000 0 to 0.4 — 2.625 — 0.5 to 2.5 ±50

3000 0.4 to 0 — 2.625 Figure 7-11 1 to 3.5 ±40

1000 0 to 0.4 — 2.625 Figure 7-12 0.5 to 1.5 ±50

Figure 7-11. Load Transient Measurement, Speed 3000 rpm, Load 0.4 to 0 Nm

Figure 7-12. Load Transient Measurement, Speed 1000 rpm, Load 0 to 0.4 Nm

7.3.3 Constant Speed Measurements – Coordinate SMO

This section presents measurements with a constant required speed and a constant load torque at a defined speed range. The recordings in Table 7-7 are obtained using the FreeMASTER project

PMSM_Sinusodial_Sensorless_Tuning.pmp with its recorder observer error tuning/start-up tuning/speed angle sine curr error recorder.

The recorder pictures are sensed using the FreeMASTER project

PMSM_Sinusodial_Sensorless_Tuning.pmp with its recorder observer error tuning/performance measurement/speed error curr beta cosine-angle error recorder. The variable transients are displayed in Figure 7-13 and Figure 7-14. The results are displayed in Table 7-7. The variables are described in Section 7.3.1, “Required Speed Step Transient – a,b Coordinate SMO”.

Table 7-7. Constant Speed Measurements

Required Speed Load Torque Sampling Period

Figure

Position Error Speed Error

rpm Nm s Degree rpm

400 0 875 — 2.0 to 2.0 ±25

1000 0 875 — 1.0 to 1.5 ±25

2000 0 875 — 0.0 to 2.0 ±30

3000 0 875 Figure 7-13 0 to 2.5 ±30

400 0.4 875 Figure 7-14 2.5 to 2.0 ±30

1000 0.4 875 — 1.0 to 1.5 ±30

2000 0.4 875 — 0 to 2.5 ±30

3000 0.4 875 — 0 to 2.5 ±30

.

Figure 7-13. Constant Speed Measurement, Speed 3000 rpm, Load 0 Nm

Figure 7-14. Constant Speed Measurement, Speed 400 rpm, Load 0.4 Nm

7.3.4 Start-up – coordinate SMO

The start-up measurement discusses the motor operations starting from 0 speed to a defined required speed. The control SW state machine starts with rotor alignment/stabilization continuing with an open-loop and regular running states.

The recorder pictures are sensed using the FreeMASTER project

PMSM_Sinusodial_Sensorless_Tuning.pmp with its recorder observer error tuning/start-up tuning/speed angle sine curr error recorder. The variable transients are displayed in Figure 7-16 and Figure 7-17. The results are displayed in Table 7-15.

Figure 7-16. Start-up Measurement, Speed 0 to 1000 rpm, Load 0 Nm Figure 7-15. Start-up Measurements

Required Speed Load Torque Sampling Period

Figure

rpm Nm ms

0 to 1000 0 5.375 Figure 7-16

0 to 1000 0.4 5.375 Figure 7-17

Figure 7-17. Start-up Measurement, Speed 0 to 1000 rpm, Load 0.4 Nm

7.4 Conclusion

The measurement results show that both SMOs give stable results over the defined speed and load torque range. As mentioned above, one of the most important features of any position and speed observer is the correct functionality over the required speed and load range. Special attention needs to be given to the dynamic response of the estimation.

The application with the d, q coordinates model gives slightly better results than the  model. However, the difference is not that significant because the BLDC motor TGT3-0065-30-320 has constant parameters over the rotor angle. The benefit of the  is a better stability and starting due to the simplified model.

For motors like the TGT3-0065-30-320, it is recommended to use the application with the  model.