Figure 1.
The transfer function block diagram of PMSM sensorless system.
Figure 1.
The transfer function block diagram of PMSM sensorless system.
Figure 2.
The equivalent control circuit.
Figure 2.
The equivalent control circuit.
Figure 3.
The output and input data of the system to be identified.
Figure 3.
The output and input data of the system to be identified.
Figure 4.
Identification result response curve.
Figure 4.
Identification result response curve.
Figure 5.
The structural diagram of SMO-PLL technology.
Figure 5.
The structural diagram of SMO-PLL technology.
Figure 6.
The curve of the ideal response.
Figure 6.
The curve of the ideal response.
Figure 7.
The structure diagram of VPDPI regulator control algorithm.
Figure 7.
The structure diagram of VPDPI regulator control algorithm.
Figure 8.
(a) The overall trend of the root locus. (b,c) show enlarged images of different proportions of poles, respectively.
Figure 8.
(a) The overall trend of the root locus. (b,c) show enlarged images of different proportions of poles, respectively.
Figure 9.
The bode diagram under the different .
Figure 9.
The bode diagram under the different .
Figure 10.
The bode diagram under the different .
Figure 10.
The bode diagram under the different .
Figure 11.
The structure diagram of sensorless PMSM drive system.
Figure 11.
The structure diagram of sensorless PMSM drive system.
Figure 12.
The speed response of VPDPI regulator under 1000 r/min. (a) Observed speed and actual speed. (b) Estimation error curve.
Figure 12.
The speed response of VPDPI regulator under 1000 r/min. (a) Observed speed and actual speed. (b) Estimation error curve.
Figure 13.
The speed response of PI regulator under 1000 r/min. (a) Observed speed and actual speed. (b) Estimation error curve.
Figure 13.
The speed response of PI regulator under 1000 r/min. (a) Observed speed and actual speed. (b) Estimation error curve.
Figure 14.
The estimation of rotor position Angle using VPDPI. (a) Observed and actual rotor position Angle. (b) Rotor position Angle observation error.
Figure 14.
The estimation of rotor position Angle using VPDPI. (a) Observed and actual rotor position Angle. (b) Rotor position Angle observation error.
Figure 15.
The estimation of rotor position Angle using PI. (a) Observed and actual rotor position Angle. (b) Rotor position Angle observation error.
Figure 15.
The estimation of rotor position Angle using PI. (a) Observed and actual rotor position Angle. (b) Rotor position Angle observation error.
Figure 16.
Three phase current response process under two control methods. (a) Current response under the proposed VPDPI control. (b) Current response under the PI control method.
Figure 16.
Three phase current response process under two control methods. (a) Current response under the proposed VPDPI control. (b) Current response under the PI control method.
Figure 17.
Torque response process under two control methods. (a) Torque response under the proposed VPDPI control. (b) Torque response under the PI control method.
Figure 17.
Torque response process under two control methods. (a) Torque response under the proposed VPDPI control. (b) Torque response under the PI control method.
Figure 18.
The speed response of VPDPI regulator under 800 r/min. (a) Observed speed and actual speed. (b) Estimation error curve.
Figure 18.
The speed response of VPDPI regulator under 800 r/min. (a) Observed speed and actual speed. (b) Estimation error curve.
Figure 19.
The speed response of PI regulator under 800 r/min. (a) Observed speed and actual speed. (b) Estimation error curve.
Figure 19.
The speed response of PI regulator under 800 r/min. (a) Observed speed and actual speed. (b) Estimation error curve.
Figure 20.
The estimation of rotor position Angle using VPDPI. (a) Observed and actual rotor position Angle. (b) Rotor position Angle observation error.
Figure 20.
The estimation of rotor position Angle using VPDPI. (a) Observed and actual rotor position Angle. (b) Rotor position Angle observation error.
Figure 21.
The estimation of rotor position Angle using PI. (a) Observed and actual rotor position Angle. (b) Rotor position Angle observation error.
Figure 21.
The estimation of rotor position Angle using PI. (a) Observed and actual rotor position Angle. (b) Rotor position Angle observation error.
Figure 22.
Phase current response process under two control methods. (a) Current response under the proposed VPDPI control. (b) Current response under the PI control method.
Figure 22.
Phase current response process under two control methods. (a) Current response under the proposed VPDPI control. (b) Current response under the PI control method.
Figure 23.
Torque response process under two control methods. (a) Torque response under the proposed VPDPI control. (b) Torque response under the PI control method.
Figure 23.
Torque response process under two control methods. (a) Torque response under the proposed VPDPI control. (b) Torque response under the PI control method.
Figure 24.
The speed response of VPDPI regulator under 1200 r/min. (a) Observed speed and actual speed. (b) Estimation error curve.
Figure 24.
The speed response of VPDPI regulator under 1200 r/min. (a) Observed speed and actual speed. (b) Estimation error curve.
Figure 25.
The speed response of PI regulator under 1200 r/min. (a) Observed speed and actual speed. (b) Estimation error curve.
Figure 25.
The speed response of PI regulator under 1200 r/min. (a) Observed speed and actual speed. (b) Estimation error curve.
Figure 26.
The estimation of rotor position Angle using VPDPI. (a) Observed and actual rotor position Angle. (b) Rotor position Angle observation error.
Figure 26.
The estimation of rotor position Angle using VPDPI. (a) Observed and actual rotor position Angle. (b) Rotor position Angle observation error.
Figure 27.
The estimation of rotor position Angle using PI. (a) Observed and actual rotor position Angle. (b) Rotor position Angle observation error.
Figure 27.
The estimation of rotor position Angle using PI. (a) Observed and actual rotor position Angle. (b) Rotor position Angle observation error.
Figure 28.
Three phase current response process under two control methods. (a) Current response under the proposed VPDPI control. (b) Current response under the PI control.
Figure 28.
Three phase current response process under two control methods. (a) Current response under the proposed VPDPI control. (b) Current response under the PI control.
Figure 29.
Torque response process under two control methods. (a) Torque response under the proposed VPDPI control. (b) Torque response under the PI control.
Figure 29.
Torque response process under two control methods. (a) Torque response under the proposed VPDPI control. (b) Torque response under the PI control.
Figure 30.
The structure of the experimental platform.
Figure 30.
The structure of the experimental platform.
Figure 31.
Experimental test platform for the proposed algorithm.
Figure 31.
Experimental test platform for the proposed algorithm.
Figure 32.
The observed speed using PI at rated speed. (a) The overall response diagram of observed speed at 1000 r/min. (b) Observed speed under no load. (c) Observed speed under 2 N·m load.
Figure 32.
The observed speed using PI at rated speed. (a) The overall response diagram of observed speed at 1000 r/min. (b) Observed speed under no load. (c) Observed speed under 2 N·m load.
Figure 33.
The observed speed using VPDPI at rated speed. (a) The overall response diagram of observed speed at 1000 r/min. (b) Observed speed under no load. (c) Observed speed under 2 N·m load.
Figure 33.
The observed speed using VPDPI at rated speed. (a) The overall response diagram of observed speed at 1000 r/min. (b) Observed speed under no load. (c) Observed speed under 2 N·m load.
Figure 34.
The observed speed using PI at 800 r/min. (a) The overall response diagram of observed speed at 800 r/min. (b) Observed speed under no load. (c) Observed speed under 2 N·m load.
Figure 34.
The observed speed using PI at 800 r/min. (a) The overall response diagram of observed speed at 800 r/min. (b) Observed speed under no load. (c) Observed speed under 2 N·m load.
Figure 35.
The observed speed using VPDPI at 800 r/min. (a) Observed speed at 800 r/min. (b) Observed speed under no load. (c) Observed speed under 2 N·m load.
Figure 35.
The observed speed using VPDPI at 800 r/min. (a) Observed speed at 800 r/min. (b) Observed speed under no load. (c) Observed speed under 2 N·m load.
Figure 36.
The observed speed using PI at 1200 r/min. (a) The overall response diagram of observed speed at 1200 r/min. (b) Observed speed under no load. (c) Observed speed under 2 N·m load.
Figure 36.
The observed speed using PI at 1200 r/min. (a) The overall response diagram of observed speed at 1200 r/min. (b) Observed speed under no load. (c) Observed speed under 2 N·m load.
Figure 37.
The observed speed using VPDPI at 1200 r/min. (a) The overall response diagram of observed speed at 1200 r/min. (b) Observed speed under no load. (c) Observed speed under 2 N·m load.
Figure 37.
The observed speed using VPDPI at 1200 r/min. (a) The overall response diagram of observed speed at 1200 r/min. (b) Observed speed under no load. (c) Observed speed under 2 N·m load.
Table 1.
The characteristics with different proportionality coefficients.
Table 1.
The characteristics with different proportionality coefficients.
Proportionality Coefficient | Magnitude Margin | Phase Margin | Stability |
---|
| | | (Yes/No) |
---|
0 | 20.3 (at 65.8 rad/s) | 11.1 (at 18.8 rad/s) | Yes |
0.1 | 12.9 (at 377 rad/s) | 81 (at 41.1 rad/s) | Yes |
0.2 | 6.89 (at 378 rad/s) | 83.8 (at 85.5 rad/s) | Yes |
0.3 | 3.39 (at 378 rad/s) | 78.8 (at 140 rad/s) | Yes |
0.4 | 0.897 (at 379 rad/s) | 18.4 (at 349 rad/s) | Yes |
0.5 | −1.04 (at 379 rad/s) | −11.9 (at 398 rad/s) | No |
Table 2.
The characteristics with different integral coefficients.
Table 2.
The characteristics with different integral coefficients.
Proportionality Coefficient | Magnitude Margin | Phase Margin | Stability |
---|
| | | (Yes/No) |
---|
0 | 6.94(at 379 rad/s) | 87.1(at 85.7 rad/s) | No |
0.2 | 6.93(at 379 rad/s) | 86.5(at 85.7 rad/s) | Yes |
0.4 | 6.92(at 379 rad/s) | 85.8(at 85.7 rad/s) | Yes |
0.6 | 6.91(at 378 rad/s) | 85.1(at 85.7 rad/s) | Yes |
0.8 | 6.9(at 378 rad/s) | 84.5(at 85.8 rad/s) | Yes |
1 | 6.89(at 378 rad/s) | 83.8(at 85.5 rad/s) | Yes |
Table 3.
The setting of regulators parameters.
Table 3.
The setting of regulators parameters.
Regulator Type | Parameter | Value |
---|
PI | Proportionality coefficient | 0.2 |
| Integral coefficient | 1 |
VPDPI | Basic proportionality coefficient | 0.2 |
| Changing proportionality coefficient | 0.4 |
| Integral coefficient | 1 |
| Proportional switching threshold c | 50 |
| Compensate switching threshold | 500 |
| Compensation coefficient | −14 |
Table 4.
The setting of PMSM parameters.
Table 4.
The setting of PMSM parameters.
Parameter | Value |
---|
Stator phase resistance | 0.011 |
d-axis and q-axis phase inductances , (mH) | 1.6, 1 |
Moment of inertia J (kg· m) | 0.0008 |
Rotor pole pairs | 3 |
Reference speed (rpm = r/min) | 1000 |
Flux linkage (Wb) | 0.077 |