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A PMSM is composed of three phase’s stator windings and permanent magnets mounted on the rotor surface (surface mounted PMSM) or buried inside the rotor (interior PMSM). The symmetrical, three-phase, smooth-air-gap machine with sinusoidal distributed windings is considered. The stator voltage equations in the d-q synchronously rotating rotor flux reference frame can be carried out as in [1-3, 5-6]:

Figure 1 A PMSM is composed of three phase’s stator windings and permanent magnets mounted on the rotor surface (surface mounted PMSM) or buried inside the rotor (interior PMSM). The symmetrical, three-phase, smooth-air-gap machine with sinusoidal distributed windings is considered. The stator voltage equations in the d-q synchronously rotating rotor flux reference frame can be carried out as in [1-3, 5-6]:

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Figure 1. Schematic diagram of a cascaded PI control of PMSM system. Figure 2. Experimental bench. Many applications, such as hybrid electrical vehicles, robotics and factory automation, require precise control of speed and position. Fig. | illustrates a schematic diagram of a basic servo control.
Figure 1. Schematic diagram of a cascaded PI control of PMSM system. Figure 2. Experimental bench. Many applications, such as hybrid electrical vehicles, robotics and factory automation, require precise control of speed and position. Fig. | illustrates a schematic diagram of a basic servo control.
The schematic of the laboratory setup is presented in Fig 2.
The schematic of the laboratory setup is presented in Fig 2.
PMSM SERVOMOTOR-DRIVER DATA B. Simulation Model
PMSM SERVOMOTOR-DRIVER DATA B. Simulation Model
Figure 3. Simulink model of a cascaded PID — field orientation vector control of a PMSM system.
Figure 3. Simulink model of a cascaded PID — field orientation vector control of a PMSM system.
Figure 4. Velocity response to 4.8[Nm] load torque pulse and 0 command. In this case the controller’s position loop is open and the velocity loop is a closed. In this control strategy, the PMSM's reference velocity is kept at 0 revolutions per minute (rpm) and at 0.5 second a step torque load equals to the continuous stall torque (4.8 Nm) is applied then removed after one second [4]. The purpose is to see how well the PMSM maintains its reference velocity.Fig.4 shows the reference and measured velocity responses. The reference velocity is 0 rpm during the test while the measured velocity decreases to about -600 rpm when the load torque is applied. The measured velocity settles again at 0 rpm in about 80 ms. When the load torque is removed the measured speed increases to about 600 rpm and settles again at 0 rpm in about 80 ms. The measured speed deviates from the reference velocity during transient periods but it maintains its reference speed in steady state also during loading.
Figure 4. Velocity response to 4.8[Nm] load torque pulse and 0 command. In this case the controller’s position loop is open and the velocity loop is a closed. In this control strategy, the PMSM's reference velocity is kept at 0 revolutions per minute (rpm) and at 0.5 second a step torque load equals to the continuous stall torque (4.8 Nm) is applied then removed after one second [4]. The purpose is to see how well the PMSM maintains its reference velocity.Fig.4 shows the reference and measured velocity responses. The reference velocity is 0 rpm during the test while the measured velocity decreases to about -600 rpm when the load torque is applied. The measured velocity settles again at 0 rpm in about 80 ms. When the load torque is removed the measured speed increases to about 600 rpm and settles again at 0 rpm in about 80 ms. The measured speed deviates from the reference velocity during transient periods but it maintains its reference speed in steady state also during loading.
Figure 6. Experimental angular velocity response to 0 velocity command. The PMSM's reference velocity is kept at 0 rpm for 4 seconds. Fig.6 shows the reference and the measured velocity. The reference velocity is 0 rpm during the experiment while the measured velocity shows oscillations around the commanded 0 rpm value though the rotor is not physically moving. The measured stator current is presented in Fig. 7. The value of the currents is not equal to zero in this case because the machine has to produce a minimum torque to overcome the viscous friction and the dry friction and also because of the non linearity of the inverter [8]. Other causes could be of small offsets introduced by the current measurement circuits and ADCs. With reference to the velocity’s ripples and according to the servo drive manufacturer [9], the key source of these velocity oscillations could come from errors in the motor feedback device. Resolver-based and low-cost encoders systems are particularly subject to this type of error, especially when the load inertia is very high or when servo gains are high. The position error from a resolver creates velocity error which, in turn, creates current ripple. This current ripple creates torque ripple in the motor which often manifests itself as excessive vibration. There are other sources of vibration, although the vibration amount is usually small.
Figure 6. Experimental angular velocity response to 0 velocity command. The PMSM's reference velocity is kept at 0 rpm for 4 seconds. Fig.6 shows the reference and the measured velocity. The reference velocity is 0 rpm during the experiment while the measured velocity shows oscillations around the commanded 0 rpm value though the rotor is not physically moving. The measured stator current is presented in Fig. 7. The value of the currents is not equal to zero in this case because the machine has to produce a minimum torque to overcome the viscous friction and the dry friction and also because of the non linearity of the inverter [8]. Other causes could be of small offsets introduced by the current measurement circuits and ADCs. With reference to the velocity’s ripples and according to the servo drive manufacturer [9], the key source of these velocity oscillations could come from errors in the motor feedback device. Resolver-based and low-cost encoders systems are particularly subject to this type of error, especially when the load inertia is very high or when servo gains are high. The position error from a resolver creates velocity error which, in turn, creates current ripple. This current ripple creates torque ripple in the motor which often manifests itself as excessive vibration. There are other sources of vibration, although the vibration amount is usually small.
Figure 5. dq-axis currents responses to 4.8[Nm] load torque pulse. The dq-axis currents shown in Fig. 5 look as expected; both currents are 0 Ampere (A) in the case of no load and only the q-axis current increases during loading of the PMSM. The d- axis current is always 0 A as expected; it deviates from 0 A only during transient periods when the load torque is applied or removed. The q-axis current settles at about 4.87 A during loading.
Figure 5. dq-axis currents responses to 4.8[Nm] load torque pulse. The dq-axis currents shown in Fig. 5 look as expected; both currents are 0 Ampere (A) in the case of no load and only the q-axis current increases during loading of the PMSM. The d- axis current is always 0 A as expected; it deviates from 0 A only during transient periods when the load torque is applied or removed. The q-axis current settles at about 4.87 A during loading.
Figure 7. Experimental measured current response to 0 velocity command. As in cases | and 2, the position loop is still open and the velocity loop is closed loop using the fitted resolver velocity feedback with a PI controller tuned using DrvieGUI at 150rpm. In order to assess the effect of the velocity ripples and to test the accuracy of resolver position feedback, a velocity command is changed in a step fashion from 0 to 150 rpm for 1.8375s (from 0.8125s to 2.65s) and then back to 0 rpm. Fig. 8 shows the reference, simulation and experimental measured velocity responses of the motor shaft. It can be observed that the responses are fallowing, with good accuracy, the reference one and because of the velocity ripples it was difficult to calculate the experimental velocity overshoot; however, in zooming on the chart it can be observed that when the velocity command is removed, the system small back overshoots appears to be about 11.2% and the settling time is about 47ms which are acceptable. To study the effect of the velocity ripples on the shaft position, the simulation and experimental position response are illustrated in Fig. 9. We can observe that the position in both experimental and simulation tests followed the same identical ramp fashion with a constant rate of change of 2.5 rev/s (i.e. 150 rpm). It seems that the position feedback signal is not affected by the speed ripples and the resolver is working satisfactorily. However; while the simulation shaft position revolute at 4.59375 revolutions the experimental one revolute at 4.6056 revelations as it can be observed from the zoomed portion of the position response chart. This 0.26% error is due to the fact that the position loop is still open and to the effect of the small offsets introduced by the DACs.
Figure 7. Experimental measured current response to 0 velocity command. As in cases | and 2, the position loop is still open and the velocity loop is closed loop using the fitted resolver velocity feedback with a PI controller tuned using DrvieGUI at 150rpm. In order to assess the effect of the velocity ripples and to test the accuracy of resolver position feedback, a velocity command is changed in a step fashion from 0 to 150 rpm for 1.8375s (from 0.8125s to 2.65s) and then back to 0 rpm. Fig. 8 shows the reference, simulation and experimental measured velocity responses of the motor shaft. It can be observed that the responses are fallowing, with good accuracy, the reference one and because of the velocity ripples it was difficult to calculate the experimental velocity overshoot; however, in zooming on the chart it can be observed that when the velocity command is removed, the system small back overshoots appears to be about 11.2% and the settling time is about 47ms which are acceptable. To study the effect of the velocity ripples on the shaft position, the simulation and experimental position response are illustrated in Fig. 9. We can observe that the position in both experimental and simulation tests followed the same identical ramp fashion with a constant rate of change of 2.5 rev/s (i.e. 150 rpm). It seems that the position feedback signal is not affected by the speed ripples and the resolver is working satisfactorily. However; while the simulation shaft position revolute at 4.59375 revolutions the experimental one revolute at 4.6056 revelations as it can be observed from the zoomed portion of the position response chart. This 0.26% error is due to the fact that the position loop is still open and to the effect of the small offsets introduced by the DACs.
Figure 7 Velocity responses to a 150rpm pulse velocity command.
Figure 7 Velocity responses to a 150rpm pulse velocity command.
Figure 10. Experimental velocity and position response to a 300rpm alternative pulse velocity command. In this case the position loops is still open and the velocity loop is closed. In this experiment we studied the effect of the small offsets introduced by the DACs on the performance of the PMSM. In this study case the velocity reference is changed from 0 to 300rpm (5 rev/s) for 0.5s and then back to 0 for 0.5s then changed to -300rpm for 0.5s then back to 0 for 0.5s. The position response followed a trapezoidal fashion as shown in Fig. 10. However; the shaft didn’t go back to its initial position as expected but exceeded it in the negative direction. This is due to the fact that the position loop is still open and to the effect of the small offsets introduced by the DACs. The digital zero velocity command issued by dSpace 3011 controller card through the DAC is not seen as an exact analog zero by the servo drive.
Figure 10. Experimental velocity and position response to a 300rpm alternative pulse velocity command. In this case the position loops is still open and the velocity loop is closed. In this experiment we studied the effect of the small offsets introduced by the DACs on the performance of the PMSM. In this study case the velocity reference is changed from 0 to 300rpm (5 rev/s) for 0.5s and then back to 0 for 0.5s then changed to -300rpm for 0.5s then back to 0 for 0.5s. The position response followed a trapezoidal fashion as shown in Fig. 10. However; the shaft didn’t go back to its initial position as expected but exceeded it in the negative direction. This is due to the fact that the position loop is still open and to the effect of the small offsets introduced by the DACs. The digital zero velocity command issued by dSpace 3011 controller card through the DAC is not seen as an exact analog zero by the servo drive.
Figure 9. Position responses to a 150rpm pulse velocity command.
Figure 9. Position responses to a 150rpm pulse velocity command.
Figure 11. Velocity responses to different step velocity commands.
Figure 11. Velocity responses to different step velocity commands.
Figure 12. Experimental position responses to different position gains. In this experiment we’ve added the position control loop on top of the speed and the current PI controllers. The measured mechanical position is subtracted from the reference mechanical position and the obtained error is fed into a proportional type controller with again Kp which generates the speed command that is to be fed to the speed control loop. The responses to a 2/2 rad. step position command with different proportional gain (80, 120, and 180) are shown in Fig.12.
Figure 12. Experimental position responses to different position gains. In this experiment we’ve added the position control loop on top of the speed and the current PI controllers. The measured mechanical position is subtracted from the reference mechanical position and the obtained error is fed into a proportional type controller with again Kp which generates the speed command that is to be fed to the speed control loop. The responses to a 2/2 rad. step position command with different proportional gain (80, 120, and 180) are shown in Fig.12.
Figure 13. Simulation results for trapezoidal motion command. Having obtained critically damped and under damped responses (with kp = 80 and kp=180), and in order to study the PMSM position controller performance in trajectory tracking tasks, a position motion profile involving trapezoidal shape is implemented in this case study. Here, a trapezoidal motion position command consisting of 3 segments is adopted as an example from [12]. Initially the motor is to rotate to 27 radians in 1.1 seconds, to keep its angular position the same for 1.95 seconds, and finally, to go down to zero radians in 1.1 seconds. The simulation and experimental responses with Kp = 80 and Kp=180 are shown in Fig. 13 and Fig. 14 respectively.
Figure 13. Simulation results for trapezoidal motion command. Having obtained critically damped and under damped responses (with kp = 80 and kp=180), and in order to study the PMSM position controller performance in trajectory tracking tasks, a position motion profile involving trapezoidal shape is implemented in this case study. Here, a trapezoidal motion position command consisting of 3 segments is adopted as an example from [12]. Initially the motor is to rotate to 27 radians in 1.1 seconds, to keep its angular position the same for 1.95 seconds, and finally, to go down to zero radians in 1.1 seconds. The simulation and experimental responses with Kp = 80 and Kp=180 are shown in Fig. 13 and Fig. 14 respectively.
‘igure 15. Simulation results for the second trapezoidal motion command. To confirm the results obtained in the previous case study, another trapezoidal profile has been applied as a position command and it is involving 7 segments and is performed in 6.8 seconds [12]. The motor is commanded to rotate to 27 radians in 1 second, to keep its position for 1 second, to increase to 4m radians in 0.5 second, to stay at 42 radians for 1.5 second s, later to increase to 62 radians in 0.4 second, to keep the same angular position for 1.6 seconds, and finally to decrease its position to zero radians in 0.8 second with the highest ve ocity of all in reverse direction. The simulation and experimental responses with Kp = 80 and Kp=180 are shown in Fig. 15 and Fig. 16 respectively.
‘igure 15. Simulation results for the second trapezoidal motion command. To confirm the results obtained in the previous case study, another trapezoidal profile has been applied as a position command and it is involving 7 segments and is performed in 6.8 seconds [12]. The motor is commanded to rotate to 27 radians in 1 second, to keep its position for 1 second, to increase to 4m radians in 0.5 second, to stay at 42 radians for 1.5 second s, later to increase to 62 radians in 0.4 second, to keep the same angular position for 1.6 seconds, and finally to decrease its position to zero radians in 0.8 second with the highest ve ocity of all in reverse direction. The simulation and experimental responses with Kp = 80 and Kp=180 are shown in Fig. 15 and Fig. 16 respectively.
Figure 16. Experimental results for the second trapezoidal motion command. The performances are close to the ones obtained in the previous case study. Through the simulation and _ the experiment, the tracking performance of the cascaded PI field oriented control algorithm of SMPM was satisfactory. The responses indicate that good performance of trajectory tracking is achieved at different operation points and with different angular velocities as shown in Fig. 17. This satisfies our servo system’s requirement. The zoomed-in velocity simulation results in Fig.17 looks almost identical to the experimental ones at different velocities and that proves the effectiveness of our simulated model as an effective mean and tool for analysis and design of PMSM control system scheme.
Figure 16. Experimental results for the second trapezoidal motion command. The performances are close to the ones obtained in the previous case study. Through the simulation and _ the experiment, the tracking performance of the cascaded PI field oriented control algorithm of SMPM was satisfactory. The responses indicate that good performance of trajectory tracking is achieved at different operation points and with different angular velocities as shown in Fig. 17. This satisfies our servo system’s requirement. The zoomed-in velocity simulation results in Fig.17 looks almost identical to the experimental ones at different velocities and that proves the effectiveness of our simulated model as an effective mean and tool for analysis and design of PMSM control system scheme.
Figure 17. Simulation and experimental angular velocity responses to the second trapezoidal motion position command.
Figure 17. Simulation and experimental angular velocity responses to the second trapezoidal motion position command.
Related topics:
Motion controlField oriented controlReal time implementation
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