1. Introduction
Permanent magnet synchronous machines (PMSM) have been adopted for improving efficiency of the mechanical drive in various industrial applications. In this area of applications, the PMSM drive was developed for low cost but robust control performance which is always the task to motor drive engineers. Presently, the cost of digital signal processor (DSP) is reducing due to technology improvements; however, the price of DSP is still one of the most expensive component in PMSM drive. Although the cost of fixed point DSP is much smaller than the cost of floating point DSP, complex and robust control algorithm cannot be easily adapted with fixed point DSP because it can only handle integer variable.
On the other hand, to achieve the robust torque control for PMSM drive, look-up table (LUT) based current control has been widely adopted to generate a current reference for precise torque generation corresponding to the torque reference. This LUT is established experimentally under extreme conditions in order to consider the inductance saturation or resistance variation, and thus the target drive has a steady torque generation against variations in the guaranteed operation range [
1]. A general LUT-based PMSM drive uses a two-dimensional look-up Table (2D-LUT), speed-torque [
2,
3,
4], or flux-torque [
1,
5,
6,
7,
8] for reference.
Figure 1 shows these control methods. A speed-torque 2D-LUT-based control method has a simple control algorithm. As shown in
Figure 1a, it does not require any specific processes for 2D-LUT usage, and it is, therefore, comparatively convenient to adapt in a low cost PMSM drive. However, there is no way to reflect the DC-link voltage variation, and the 2D-LUT has to be made under the minimum voltage of DC-link for a stable operation against the variation in DC-link voltage. Due to this reason, the controllable power is reduced to a level that can occur at the minimum DC link voltage. To reflect this variation in the DC-link voltage, a torque control method using flux-torque table is generally applied on the PMSM drive as shown in
Figure 1b. Although a flux estimator and a torque limiter are required, controllable power is enlarged due to the estimated flux automatically reflects the DC-link voltage variation. However, to implement this method in a low cost DSP, the flux estimator has a considerable processing burden because it requires a variable division calculation [
5,
7] or a controller with variable gain, which has been obtained from experiments conducted under various DC-link voltage conditions [
6,
8]. Other studies have reflected the variation in DC-link voltage, and the method in [
1,
9] uses a three-dimensional LUT (3D-LUT), which increases the number of LUT inputs for reflecting the DC-link voltage. However, these methods require excessive amounts of experimental data and allowable memory, as well as a complex interpolation method. To exclude methods using a flux estimator and 3D-LUT, a speed-torque 2D-LUT-based control method considering the variation in DC-link voltage is proposed in [
10,
11,
12,
13]. These studies indicate that if the ratio of the current to nominal value of the DC-link voltage is applied to the speed information, it can control the motor reflecting the variation in DC-link voltage despite the use of speed-torque 2D-LUT. However, these methods also require a variable division calculation to obtain the voltage ratio, and as a result, they cannot be easily implemented in a low cost DSP.
In this paper, a simple torque control method for PMSM is proposed considering the variation in DC-link voltage, which can be easily adopted in a low cost DSP. The proposed method uses a speed-torque 2D-LUT for the generation of the
d-/
q-axis currents reference. However, a calculation process to obtain the DC-link voltage ratio is not needed, which is essential for reflecting the current DC-link voltage in [
10,
11,
12,
13]. The proposed control method was verified through an experiment under various DC-link voltage conditions.
This paper is organized as follows. In
Section 2, the concept of the proposed method is given and how to establish the speed-torque table considering DC-link voltage variation are presented with the experimental set-up for verification. In
Section 3, experiments are conducted to prove the proposed method. The conclusion of this paper is given in
Section 4.
3. Results and Discussion
The speed-torque 2D-LUT is created based on a DC-link voltage of 260 V, and the speed data should be modified into the speed data based on a DC-link voltage of 380 V using the method presented in
Section 3, and stored into memory.
Figure 6 shows the current map stored into memory.
Because the value of calculated by (7) is 0.6842, the current map data should be generated for a maximum motor speed of at least 11,693 rpm. In conclusion, the maximum motor speed for the stored current data should be higher than the actual maximum motor speed to compensate the current reference in case of a variation in the DC-link voltage by adjusting .
The proposed 2D-LUT, however, can perform the maximum power control with different DC-link voltages.
Figure 7 shows the experimental result of maximum power control under minimum and maximum DC-link voltage and this experiment was conducted in room temperature.
Figure 7a,b are waveforms under maximum (380 V) and minimum (260 V) DC-link voltage respectively, and it is shown that the output is varied according to the input voltage. Also, the motor speed is varied from rated speed to 8000 rpm by the load motor during the experiment.
As mentioned earlier, the proposed d-/q-axis currents map is obtained under the allowable maximum temperature for the stable performance in the circumstance variation. Since the resistance value increases/decreases as the temperature increases/decreases, the voltage limit ellipse is shrunk/extended according to the operating temperatures. Therefore, the proposed method automatically generates proper current map corresponding to 8000 rpm which is the maximum speed for varied voltage limit ellipse in any operating conditions.
As shown in
Figure 7b, the value of
is 11,650 rpm during the motor is rotating at 8000 rpm, which current map data are for the more extended voltage limit ellipse, while the value from the calculation is 11,693 rpm. This is because the voltage drop from the resistance is reduced resulting in voltage limit ellipse extension.
Meanwhile,
Figure 7a shows that
has the same value as the actual speed of the motor. The reason is as follows. Even if the converted
gain value is applied to the map, the converted speed,
should be smaller value than the speed of the map. Because, stored
d-/
q-axis currents data is under high temperature experiment for reflecting the largest ohmic voltage drop.
However, the proposed voltage controller controls less then the practical speed, increasing maximum power in flux-weakening region due to increasing DC-link voltage is restricted, even though practical controllable power is extended due to diminished ohmic voltage drop from room temperature. Although the limit is existed in the proposed control method, the difference is not significant because it is as much an error as an ohmic voltage drop caused from the temperature variation.
Figure 8 shows the
d-/
q-axis currents trajectories when the DC-link voltage is varied by 20 V from 380 V to 260 V, and 130 Nm of the torque reference is input at a constant motor speed of 3000 rpm.
From 380 V to 340 V of the DC-link voltage, the current references are the same because the DC-link voltage is capable of achieving the maximum torque control from the MTPA curve. When the DC-link voltage is changed from 340 V to 260 V, the current references are changed into the references for a flux-weakening operation because the torque controller can no longer track the MTPA curve with a decreased DC-link voltage.
It has been shown that even if the DC-link voltage is changed during the operation, the proposed method achieves the maximum torque control according to the DC-link voltage variation when adjusting the current references along with the DC-link voltage.
Figure 9 shows the experimental results for constant torque control with a variable DC-link voltage.
Using the proposed method, the speed of the motor is controlled at 4800 rpm, the torque is 80 [Nm], the DC-link voltage is 320 V, and is calculated as 5700 rpm.
When the DC-link voltage is changed to 380 V, the calculated speed is decreased to 4800 rpm to maintain the output torque. As a result, the output torque incurs a small fluctuation but remains almost unchanged.
When the DC-link voltage is returned to 320 V and then changed to 260 V, the calculated speed is increased to 7015 rpm to maintain the torque, which as before is also not severely changed.
In conclusion, if the DC-link voltage increases, gradually decreases and increases if the DC-link voltage decreases, resulting in almost the same output torque without an additional device or excessive memory capacity.
Figure 10 shows the experiment results of the maximum torque and power under various conditions of the DC-link voltage. An increase or decrease in the DC-link voltage is reflected by the feedback controller, which tunes the speed input of the 2D-LUT. As shown in the figure, the rated speed is increased in accordance with the increased DC-link voltage. For this reason, the maximum torque at the specific speed in the flux weakening region is increased even it does not use the flux-torque 2D-LUT to reflect the DC-link voltage. Therefore, the maximum power is also extended in accordance with increasing DC-link voltage.
These results prove that an appropriate torque control is achieved, not only at a DC-link voltage of 260 V but also at 320 V and 380 V by means of a general feedback control using a novel speed-torque 2D-LUT.