- Email: [email protected]
Novel integrated position measurement unit for stepping motor servo control
Measurement 44 (2011) 80–87
Contents lists available at ScienceDirect
Measurement journal homepage: www.elsevier.com/locate/measurement
Novel integrated position measurement unit for stepping motor servo control Shi Jingzhuo ⇑, Zhang Huimin, Liu Xun School of Electronic & Information Engineering, Henan University of Science and Technology, Luoyang 471003, China
a r t i c l e
i n f o
Article history: Received 24 April 2010 Received in revised form 5 September 2010 Accepted 14 September 2010 Available online 21 September 2010 Keywords: Position sensor Inductance detection Servo control Stepping motor
a b s t r a c t Rotor position detection is important for motor servo system design. In general, there are two kinds of methods to obtain the position information in real time, sensor or sensorless methods. The sensor methods use position sensors such as optical encoder. This will greatly increase the cost of the system, and the sensor with high precision is difficult to be installed. On the other hand, the sensorless method can reduce the cost, but the reliability and complexity of the algorithm is still the problems. In this paper, a new low-cost integrated position feedback unit, which is composed of the integrated position sensor, signal processing hardware and software, is described. The sensor is easy to manufacture and has better precision with the help of signal processing circuit and software based on DSP. The sensor can obtain absolute rotating angle using inductance detection method, and it is originally designed and used for a 2-phase hybrid stepping motor position servo system. The integrated sensor and the proper control strategy make the system become a low-cost high-performance position servo system. Even though the feedback unit is originally designed for a 2-phase hybrid stepping motor, the same unit also can be used with other types of motors. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction Rotor position detection is important for servo system. Researchers have investigated many sensorless position detection techniques for double salient motors such as stepping motor, SRM or PMSM. The fundamental principle of these sensorless techniques is that, rotor position information can be extracted from the stator circuit measurements or their derived parameters such as the back EMF, the winding inductance, and the flux linkage [1–4]. Because of the back EMF is in proportion to speed, it can not be used at standstill and low speed. Lyons proposed a technique for SRM that utilized the relationship between flux linkage and current [5]. The method can be applied even if no non-energized phase winding is present. But the accuracy is dependent on the precise measurement of
⇑ Corresponding author. Tel.: +86 379 64231757; fax: +86 379 64231910. E-mail address: [email protected] (S. Jingzhuo). 0263-2241/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.measurement.2010.09.032
the flux linkage look-up table, and because the calculation complicacy, this method cannot work well while the motor’s rotating speed is high [6]. There are some methods that using winding inductance to detect the rotor position [7–12]. Ehsani worked out an external modulation circuit to drive the no-current phase winding and then, obtain the winding’s inductance [9]. This method needs to find the suitable no-current phase winding to measure the inductance. Horber described a ‘‘sensorimotor” in [10]. The motor is a P.M. synchronous motor that has 24 salient poles on the stator. Four of these poles are wounded with testing coils, and the other poles are wounded with phase windings. The position information can be detected by measuring the testing coil’s inductance using modulation technique. Because the four poles are used to detect the position, the pullout torque is decreased. Marushima developed this method by wounded smaller testing coils and phase windings on the same stator poles [11]. This method is easy and low-cost. But because the testing coils are wounded on the motor’s
S. Jingzhuo et al. / Measurement 44 (2011) 80–87
stator poles, the testing coils have full magnetic connection with the windings of stator, the electronic and magnetic situation of the stator windings will badly affect the sensor coils. It makes the process of signal processing to be more complex and also influence the precision. In this paper, a new ‘‘integrated position feedback unit” for hybrid stepping motor is proposed. The remainder of this paper is organized as follows. The structure and the detection theory is described in Section 2. In Sections 3 and 4, the signal processing circuit and software implemented in DSP chip is presented. In Section 5, the position feedback unit is used in a hybrid stepping motor servo system and some results are presented.
2. Structure of the sensor This sensor is just produced with the motor, and has the same structure with the motor. The sensor has no electronic and less magnetic connection with the motor. The sensor is easy to manufacture and has better precision with easier signal processing circuit. The sensor is just produced with the motor. Fig. 1 is the structure of the integrated position sensor. The motor is a 2-phase 8-pole hybrid stepping motor that has 50 teeth on the rotor. The sensor is double salient structure, has its own stator, rotor and stator windings (testing coils); just like a small single stack 2-phase VR stepping motor. The sensor’s stator is aligned with the motor’s stator, and its rotor is aligned with one stack of the hybrid stepping motor’s rotor (unaligned with the other stack). The inductance of the testing coil is the function of the rotor position. So the motor’s rotor position can be detected by measuring the inductance on-line. This sensor not only for the stepping motor, but also can produced with other types of motors as a general used position sensor for servo system. The testing coils are connected to make four testing windings as the left one in Fig. 1. Each testing winding includes two testing coils that anti-connected each other. This connection method can greatly decreases the backEMF signal in the testing coils that produced by the magnetic couple. There is an aluminum ring between the motor’s rotor and the sensor’s rotor that making the magnetic connection between motor and sensor is very little. The structure of the sensor makes it possible and easier to detect the rotor position signal.
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Because the current in the testing coils is very small (several mA) and the magnetic couple between the motor and the sensor is also very small, the magnetic field in the sensor cannot be saturated. The inductance of the testing coil is just a function of the rotor position. If the high order harmonics are ignored (the design of the rotor/stator tooth ensured the magnetic field is nearly sin-wave field), the four testing windings’ inductance can be described as:
8 LA ¼ L0 þ L1 sin he > > > < LB ¼ L0 þ L1 cos he > > LC ¼ L0 L1 sin he > : LD ¼ L0 L1 cos he
ð1Þ
Here, L0 is the inductance’s even value and L1 is the value of the first harmonic. If the change of the inductance, L1 sin he and L1 cos he can be detected on-line, then the rotor position is known. 3. Sensor signal processing circuit The sensor processing circuit is designed to detect the change of the inductance using amplitude-modulation technique. Fig. 2 is the sketch map of the processing circuit. In the circuit, each of the testing winding is connected with a capacitor to make a LC resonance circuit. And two windings (A and C, B and D) are connected serially. This makes the inductance of each branch become constant:
LA þ LC ¼ 2L0 LB þ LD ¼ 2L0
ð2Þ
The inductance can be detected from the envelope of the modulation signal. For the modulation circuit, the modulation frequency must higher than the maximum frequency of the inductance changing. And if the modulation frequency is higher, the precision will also higher. In the servo system, the required highest speed is 3000 r/min, which means the maximum frequency of the inductance changing is 2500 Hz. So, the modulation frequency must be higher than 5 kHz. On the other hand, the frequency of the modulation voltage influences the magnetic field in the sensor. Because the sensor windings are in the magnetic field of the sensor, and the inductance is also a value connect with the magnetic field. So, the difference modulation frequency also gives out different inductance
Fig. 1. Structure of the integrated position sensor.
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Amplitude-modulation circuit
Low-pass filter
Calculation circuit
Position feedback signal to DSP
Phase-sense circuit
Testing coils
Fig. 2. Sketch map of the position processing circuit.
/F ðxÞ ¼ tg
2n xxn
3 2 1 0 -1 -2 -3 -4
0
10
20
30
40
50
Time (ms)
#
Fig. 4. Modulation signal waveform.
ð3Þ
1 ðxxn Þ2
5
Here, n is the damping coefficient, xn is the inherent oscillation frequency, and x is the frequency of input signal. According to the equation and values of real components, the phase-frequency characteristic of the filter can be obtained as shown in Fig. 5. The range of the input signal’s frequency in Fig. 5 is 0–2500 Hz, and the corresponding range of rotating speed is about 0–3000 r/min. This range contains the whole range of speed modulation. Fig. 5 shows that, the characteristic has good linearity. The linearity makes the phase lag can be compensated in software using simple look-up table. In real-time implementation of control, the table is checked using the current value of signal frequency as index. According to the values looked in the table, the current value of lag phase can be obtained using linear curvefitting. Then the lag degrees should be added to the real phase angel calculation process to avoid the lag.
0
Delay angle (degree)
" 1
4
Voltage (V)
detection signal. Fig. 3 shows the change of the value of L1 with the different modulation frequency. According to this figure, the modulation frequency is chosen as 32 kHz. The capacitor connected with the testing winding should be chosen to ensure the LC resonance. Here, four 0.1 lF capacitors are used. Fig. 4 shows the modulation signal waveform. A 2-level low-pass filter is used to demodulate the signal. The filter will make the signal’s phase angle lag behind the real one. This can be avoided by software compensation. Here, the load of the filter is A/D converter (ADC). The input current of the ADC is several lA, so the influence of cascade connection between the filter and ADC can be ignored. Then, the phase-frequency characteristic of the filter can be described as:
-5 -10 -15 -20 -25 -30 -35 0
500
1000
1500
2000
2500
Frequency (Hz) Fig. 5. Phase-frequency characteristic of the 2-level low-pass filter.
Fig. 6 presents the result of the low-pass filter after the software compensation. It is the final position feedback signals connected to the ADCs in the DSP TMS320F240.
Change of inductance (mH)
0.35
4. Sensor signal processing software based on DSP
0.30 0.25 0.20 0.15 0.10 1
10
Frequency (kHz) Fig. 3. L1 vs. modulation frequency.
100
For most of the servo system, not only the position angle but also the sine and cosine value of the angle is needed. The software controls the ADC convert the analog signals to digital numbers, then, obtain the rotor position angle and the sine and cosine value of this angle. Several look-up tables should be used here. Fig. 7 shows the signal processing software structure while the sensor is used in a vector control servo system. Fig. 8 is the testing results of the rotor position detection while the rotating direction is CW and CCW. The figure shows that, it is easy to find out the rotating direction from the position feedback. Because the position sensor is based
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5.0
360
Electrical Angle (degree)
Position feedback (V)
4.5 4.0 3.5 3.0 2.5 2.0 1.5 1.0
A B
0.5
300 240 180 120 60 0
0.0 0
1
2
3
4
5
6
7
8
0
2
4
6
Time (ms)
8
10
12
14
16
Time (ms)
(a) Position feedback while CW direction
Fig. 6. Waveform after demodulation.
on the inductance detection, it is also easy to know the start position while standstill. Fig. 9 is the testing results of the rotor position detection while the motor start. To increase the precision of the position sensor, some steps should be taken in the software. 4.1. Mutual-compensation of two position feedback signals In theory, the rotor position information can be obtained according to only one position feedback signal and the phase relation between two signals is used to decide the rotation direction. Because the sampling value of the position signals should be converted into angle value and sinusoidal signal has different slope at different points. Considering the influence of disturbance in factual system and the byte length limitation of DSP, the conversion has higher accuracy in the section with higher slope. In the section where the sinusoidal signal is close to the positive or negative extremum, the slope is small and the conversion accuracy is lower accordingly. In order to raise the conversion accuracy, it is necessary to compensate the quadrature feedback signals and obtain the current position angle information using the position feedback signal that has higher slope. As shown in Fig. 6, there are two feedback signals in quadrature with each other, which can be described as sin and cos respectively. When one signal (for example, sin signal), is at the positive or negative extremum position and so has zero slope, the other one (cos signal) just has the largest slope. So, in the section where the sin signal is close to the positive or negative extremum, the cos signal can be used to obtain the
Position feedback signals
look-up table 1
Position ref. Position feedback
Electric angle θ
ADC
Electrical Angle (degree)
360 300 240 180 120 60 0 0
2
4
id, iq
8
10
12
14
16
18
Time (ms)
(b) Position feedback while CCW direction Fig. 8. Position feedback signals while CW and CCW direction.
position angle information instead. This is called ‘‘mutual-compensation”. Fig. 10 gives out the testing results of compensation and non-compensation. It shows that mutual-compensation raises the conversion accuracy, makes the position feedback approaches the actual conditions more. 4.2. Elimination of low frequency amplitude modulation Position feedback signals contain low frequency amplitude modulation. Besides, because of the temperature excursion influence of the components in circuit, the signals’ zero-point also has some excursion. This behaves as little variation of signal amplitude and excursion of
+ _ S
Position controller Speed feedback
e
obtain sin θ e , cos θ e from look-up table 2 + Current controller + _ _
2/2 transform
Vector control
6
Fig. 7. Position feedback signal processing software structure.
Drive the motor ia, ib
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Electrical Angle (degree)
1000
ADC Result
800 600 400 200 0
360 300 240 180 120 60 0
0
2 4
0
6 8 10 12 14 16 18 20 22 24 26 28 30 32
2 4
6 8 10 12 14 16 18 20 22 24 26 28 30 32
Time (ms)
Time (ms)
(a) Position feedback waveform
(b) Position angle feedback waveform
360
360
300
300
Electrical Angle (dgree)
Electrical Angle (degree)
Fig. 9. Position feedback signals while motor start.
240 180 120 60 0
240 180 120 60 0
0
1
2
3
4
5
6
0
1
2
3
4
5
Time (ms)
Time (ms)
(a) The detected angle before compensation
(b) The detected angle after compensation
6
Fig. 10. Compensation of the position feedback signals.
the whole signal waveform. It can make the position feedback lose veracity. The signals’ zero-excursion can be modified through adding into feedback-loop in the circuit, but the temperature property problem of circuit components is still in existence. To the problem of low frequency amplitude modulation, because the position feedback signals are demanded to range from 0 to 2.5 kHz, it is difficult to be modified in the hardware. This problem can be worked out in software. The program can detect the maximum and minimum value of position feedback signal, calculate the amplitude and zeropoint that can be used during the next feedback signal’s period. Fig. 11 gives out the effect after such processing. The left curve shows the position feedback sampling signals, where Y-coordinate represents the sampling value. The normal value is between the up and down dash lines. The signals given in the figure are obtained after artificially modulation and magnify the variation of signal amplitude and zero-point. The right curve shows the position angle value. The calculation is based on the initial value in the first period, so the instantaneous angle is not too accurate. But the values of the following periods are more accurate, it shows that the automatic modulation in software is effective.
4.3. Elimination of position feedback disturbance Because the electromagnetic disturbance inside and outside the system, position feedback signals often contain peak disturbance that can make the position feedback signals have deviation. Fig. 12 shows that the peak disturbance in the position feedback signals results in large disturbance of the electrical angle obtained from calculation. This disturbance does not produce accumulating error, that is, it does not affect the final location precision. But it can affect the current reference at that time, then affect the system’s dynamic process. Dispose in circuit is difficult to eliminate this disturbance, so preventive steps should be adopted at the same time. Because the suddenness of the peak disturbance and wider frequency bandwidth of the position feedback signals, it is difficult to eliminate disturbance using routine digital filter such as FIR or IIR. Considering the process real time property, the authors have adopted several FIR and IIR digital filter to process the position feedback sampling signals. The effect was not good enough. Because the position feedback signals are approximate sine signals, the electrical angles obtained from calculation are approximate linearity. It is possible to use some
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360
900
Electrical angle (degree)
Position ADC feedback
1000 800 A B
700 600 500 400 300 200 100
300 240 180 120 60 0
0 0
5
10
15
20
25
30
0
5
10
Time (ms)
15
20
25
30
Time (ms)
Fig. 11. Software correction of the amplitude modulation.
1024
360
Position (elec. degree)
Position (ADC result)
896 768 640 512 384 256 128
300 240 180 120 60
0
0
0
5
10
15
20
25
0
5
10
Time (ms)
15
20
25
Time (ms)
Fig. 12. Effect of the disturbance in the position feedback signal.
if jDP ADn DP ADðn1Þ j > 500 DPADðn1Þ end if
then
P ADn ¼ P ADðn1Þ þ
Here, P ADn is the sampling value of position feedback signal on n point. DP ADn is the balance of previous and current sampling values: DPADn ¼ P ADn P ADðn1Þ . This rule can eliminate the great amplitude disturbance in feedback signals. Pn is defined as the electrical angle value on the nth point. And the increment between adjacent points is DPn ¼ P n P ðn1Þ . Then, let us define DPn4 as:
DPn4 ¼ ðDPn þ DPðn1Þ þ DP ðn2Þ þ DPðn3Þ Þ=4 According to the maximum acceleration the system can reached, the value of jDPn DPðn1Þ j should less than 2. Considering the noise, let jDP n DP ðn1Þ4 j < 32. Based on this opinion, the electrical angle values can be processed using following rules:
if jDPn DPðn1Þ4 j > 32 then Pn ¼ P ðn1Þ þ DP ðn1Þ4 end if 5. Application of the integrated position sensor Firstly, an optical rotary encoder coupled with the motor, is used to examine the precision of the proposed method. The encoder is an incremental one, and it can give out 4000 pulses per cycle. Fig. 13 is the tested result while the
360
Position/Electrical degree
experience-rules to eliminate great amplitude disturbance in the position feedback signals. This paper adopts the linearity reasoning forecast method to process the electrical angle for the aim to eliminate peak disturbance completely. To the process of position feedback signals, following rules is used:
300 240
Feedback Encoder
180 120 60 0 0.0
0.5
1.0
1.5
t/ms Fig. 13. Examination of the proposed position measurement unit.
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Reference model
+
-
Neural network + + • Position reference
• -
Position control
+
•
Speed control
T
+ Vector control
TL uA
s d
i * +
+
-
Current controller
s q
ω Motor
1 s
•
uB
i *
•
360
1000
300
800
Speed (r/min)
Position (mech degree)
Fig. 14. Structure of the 2-phase hybrid stepping motor vector control position servo system.
240 180 120
600 400 200
60 0 0 0
50
100
150
200
250
300
350
400
0
50
100
150
Time (ms)
200
250
300
350
400
Time (ms)
Fig. 15. Testing result of the vector control system (no load, 360°).
rotating speed of motor is constant, 800 r/min. The output signals of encoder are processed using the capture module of DSP, and the ADC module of DSP is used to implement the proposed method. In Fig. 13, the dash line represents the position angle measured by the encoder, and the real line is the position feedback obtained using the proposed method. The largest error between the two lines is less than ±1 pulse of the encoder, about ±0.09°. Then, the proposed integrated sensor is used in a 2-phase hybrid stepping motor vector control position servo system. Fig. 14 is the structure of the servo system. The position controller is IP controller. The neural network and model reference adaptive controller is used to avoid the influence of the system’s non-modeled non-linearity. The DSP TMS320F240 that can execute 20-million instruments per second is used to implement the control strategy and the sensor processing software. The integrated sensor and the proper control strategy make the system become a low-cost high-performance position servo system. Fig. 15 shows the testing results of the position servo system while the position reference is one circle (360°). The left curve is position response, and the right one is the change of rotating speed during the response time. The exact position feedback helps to maintain the orientation of vector control, and also helps to avoid the position error. The speed curve shows that, to track the position reference as soon as possible, the speed raises to enough value immediately. Therefore, the position response is even, fast, and has no stable error.
6. Conclusions The integrated sensor increases the length and weight of the motor, but the system is still simpler and cheaper than the position sensors used now. This type of position signal detection method has more complex mechanism than the sensorless methods. But the signal processing process is simpler and the precision is higher, and the rotor position can be detected anytime without influence of the motor’s situation. The integrated sensor also can be produced independent and as a normal position sensor for all kinds of rotating machines. With the help of the signal processing hardware and software, this kind of sensor can give out high precision.
Acknowledgment The authors are grateful for the support by the Natural Science Foundation of Henan Province through Grant No. 092300410164.
References [1] N. Bianchi, S. Bolognani, Jang Ji-Hoon, Sul Seung-Ki, Comparison of PM motor structures and sensorless control techniques for zerospeed rotor position detection, IEEE Transactions on Power Electronics 22 (6) (2007) 2466–2475. [2] B. Fahimi, A. Emadi, B. Sepe Jr., Position sensorless control, IEEE Industry Applications Magazine 10 (1) (2004) 40–47.
S. Jingzhuo et al. / Measurement 44 (2011) 80–87 [3] S. Morimoto, M. Sanada, Y. Takeda, Mechanical sensorless drives of IPMSM with online parameter identification, IEEE Transactions on Industry Applications 42 (5) (2006) 1241–1248. [4] K. Ohyama, G.M. Asher, M. Sumner, Comparative analysis of experimental performance and stability of sensorless induction motor drives, IEEE Transactions on Industrial Electronics 53 (1) (2005) 178–186. [5] J.P. Lyons, S.R. MacMinn, M.A. Preston, Flux/current methods for SRM rotor position estimation, Conf. Rec. of IEEE Industry Applications Soc. Annual Meeting (1991) 482–487. [6] Gabriel Gallegos-Lopez, Philip C. Kjaer, T.J.E. Miller, High-grade position estimation for SRM drives using flux/current correction model, IEEE Transactions on Industry Applications 35 (4) (1999) 859–869. [7] G. Suresh, B. Fahimi, K.M. Rahman, M. Ehsani. Inductance based position encoding for sensorless SRM drives, in: Proc. of 30th Annual IEEE Power Electronics Specialists Conference, vol. 2, 1999, pp. 832–837. [8] Gao Hongwei, F.R. Salmasi, M. Ehsani, Inductance model-based sensorless control of the switched reluctance motor drive at low
[9]
[10]
[11]
[12]
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speed, IEEE Transactions on Power Electronics 19 (6) (2004) 1568– 1573. Mehrdad Ehsani, Iqbal Husain, Shailendra Mahajan, K.R. Ramani, New modulation encoding techniques for indirect rotor position sensing in switched reluctance motors, IEEE Transactions on Industry Applications 30 (1) (1994) 85–91. Ralph Horber, Sensorimotor: P.M. synchronous motor with fully integrated position sensor, in: Proc. Of 19th Symp. On Increment Motion Control & System Design, University of Illinois, Illinois, USA, 1990, pp. 243–250. K. Marushima, Ralph W. Horber, Development of a highperformance sensorimotor with sensor and driving coils, in: Proc. of 23rd Symp. on Increment Motion Control & System Design, University of Illinois, Illinois, USA, 1994, pp. 59–69. Jang Ji-Hoon, Ha Jung-Ik, M. Ohto, K. Ide, Sul Seung-Ki, Analysis of permanent-magnet machine for sensorless control based on highfrequency signal injection, IEEE Transactions on Industry Applications 40 (6) (2004) 1595–1604.
Contents lists available at ScienceDirect
Measurement journal homepage: www.elsevier.com/locate/measurement
Novel integrated position measurement unit for stepping motor servo control Shi Jingzhuo ⇑, Zhang Huimin, Liu Xun School of Electronic & Information Engineering, Henan University of Science and Technology, Luoyang 471003, China
a r t i c l e
i n f o
Article history: Received 24 April 2010 Received in revised form 5 September 2010 Accepted 14 September 2010 Available online 21 September 2010 Keywords: Position sensor Inductance detection Servo control Stepping motor
a b s t r a c t Rotor position detection is important for motor servo system design. In general, there are two kinds of methods to obtain the position information in real time, sensor or sensorless methods. The sensor methods use position sensors such as optical encoder. This will greatly increase the cost of the system, and the sensor with high precision is difficult to be installed. On the other hand, the sensorless method can reduce the cost, but the reliability and complexity of the algorithm is still the problems. In this paper, a new low-cost integrated position feedback unit, which is composed of the integrated position sensor, signal processing hardware and software, is described. The sensor is easy to manufacture and has better precision with the help of signal processing circuit and software based on DSP. The sensor can obtain absolute rotating angle using inductance detection method, and it is originally designed and used for a 2-phase hybrid stepping motor position servo system. The integrated sensor and the proper control strategy make the system become a low-cost high-performance position servo system. Even though the feedback unit is originally designed for a 2-phase hybrid stepping motor, the same unit also can be used with other types of motors. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction Rotor position detection is important for servo system. Researchers have investigated many sensorless position detection techniques for double salient motors such as stepping motor, SRM or PMSM. The fundamental principle of these sensorless techniques is that, rotor position information can be extracted from the stator circuit measurements or their derived parameters such as the back EMF, the winding inductance, and the flux linkage [1–4]. Because of the back EMF is in proportion to speed, it can not be used at standstill and low speed. Lyons proposed a technique for SRM that utilized the relationship between flux linkage and current [5]. The method can be applied even if no non-energized phase winding is present. But the accuracy is dependent on the precise measurement of
⇑ Corresponding author. Tel.: +86 379 64231757; fax: +86 379 64231910. E-mail address: [email protected] (S. Jingzhuo). 0263-2241/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.measurement.2010.09.032
the flux linkage look-up table, and because the calculation complicacy, this method cannot work well while the motor’s rotating speed is high [6]. There are some methods that using winding inductance to detect the rotor position [7–12]. Ehsani worked out an external modulation circuit to drive the no-current phase winding and then, obtain the winding’s inductance [9]. This method needs to find the suitable no-current phase winding to measure the inductance. Horber described a ‘‘sensorimotor” in [10]. The motor is a P.M. synchronous motor that has 24 salient poles on the stator. Four of these poles are wounded with testing coils, and the other poles are wounded with phase windings. The position information can be detected by measuring the testing coil’s inductance using modulation technique. Because the four poles are used to detect the position, the pullout torque is decreased. Marushima developed this method by wounded smaller testing coils and phase windings on the same stator poles [11]. This method is easy and low-cost. But because the testing coils are wounded on the motor’s
S. Jingzhuo et al. / Measurement 44 (2011) 80–87
stator poles, the testing coils have full magnetic connection with the windings of stator, the electronic and magnetic situation of the stator windings will badly affect the sensor coils. It makes the process of signal processing to be more complex and also influence the precision. In this paper, a new ‘‘integrated position feedback unit” for hybrid stepping motor is proposed. The remainder of this paper is organized as follows. The structure and the detection theory is described in Section 2. In Sections 3 and 4, the signal processing circuit and software implemented in DSP chip is presented. In Section 5, the position feedback unit is used in a hybrid stepping motor servo system and some results are presented.
2. Structure of the sensor This sensor is just produced with the motor, and has the same structure with the motor. The sensor has no electronic and less magnetic connection with the motor. The sensor is easy to manufacture and has better precision with easier signal processing circuit. The sensor is just produced with the motor. Fig. 1 is the structure of the integrated position sensor. The motor is a 2-phase 8-pole hybrid stepping motor that has 50 teeth on the rotor. The sensor is double salient structure, has its own stator, rotor and stator windings (testing coils); just like a small single stack 2-phase VR stepping motor. The sensor’s stator is aligned with the motor’s stator, and its rotor is aligned with one stack of the hybrid stepping motor’s rotor (unaligned with the other stack). The inductance of the testing coil is the function of the rotor position. So the motor’s rotor position can be detected by measuring the inductance on-line. This sensor not only for the stepping motor, but also can produced with other types of motors as a general used position sensor for servo system. The testing coils are connected to make four testing windings as the left one in Fig. 1. Each testing winding includes two testing coils that anti-connected each other. This connection method can greatly decreases the backEMF signal in the testing coils that produced by the magnetic couple. There is an aluminum ring between the motor’s rotor and the sensor’s rotor that making the magnetic connection between motor and sensor is very little. The structure of the sensor makes it possible and easier to detect the rotor position signal.
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Because the current in the testing coils is very small (several mA) and the magnetic couple between the motor and the sensor is also very small, the magnetic field in the sensor cannot be saturated. The inductance of the testing coil is just a function of the rotor position. If the high order harmonics are ignored (the design of the rotor/stator tooth ensured the magnetic field is nearly sin-wave field), the four testing windings’ inductance can be described as:
8 LA ¼ L0 þ L1 sin he > > > < LB ¼ L0 þ L1 cos he > > LC ¼ L0 L1 sin he > : LD ¼ L0 L1 cos he
ð1Þ
Here, L0 is the inductance’s even value and L1 is the value of the first harmonic. If the change of the inductance, L1 sin he and L1 cos he can be detected on-line, then the rotor position is known. 3. Sensor signal processing circuit The sensor processing circuit is designed to detect the change of the inductance using amplitude-modulation technique. Fig. 2 is the sketch map of the processing circuit. In the circuit, each of the testing winding is connected with a capacitor to make a LC resonance circuit. And two windings (A and C, B and D) are connected serially. This makes the inductance of each branch become constant:
LA þ LC ¼ 2L0 LB þ LD ¼ 2L0
ð2Þ
The inductance can be detected from the envelope of the modulation signal. For the modulation circuit, the modulation frequency must higher than the maximum frequency of the inductance changing. And if the modulation frequency is higher, the precision will also higher. In the servo system, the required highest speed is 3000 r/min, which means the maximum frequency of the inductance changing is 2500 Hz. So, the modulation frequency must be higher than 5 kHz. On the other hand, the frequency of the modulation voltage influences the magnetic field in the sensor. Because the sensor windings are in the magnetic field of the sensor, and the inductance is also a value connect with the magnetic field. So, the difference modulation frequency also gives out different inductance
Fig. 1. Structure of the integrated position sensor.
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Amplitude-modulation circuit
Low-pass filter
Calculation circuit
Position feedback signal to DSP
Phase-sense circuit
Testing coils
Fig. 2. Sketch map of the position processing circuit.
/F ðxÞ ¼ tg
2n xxn
3 2 1 0 -1 -2 -3 -4
0
10
20
30
40
50
Time (ms)
#
Fig. 4. Modulation signal waveform.
ð3Þ
1 ðxxn Þ2
5
Here, n is the damping coefficient, xn is the inherent oscillation frequency, and x is the frequency of input signal. According to the equation and values of real components, the phase-frequency characteristic of the filter can be obtained as shown in Fig. 5. The range of the input signal’s frequency in Fig. 5 is 0–2500 Hz, and the corresponding range of rotating speed is about 0–3000 r/min. This range contains the whole range of speed modulation. Fig. 5 shows that, the characteristic has good linearity. The linearity makes the phase lag can be compensated in software using simple look-up table. In real-time implementation of control, the table is checked using the current value of signal frequency as index. According to the values looked in the table, the current value of lag phase can be obtained using linear curvefitting. Then the lag degrees should be added to the real phase angel calculation process to avoid the lag.
0
Delay angle (degree)
" 1
4
Voltage (V)
detection signal. Fig. 3 shows the change of the value of L1 with the different modulation frequency. According to this figure, the modulation frequency is chosen as 32 kHz. The capacitor connected with the testing winding should be chosen to ensure the LC resonance. Here, four 0.1 lF capacitors are used. Fig. 4 shows the modulation signal waveform. A 2-level low-pass filter is used to demodulate the signal. The filter will make the signal’s phase angle lag behind the real one. This can be avoided by software compensation. Here, the load of the filter is A/D converter (ADC). The input current of the ADC is several lA, so the influence of cascade connection between the filter and ADC can be ignored. Then, the phase-frequency characteristic of the filter can be described as:
-5 -10 -15 -20 -25 -30 -35 0
500
1000
1500
2000
2500
Frequency (Hz) Fig. 5. Phase-frequency characteristic of the 2-level low-pass filter.
Fig. 6 presents the result of the low-pass filter after the software compensation. It is the final position feedback signals connected to the ADCs in the DSP TMS320F240.
Change of inductance (mH)
0.35
4. Sensor signal processing software based on DSP
0.30 0.25 0.20 0.15 0.10 1
10
Frequency (kHz) Fig. 3. L1 vs. modulation frequency.
100
For most of the servo system, not only the position angle but also the sine and cosine value of the angle is needed. The software controls the ADC convert the analog signals to digital numbers, then, obtain the rotor position angle and the sine and cosine value of this angle. Several look-up tables should be used here. Fig. 7 shows the signal processing software structure while the sensor is used in a vector control servo system. Fig. 8 is the testing results of the rotor position detection while the rotating direction is CW and CCW. The figure shows that, it is easy to find out the rotating direction from the position feedback. Because the position sensor is based
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5.0
360
Electrical Angle (degree)
Position feedback (V)
4.5 4.0 3.5 3.0 2.5 2.0 1.5 1.0
A B
0.5
300 240 180 120 60 0
0.0 0
1
2
3
4
5
6
7
8
0
2
4
6
Time (ms)
8
10
12
14
16
Time (ms)
(a) Position feedback while CW direction
Fig. 6. Waveform after demodulation.
on the inductance detection, it is also easy to know the start position while standstill. Fig. 9 is the testing results of the rotor position detection while the motor start. To increase the precision of the position sensor, some steps should be taken in the software. 4.1. Mutual-compensation of two position feedback signals In theory, the rotor position information can be obtained according to only one position feedback signal and the phase relation between two signals is used to decide the rotation direction. Because the sampling value of the position signals should be converted into angle value and sinusoidal signal has different slope at different points. Considering the influence of disturbance in factual system and the byte length limitation of DSP, the conversion has higher accuracy in the section with higher slope. In the section where the sinusoidal signal is close to the positive or negative extremum, the slope is small and the conversion accuracy is lower accordingly. In order to raise the conversion accuracy, it is necessary to compensate the quadrature feedback signals and obtain the current position angle information using the position feedback signal that has higher slope. As shown in Fig. 6, there are two feedback signals in quadrature with each other, which can be described as sin and cos respectively. When one signal (for example, sin signal), is at the positive or negative extremum position and so has zero slope, the other one (cos signal) just has the largest slope. So, in the section where the sin signal is close to the positive or negative extremum, the cos signal can be used to obtain the
Position feedback signals
look-up table 1
Position ref. Position feedback
Electric angle θ
ADC
Electrical Angle (degree)
360 300 240 180 120 60 0 0
2
4
id, iq
8
10
12
14
16
18
Time (ms)
(b) Position feedback while CCW direction Fig. 8. Position feedback signals while CW and CCW direction.
position angle information instead. This is called ‘‘mutual-compensation”. Fig. 10 gives out the testing results of compensation and non-compensation. It shows that mutual-compensation raises the conversion accuracy, makes the position feedback approaches the actual conditions more. 4.2. Elimination of low frequency amplitude modulation Position feedback signals contain low frequency amplitude modulation. Besides, because of the temperature excursion influence of the components in circuit, the signals’ zero-point also has some excursion. This behaves as little variation of signal amplitude and excursion of
+ _ S
Position controller Speed feedback
e
obtain sin θ e , cos θ e from look-up table 2 + Current controller + _ _
2/2 transform
Vector control
6
Fig. 7. Position feedback signal processing software structure.
Drive the motor ia, ib
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Electrical Angle (degree)
1000
ADC Result
800 600 400 200 0
360 300 240 180 120 60 0
0
2 4
0
6 8 10 12 14 16 18 20 22 24 26 28 30 32
2 4
6 8 10 12 14 16 18 20 22 24 26 28 30 32
Time (ms)
Time (ms)
(a) Position feedback waveform
(b) Position angle feedback waveform
360
360
300
300
Electrical Angle (dgree)
Electrical Angle (degree)
Fig. 9. Position feedback signals while motor start.
240 180 120 60 0
240 180 120 60 0
0
1
2
3
4
5
6
0
1
2
3
4
5
Time (ms)
Time (ms)
(a) The detected angle before compensation
(b) The detected angle after compensation
6
Fig. 10. Compensation of the position feedback signals.
the whole signal waveform. It can make the position feedback lose veracity. The signals’ zero-excursion can be modified through adding into feedback-loop in the circuit, but the temperature property problem of circuit components is still in existence. To the problem of low frequency amplitude modulation, because the position feedback signals are demanded to range from 0 to 2.5 kHz, it is difficult to be modified in the hardware. This problem can be worked out in software. The program can detect the maximum and minimum value of position feedback signal, calculate the amplitude and zeropoint that can be used during the next feedback signal’s period. Fig. 11 gives out the effect after such processing. The left curve shows the position feedback sampling signals, where Y-coordinate represents the sampling value. The normal value is between the up and down dash lines. The signals given in the figure are obtained after artificially modulation and magnify the variation of signal amplitude and zero-point. The right curve shows the position angle value. The calculation is based on the initial value in the first period, so the instantaneous angle is not too accurate. But the values of the following periods are more accurate, it shows that the automatic modulation in software is effective.
4.3. Elimination of position feedback disturbance Because the electromagnetic disturbance inside and outside the system, position feedback signals often contain peak disturbance that can make the position feedback signals have deviation. Fig. 12 shows that the peak disturbance in the position feedback signals results in large disturbance of the electrical angle obtained from calculation. This disturbance does not produce accumulating error, that is, it does not affect the final location precision. But it can affect the current reference at that time, then affect the system’s dynamic process. Dispose in circuit is difficult to eliminate this disturbance, so preventive steps should be adopted at the same time. Because the suddenness of the peak disturbance and wider frequency bandwidth of the position feedback signals, it is difficult to eliminate disturbance using routine digital filter such as FIR or IIR. Considering the process real time property, the authors have adopted several FIR and IIR digital filter to process the position feedback sampling signals. The effect was not good enough. Because the position feedback signals are approximate sine signals, the electrical angles obtained from calculation are approximate linearity. It is possible to use some
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360
900
Electrical angle (degree)
Position ADC feedback
1000 800 A B
700 600 500 400 300 200 100
300 240 180 120 60 0
0 0
5
10
15
20
25
30
0
5
10
Time (ms)
15
20
25
30
Time (ms)
Fig. 11. Software correction of the amplitude modulation.
1024
360
Position (elec. degree)
Position (ADC result)
896 768 640 512 384 256 128
300 240 180 120 60
0
0
0
5
10
15
20
25
0
5
10
Time (ms)
15
20
25
Time (ms)
Fig. 12. Effect of the disturbance in the position feedback signal.
if jDP ADn DP ADðn1Þ j > 500 DPADðn1Þ end if
then
P ADn ¼ P ADðn1Þ þ
Here, P ADn is the sampling value of position feedback signal on n point. DP ADn is the balance of previous and current sampling values: DPADn ¼ P ADn P ADðn1Þ . This rule can eliminate the great amplitude disturbance in feedback signals. Pn is defined as the electrical angle value on the nth point. And the increment between adjacent points is DPn ¼ P n P ðn1Þ . Then, let us define DPn4 as:
DPn4 ¼ ðDPn þ DPðn1Þ þ DP ðn2Þ þ DPðn3Þ Þ=4 According to the maximum acceleration the system can reached, the value of jDPn DPðn1Þ j should less than 2. Considering the noise, let jDP n DP ðn1Þ4 j < 32. Based on this opinion, the electrical angle values can be processed using following rules:
if jDPn DPðn1Þ4 j > 32 then Pn ¼ P ðn1Þ þ DP ðn1Þ4 end if 5. Application of the integrated position sensor Firstly, an optical rotary encoder coupled with the motor, is used to examine the precision of the proposed method. The encoder is an incremental one, and it can give out 4000 pulses per cycle. Fig. 13 is the tested result while the
360
Position/Electrical degree
experience-rules to eliminate great amplitude disturbance in the position feedback signals. This paper adopts the linearity reasoning forecast method to process the electrical angle for the aim to eliminate peak disturbance completely. To the process of position feedback signals, following rules is used:
300 240
Feedback Encoder
180 120 60 0 0.0
0.5
1.0
1.5
t/ms Fig. 13. Examination of the proposed position measurement unit.
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Reference model
+
-
Neural network + + • Position reference
• -
Position control
+
•
Speed control
T
+ Vector control
TL uA
s d
i * +
+
-
Current controller
s q
ω Motor
1 s
•
uB
i *
•
360
1000
300
800
Speed (r/min)
Position (mech degree)
Fig. 14. Structure of the 2-phase hybrid stepping motor vector control position servo system.
240 180 120
600 400 200
60 0 0 0
50
100
150
200
250
300
350
400
0
50
100
150
Time (ms)
200
250
300
350
400
Time (ms)
Fig. 15. Testing result of the vector control system (no load, 360°).
rotating speed of motor is constant, 800 r/min. The output signals of encoder are processed using the capture module of DSP, and the ADC module of DSP is used to implement the proposed method. In Fig. 13, the dash line represents the position angle measured by the encoder, and the real line is the position feedback obtained using the proposed method. The largest error between the two lines is less than ±1 pulse of the encoder, about ±0.09°. Then, the proposed integrated sensor is used in a 2-phase hybrid stepping motor vector control position servo system. Fig. 14 is the structure of the servo system. The position controller is IP controller. The neural network and model reference adaptive controller is used to avoid the influence of the system’s non-modeled non-linearity. The DSP TMS320F240 that can execute 20-million instruments per second is used to implement the control strategy and the sensor processing software. The integrated sensor and the proper control strategy make the system become a low-cost high-performance position servo system. Fig. 15 shows the testing results of the position servo system while the position reference is one circle (360°). The left curve is position response, and the right one is the change of rotating speed during the response time. The exact position feedback helps to maintain the orientation of vector control, and also helps to avoid the position error. The speed curve shows that, to track the position reference as soon as possible, the speed raises to enough value immediately. Therefore, the position response is even, fast, and has no stable error.
6. Conclusions The integrated sensor increases the length and weight of the motor, but the system is still simpler and cheaper than the position sensors used now. This type of position signal detection method has more complex mechanism than the sensorless methods. But the signal processing process is simpler and the precision is higher, and the rotor position can be detected anytime without influence of the motor’s situation. The integrated sensor also can be produced independent and as a normal position sensor for all kinds of rotating machines. With the help of the signal processing hardware and software, this kind of sensor can give out high precision.
Acknowledgment The authors are grateful for the support by the Natural Science Foundation of Henan Province through Grant No. 092300410164.
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