Proceedings of 2016 IEEE International Conference on Mechatronics and Automation August 7 - 10, Harbin, China
Research of PMSM Fuzzy Direct Torque Controller Based on Sliding Mode Observer GAO Ya School of Electronic Information Engineering
GAO Yi School of Electronic Engineering
Xi'an Technological University Xi’an, Shaanxi Province, China
[email protected]
Xi’an Shiyou University Xi’an, Shaanxi Province, China
[email protected] calculation and needs the statistical parameters of random errors those are obtained by a series of debugging test. Whereas, sliding mode observer has a full adaptability for the change of system parameters, the disturbance of external environment and internal perturbations. It has a low request for mathematical model of system, fast dynamic response, and it is easy to project implementation. Now, there is a wide application [6-8]. Thirdly, high frequency voltage or current injection method those are based on salient-pole effect [9]. Although this method can be applied to a wide speed range and has an exact estimate result in low speed, but there are multiple filters those make time lag and the result is to make dynamic performance of motor bad. Furthermore, injection of high-frequency signal brings into high-frequency noise and need special hardware support. Aiming at the big torque and flux linkage ripple problem of traditional PMSM DTC system, this paper introduces the fuzzy controller in pre-system, and uses it to replace the hysteresis-loop comparator and fractionize the error value. That will give birth to a more appropriate stator voltage. In this paper, in order to reduce the number of fuzzy rules, the method of stator flux linkage angle mapping is used to make the control system easy. In the new system, uses SVPWM to modulating voltages. From the principle of DTC system, we know that the veracity degree of stator flux linkage value has a large influence, and it is very important for the whole control system. So, the full-order state observer for stator flux linkage was designed to reduce the dc drift, integral error accumulation and other shortcomings. According to PMSM mathematical model, a new position observing system was designed based on sliding mode theory in this paper, and the observing signal was used in PMSM DTC control system. This design replaced the traditional switch functions with continuous saturation functions in the sliding mode observer. The results showed that system performance of fuzzy control system with SVPWM is better than the system performance of traditional DTC with SPWM, and the sliding mode observer are feasibility and accuracy.
Abstract - In this paper, fuzzy control is introduced to reduce the big flux linkage and torque ripple of traditional PMSM DTC system. Simultaneously, using SVPWM to modulating voltages, using the full-order state observer to replace the integral part of the stator flux linkage observer, those method effectively reduce the dc drift, the integral error accumulation, other shortcomings and modulation precision. Moreover, a new position observing system was designed instead of the traditional position sensor in this control system. This design replaced the traditional switch functions with continuous saturation functions in the sliding mode observer, and the result showed the high frequency noise signal could be reduced effectively. By the experimenting for the traditional PMSM DTC system with stator flux linkage integral observer and the PMSM fuzzy DTC system with full-order state observer and sliding mode observer those are designed in this paper, the results show the control performance of the new fuzzy DTC system is better than the one of traditional DTC system evidently. The stator flux linkage and torque ripple of new system are decreased significantly. The new sliding mode observer could accurate observing position signal. Index Terms - Permanent magnetic synchronous motor, Fuzzy control, Full-order state observer, Sliding mode observer, Space vector pulse width modulation.
I. INTRODUCTION Direct torque control (DTC) is a new high-performance AC frequency conversion control technology, it is based on the space vector control theory. It has a very well application in controlling of asynchrony motor[1-3]. So, DTC has been researched hotspot in the field of PMSM in recent years. Permanent magnet synchronous motor has a lot of advantages, such as simple structure, small size, light weight, high efficiency and moment of inertia etc. Currently, there are three sensorless detection methods those are used widely. Firstly, the method is to calculate the position according to the electromagnetic internal relationship of motors or the current, voltage and electromotive force (EMF) internal relationship. However, this method is sensitive to the change of motor parameters, and it is not accurate in lower speed. Secondly, the method is EMF estimation that is based on observer. Such as the Kalman filter observer and sliding mode observer, etc. [45]. But the algorithm of Kalman filter observer is complicated. It needs matrix inversion that is large
978-1-5090-2396-7/16/$31.00 ©2016 IEEE
II. THE FUZZY DTC OF PMSM SYSTEM BASED ON THE SLIDING MODE OBSERVER
17
Comparing with the vector control, DTC don’t need to make the mathematical model of motor decoupling, and emphasizes the direct control for motor torque. It utilizes the discrete hysteresis-loop comparator to generate PWM signal that can be used to control the switching state of inverter directly. But it makes use of the relay character of the hysteresis-loop comparator, and can not accurately distinguish the error values for the torque and flux linkage. So, it can’t generate an appropriate switching vector. Consequently, it makes the torque and flux ripple of system larger [3].
/ 3 as the voltage base value, standardize the above equation, known: Ts ( 3U D U E ) °T1 (4) 2 ® °T2 TsU E ¯
Take the maximum phase voltage V
DC
Making use of the above step, the working time of the other bridges can be obtained. Lastly, use the seven-segment method of bilateral space vector modulation to assign the working sequence of the other bridges. (Fig.2 is the working sequence of bridges in the first sector. )
A. The Principle of SVPWM The SVPWM principle is how to generate an ideal round magnetic field by reference voltages vector. The vector is formed by using eight kinds switch state of threephase inverter. The output voltage utilization ratio is high, it does not cause harmonic current. Fig.1 shows the 8 kinds of switch state which include six effective voltage vectors U1 ~ U 6 and two zero voltage vectors U 7 , U8 .
T0 4
T1 2
T2 2
T0 2
T2 2
T1 2
T0 4
U7
U1
U2
U8
U2
U1
U7
A
B C Fig 2. The working sequence of bridge in the first sector
B. The Position Estimating of Sliding Mode Observer Based on the mathematical model of PMSM, a new sliding mode observer of position was designed in PMSM fuzzy DTC system. The inputs of sliding mode observer are stator current and stator voltage in DE coordinate axis. The next is the designing process of sliding mode observer. The mathematical model of PMSM in DE coordinate axis is:
Fig 1. Space Voltage Vector and Sector
For example, in the first sector of Fig.1, the synthesis expressing of voltage space vector is: U sTs U1T1 U 2T2 U 0 T0 U sTs U1T1 U 2T2 Or (1) In above equation, T1 Ε T2 are the working time of U1 Ε U 2 vector;
ª diD « dt « « diE ¬« dt
ªiD º 1 ª uD º 1 ª eD º «i » « » « » ¬ E ¼ Ls ¬ uE ¼ Ls ¬ e E ¼
keZr sin T keZr cos T
(5) (6) (7)
In above equation , iD , iE , uD , uE , eD and e E express the stator current , stator voltage and reverse electromotive force in DE coordinate axis respectively; Rs is resistance; Ls is inductance; k is the coefficient of reverse
of U1 Ε U 2 and U 0 in a specific time period. Form the above equation, it can be showed: T1 T2 °U s T U1 T U 2 (2) s s ® °T T T T 1 2 0 ¯ By vector decomposing in DE coordinate, known:
T2 U 2 sin 60q Ts
Rs Ls
eE
reference vector. equation 1.8 shows the U s Integration effect in Ts is the same with the synthetic Integration effect
T T1 U1 2 U 2 cos 60q Ts Ts
eD
respectively; T0 is the working time of zero Ts is the discrete sampling period; U s is the
°U D ° ® °U °¯ E
º » » » ¼»
e
electromotive; Zr is speed of motor; T is the position angle of motor. Simplified (5)is: (8) i Ai Bu Be According to mathematical model of PMSM, designed a sliding mode observer that stator current was regarded as the state variable. The expressing equation is: (9) iˆ Aiˆ Bu Bk w sign (iˆ i )
(3)
18
iˆ is the estimating value of stator current i ; k w is the switch coefficient of sliding mode observer. In above equation, the sign can be expressed: sign (iˆ i )
1 ° ®0 ° ¯ 1
iˆ i ! 0 iˆ i 0 iˆ i 0
fractionizes the original voltage vector signal. Fig.3 shows the block diagram of PMSM fuzzy DTC system based on the full-order state observer for stator flux linkage. In the fuzzy controller, the method of stator flux linkage angle mapping was introduced to reduce the number of fuzzy rules.
(10)
Z* ˇ Z
The new design used the continuous saturation function sat (iˆ i ) instead of the above switch function sign(iˆ i ) to decrease shaking. The equation is: sat (iˆ i )
1 ° ˆ ® k (i i ) ° 1 ¯
iˆ i '
Equation (9) can be expressed as: iˆ Aiˆ Bu Bk w sat (iˆ i )
1 '
iˆ i
Uses (12) to subtract (8): er Aer Be Bk w sat (er )
T*
ˇ
Fuzzy Controlled
ˉ ˇ
Udc
ua ub
SVPWM
uc
Inverter of Voltage Source
ˉ
- S / 6 , S / 6 ] likeΰ21α. So, only one table needs to be looked for, and the result is added a certain value that value represents the GLIIHUHQWUHJLRQVRIDQJOHșLQIX]]\FRQWUROOHU7KDWmethod can achieve the same effect as looking up the whole table, reduce the number of rules, and make the system's response time shorten. Tab. I LVWKH UXOH WDEOH RI ș LQ [- S / 6 , S / 6 ]. «¬ »¼ represents adopting the next nearest integer.
T'
S» « T » S« 6 T « » 3« S » ¬
a. the amplitude of stator flux linkage (Wb/ms) b. torqueΰN·m/msα Fig.6. the experimental results of the PMSM fuzzy DTC with full-order state observer and sliding mode observer
The position comparing curves are shown in fig.7.a and fig.7.b. Fig.7.a shows the position estimate value that is got by integral observer according to mathematical model of control system and the position realistic value that is got by sensor at the beginning of the experiment. Fig.7.b shows the position estimate value that is got by sliding mode observer and the position realistic value. Comparing Fig.7.a with Fig.7.b, it shows the sliding mode observer is better than the integral observer in terms of accuracy and rapidity.
(21)
3 ¼
III. EXPERIMENTAL AND SIMULATING RESULTS
E
rotor position (rad)
This paper established the PMSM fuzzy DTC system with full-order state observer for stator flux linkage and sliding mode observer. The motor parameters are: rated voltage U=160V, rated speed n=1500 r/min, P = 4, Rs =0.62ȍ Ld = Lq = 2.075*10-3 H, J= 3.617*10-4 kg·m2, 0.002 , < f =0.08627Wb. When t =0 s, set the load
time (s)
Te =1N·m; when t =0.002s, set the load Te =2N·m. Fig.5.a and Fig. 6.a show two stator flux linkages in two different control methods separately. Fig.5.b and Fig.6.b show two torques o two different control methods separately. Fig.5.b and Fig.6.b show: when the system is the accelerating process in the beginning, the torque is maximum value. When the speed reaches the set value, the final torque will be close to the load torque through some adjustment. Fig.5 is the experimental result of the traditional DTC system with integral observer. Fig.6 is the experimental result of the fuzzy DTC system with fullorder state observer and sliding mode observer. Comparing and analyzing the two results show: the torque and stator flux linkage curves of fuzzy DTC system are better than the traditional DTC system’s significantly. In other words, the performance of fuzzy DTC system is better than the traditional DTC system.
rotor position (rad)
(a) integral and actual curves
time (s)
ΰbαsliding mode observer and actual curves Fig.7.The actual position curve and two observer position curves
IV. CONCLUSION In this paper, designed a PMSM fuzzy DTC system with full-order state observer for stator flux linkage and sliding mode observer of the senorless position observing system. This sliding mode observer replaced the traditional switch functions with continuous saturation functions. The observing result was used in the control system of PMSM with SVPWM. By experimenting for the traditional PMSM DTC system and PMSM fuzzy DTC system, the results show that the performance of improved control system is better than pre-control system. In other words, the stator flux linkage and torque ripple of the improved control system decrease significantly.
a. the amplitude of stator flux linkage(Wb/ms) b. torqueΰN·m/msα Fig.5. experimental results of traditional PMSM DTC with integral observer
ACKNOWLEDGMENT
20
[4] Qiu Albert, Wu Bin. Sensorless control of permanent magnet synchronous motor using extended Kalman filter[C]. Canadian Conference on Electrical and Computer, 2004, 3: 1557-1562. [5] Bolognani S, Tubiana L, Zigliotto M. Extended Kalman filter tuning in sensorless PMSM drives[J]. IEEE Transactions on Industry Applications, 2003, 39 (6): 1741-1747. [6] Ding Kun. Active power factor correction using sliding mode control with reaching law [C]. Second IEEE Conference on Industrial Electronics and Applications,2007:1165-1167. [7] Huang Fei, Pi Youguo. Study of Position Sensorless Control for Permanent Magnet Synchronous Motor Based on Sliding Mode Observer[J]. Computing Technology and Automation, 2009, 28(2): 3236. [8] Kye Lyong Kang, et al. Sensorless control of PMSM in high speed range with iterative sliding mode observer[C] IEEE Applied Power Electronics Conference and Exposition APEC, 2004, 2: 1111-1116. [9] Jia Hongping, He Yikang. Study on inspection of the initial rotor position of a PMSM based on high-frequency signal injection[J]. Proceedings of the CSEE, 2005, 25(15)Κ15-20. [10]ZHU Jing. Fuzzy control principle and application[M]. Beijing:China MachinePress,1998.
This research was supported by grants from the Agricultural Technology Innovation and Research Project of Shaanxi Province, China (No. 2016NY-164); This research was supported by grants from the Agricultural Technology Innovation and Research Project of Shaanxi Province, China (No. 2016NY-164); The Project Supported by Natural Science Basic Research Plan in Shaanxi Province of China (No. 2014JM2-6093). REFERENCES [1] Mario Pacas,Jürgen Weber. Predictive Direct Torque Control for the PM Synchronous Machine [J]. IEEE Transactions on Industrial Electronics, 2005,52(5):1350-1356. [2] Thomas J Vyncke, RenéK Boel, Jan A A Melkebeek. Direct Torque Control of Permanent Magnet Synchronous Motors-An Overview[C]. 3RD IEEE Benelux Young Researchers Symposium in Electrical Power Engineering, Ghent, Bel-gium,2006. [3] JainA K, MathapatiS, RanganthanVT, eta.l Integrat-ed starter generator for 42-V powernet using induction machine and direct torque control technique[J]. IEEE Trans on PowerElectronics. 2006, 21(3):701-71.
21
