Proceedings VCM 2012 114 xây dựng hệ điều khiển véc tơ cho động cơ tự nâng kiểu mới

834 Nguyen Quang Dich and Nguyen Huy Phuong VCM2012 Development of Vector Control System for a Novel Self-Bearing Motor Xây dựng hệ điều khiển véc tơ cho động cơ tự nâng kiểu mới Nguyen Quang Dich and Nguyen Huy Phuong Hanoi University of Science and Technology e-Mail: dichnq@mail.hut.edu.vn Abstract: Magnetic bearing motors have many advantages such as no friction loss, no abrasion, no lubrication and so forth. However, they are not widely used due to their high cost, complex control and large size. In order to solve these problems, a self-bearing motor is a reasonable trend in current researches. This paper will introduce a salient permanent magnet type axial-gap self-bearing motor (ASBM), which is an electrical combination of an axial thrust bearing and an axial-flux motor, as well as the method of controlling axial position and rotating speed of the ASBM. First, the axial force and the motoring torque are analyzed theoretically and then the control method is derived. In order to confirm the proposed technique, an ASBM has been made and tested. The experimental results confirm that the ASBM works stably with the proposed vector control. Moreover, the rotating torque and the axial force can be controlled independently as well. Tóm tắt: Các động cơ sử dụng ổ từ thường có các ưu điểm như là không có tổn hao do ma sát, không có hao mòn, không cần bôi trơn Tuy nhiên động cơ dùng ổ từ lại thường không được sử dụng phổ biến hiện nay do chúng thường có kích thước lớn, hệ điều khiển phức tạp và giá thành cao. Để giải quyết những vấn đề này, động cơ tự nâng –động cơ điện có tích hợp chức năng của ổ từ - đang được nhiều nhà nghiên cứu quan tâm. Bài báo này sẽ giới thiệu một loại động cơ tự nâng kích thích vĩnh cửu loại từ trường dọc trục (ASBM) cũng như phương pháp điều khiển vị trí dọc trục và tốc độ quay của nó. Đầu tiên, lực nâng và mô men quay được phân tích về mặt lý thuyết, sau đó phương pháp điều khiển được giới thiệu. Để minh chứng cho phương pháp điều khiển được giới thiệu ở trên, động cơ ASBM được chế tạo và thử nghiệm. Kết quả thực nghiệm chỉ ra rằng ASBM hoạt động ổn định với phương pháp điều khiển vector được giới thiệu. Hơn nữa, mô men quay và lực nâng dọc trục có thể được điều khiển một cách độc lập với nhau. Nomenclature Name Unit Description g and z mm Air gap and displacement g 0 mm Air gap at equilibrium point F N Axial levitation force T Nm Rotating torque L sd , L sq H d and q-axis phase inductances of stator L sl , L fl H Leakage phase inductances of stator and rotor  sd ,  sq Wb d and q-axis fluxes of stator  m Wb Flux linkage  f Wb Permanet magnet flux i d , i q A d and q-axis controlled currents i do A Bias current W Magnetic field energy i f A Fictious rotor current Acronyms PM Permanet Magnet ASBM Axial-gap Self-bearing Motor 1. Introduction Recently, magnetic bearing motors have been designed to overcome the deficiencies of conventional mechanical bearing motors. They show the abilities to work in vacuum with no lubrication and no contamination, or to run at high speed, and to shape novel rotor dynamics. Therefore, they are very valuable machines with a number of novel features, and with a vast range of diverse applications [1]. The conventional magnetic bearing motor usually has structures like a rotary motor installed between two radial magnetic bearings or mechanical combination of rotary motor and radial magnetic bearing as shown in Figs. 1 and 2, in Tuyển tập công trình Hội nghị Cơ điện tử toàn quốc lần thứ 6 835 Mã bài: 177 which, two radial magnetic bearings create radial levitation forces for rotor, whilst an axial magnetic bearing produces a thrust force to keep the rotor in right axial position to the stator. However, these types of magnetic bearing motor are large size, heavy weight and complex control, which cause problems in some applications that have limit space [2],[3]. For this reason, simpler and smaller construction and less complex control system are desirable. The Earnshaw’s theorem shows that a rotor can be supported stably by static magnetic field when being controlled by one axis actively. Therefore, if a stator has capabilities of producing a rotating torque and controlling one axis actively, the non- contact levitation can be realized in small and simple structure. Based on this feature, an axial- gap self- bearing motor (ASBM) has been introduced as in Fig. 3. It is an electrical combination of an axial flux motor and an axial magnetic bearing, which is simpler in structure and control than the conventional magnetic bearing motor since hardware components can be reduced [4],[5],[6]. This type of motor can be realized as induction (IM) [5], or permanent magnet (PM) motor [6],[7],[8]. The PM type motor is specially paid attention, due to its high power factor, high efficiency and simplicity in production. In this paper, the salient 2-pole ASBM with double stators is introduced. The closed-loop vector control method for the axial position and the speed is developed in the way of eliminating the influence of each other. Moreover, the compensational method for reference currents based on the difference between d and q axis inductances is also recommended. In order to confirm the presented technique, an experimental setup has been made and tested. 2. Modeling and Control Fig. 4 illustrates the principle structure of the proposed axial gap self-bearing motor. The radial motions x, y, θ x , θ y of the rotor are constrained by radial magnetic bearings such as the repulsive bearing. Only rotational motion and translation of rotor along z axis are considered. The motor has two degrees of freedom. The rotor is a flat disc with permanent magnet (PM) inserted on two faces of disc to create a salient-pole rotor. Two stators, one in each side of the rotor, have three-phase windings to generate the rotating magnetic flux in the air gap that produces the motoring torque T 1 and T 2 to the rotor and generates the attractive force between the rotor and the stators F 1 and F 2 . The total motoring torque T is sum of those torques and the axial force F is different between two attractive forces. To get mathematical model of the ASBM, first, the axial force F s and motoring torque T s are calculated for one stator. Similar to the conventional permanent magnet motor, the mathematical model of the ASBM is also presented in rotor field oriented reference frame or Fig. 4. The principle structure of the axial gap self bearing motor. u-vw -w v -u w u d wqv 2 2 2 Rotor Stator Fig.5. Coordinates Fig. 1. Structure of conventional magnetic bearing motor. Fig.2. Structure of radial combined magnetic bearing motor Fig.3. Structure of axial gap self bearing motor 836 Nguyen Quang Dich and Nguyen Huy Phuong VCM2012 so-called d, q coordinates as indicated in Fig. 5, where the d axis is aligned with the center lines of permanent magnets and the q axis between the magnets. The axes u, v and w indicate the direction of the flux produced by corresponding phase windings. The power invariant principle is used for transforming between coordinates. The phase difference between the u axis and d axis is an angular position θ of the rotor or the rotor flux vector. Since the permanent magnet with unity permeability is used, the rotor is salient type, hence the self phase inductance of the stator is dependent on the rotor angular position, which means d axis inductance is different from q axis inductance. Furthermore, the self phase inductance is a function of the air gap g between rotor and stator. Normally, the self phase inductance is inversely proportional to the air gap, so the d and q axis phase inductance of the stator windings may be approximated by 0 0 3 2 3 2 sd sd sl sq sq sl L L L g L L L g              (1) in which 0 0 sd sq L ,L   are effective inductances per unit gap in d and q axis, and L sl is leakage inductance. Then, the stator voltage and flux of the ASBM in the d,q coordinates can be expressed in the following equations: sd sd s sd sd sq sq sq sq s sq sq sd sd m sd sd sd m sq sq sq di u R i L L i dt di u R i L L i dt L i L i                          (2) with  m is the flux linkage caused by rotor magnetic field. For simplicity, the permanent magnet of the rotor is replaced by an equivalent winding with current i f and inductance of rotor winding L f . It can be expressed only in d axis as follows f fd f f m sd i L L i      (3) with 0 3 2 sd f fl L L L g    (4) and mutual inductance 0 3 / 2 m sd L L g   (5) From (1) to (3), the magnetic energy in the air gap is calculated as ( ) / 2 f f sd sd sq sq W i i i       (6) Therefore, the attractive force of a stator is received by derivative of magnetic energy with air gap   2 0 2 0 2 2 3 3 4 4 sq sd s sd f sq L LW F i i i g g g          (7) and motoring torque of a stator is derived by using Fleming left hand rule 0 0 0 ( ) 3 ( ) 3 2 2 s sd sq sq sd sd sq sd f sq sd sq T P i i P L L PL i i i i g g            (8) with P is number of pole pairs. From (8) we can see that output torque is a combination of excitation torque and reluctance torque. That means, in every operation mode, the motor has to produce an additional torque to compensate the reluctance torque. In the non- salient pole rotor, this reluctance torque can be ignored to make control system become more simply. But in the salient pole rotor when the reluctance torque can reach the relative high amplitude, the neglect of this torque component will reduce the quality of system, especially in operation mode with axial load (i d ≠ 0). From (7) and (8) 1 F and 1 T are calculated by substituting 0 g g z   , 1 sd d i i  and 1 sq q i i  , and 2 F and 2 T are calculated by substituting 0 g g z   , 2 sd d i i  and 2 sq q i i  . Thus, the total axial force F and torque T are given by: 2 1 F F F   (9) 1 2 T T T   (10) here, 0 g is the axial gap at the equilibrium point and z is the displacement. For linearization at the equilibrium point (z = 0) we expand (9) and (10) into Mac Laurin series and take the first order term, the result is:         1 2 2 1 0 1 1 2 2 2 2 1 1 0 T q q T q q R d q d q R d q d q z T K i i K i i g z K i i i i K i i i i g         (11)                 2 2 2 2 2 1 2 1 2 2 2 2 2 1 2 1 0 0 2 2 Fd d f d f Fq q q Fd d f d f Fq q q F K i i i i K i i z z K i i i i K i i g g             (12) Tuyển tập công trình Hội nghị Cơ điện tử toàn quốc lần thứ 6 837 Mã bài: 177 in which 2 2 0 0 0 0 3 / 4 and 3 / 4 Fd sd Fq sq K L g K L g     are force factors, 0 0 3 /2 T sd f K PL i g    and   0 0 0 3 / 2 R sd sq K L L g      are torque factors. To increase the total moment twice the component moment created by one stator, the moment-generated current must be same direction and value. In order to keep the rotor in right position between two stators, the forces acting on rotor from both sides must be same value but inverse, i.e. under the effect of axial load, if the force-generated current of one side increases then that current of other side has to decrease the same amount, correspondingly. The rotating torque can be controlled effectively by using q-axis current, and the axial force can be controlled by changing the d-axis current. We suppose that 1 2 1 0 2 0 q q q d d d d d d i i i i i i i i i            (13) with i d0 is an offset current, and the value can be zero or a small value around zero, then by inserting (13) into (11) and (12), we receive 0 0 0 2 2 2 / T q R d q R d q eff rl rlz T K i K i i K i i z g T T T       (14)   2 2 2 2 0 0 0 0 4 ( ) 2 +4 ( ) Fd d d f Fd f d Fq q Fd f d d z F K i i i K i i K i g K i i i        (15) From (14), the total torque consists of three components: The first component 2 eff T q T K i  is the efficient torque, this is main component of the output torque. The second one 0 0 2 rl R d q T K i i  is the reluctance torque caused by bias current i d0 . Therefore, if we can assure that 1 2 d d d i i i     i.e. 0 0 d i  then this reluctance torque is eliminated. The last one 0 2 / rlz R d q T K i i z g  is reluctance torque caused by current i d under the effect of the displacement z. When the displacement is well controlled to be zero, or very small in comparison with air gap at the equilibrium point g 0 , the influence of this component can be neglected. Then the total torque becomes as follows 2 T q T K i  (16) By using above control law, we also receive the axial force as follows 4 Fd f d F K i i  (17) Obviously, the effect of the inductance difference to axial force is also vanished. From (16) and (17), it is easy to see that the total torque can be controlled with the quadrate axis current and axial force can be controlled with the direct axis current. And in combination with (1) the mathematic model of the ASBM is totally constructed with voltage, force and torque equations. It is supposed that they are simple linear equations, so the control system can be easily implemented with the conventional controllers. For simplicity, it is assumed that the radial motion of the rotor is restricted by ideal radial bearings. Therefore, the axial motion of the rotor is independent from radial motion. The dynamic equation of the axial motion of the rotor is Fig. 6. The control scheme of the axial gap self bearing motor. 838 Nguyen Quang Dich and Nguyen Huy Phuong VCM2012 F mz   (18) where m is mass of moving part, and F is the axial force shown in (15). Then by substituting (15) into (18), we receive   2 2 2 0 4 4 ( ) 4 Fd f d Fd d f Fq q z mz K i i K i i K i g      (19) or summarized as z m d mz K z K i    (20) with 2 2 2 4 ( ) 4 z Fd d f Fq q K K i i K i     is stiffness of the ASBM and 4 m Fd f K K i  is force gain. It is easy to realize that K z is negative, which means this system is unstable. To stabilize the system, the controller with derivative component must be used. Assuming that, the proportional derivative controller (PD) is used, the output of the controller will represent the direct axis reference current, i.e. d p d i K z K z     (21) with K p and K d are proportional and derivative constant of the axial position controller. By substituting (21) into (20), we get   0 m d z m p mz K K z K K K z       (22) The necessary condition for the system becomes stable only when all constant coefficients of the polynomial function are the same sign. Therefore, if K d > 0, the proportional constant must satisfy the condition 2 2 2 ( ) Fd d f Fq q z p m Fd f K i i K i K K K K i      (23) to ensure that the system is stable. Actually, there has steady-state error when only PD controller is used, hence to remove the steady- state error, the PID controller should be used. As stated above, the motoring torque of the ASBM can be controlled by q-axis current (i q ), while the axial force can be controlled by d-axis current (i d ). Therefore, the control scheme proposed for the ASBM drive is shown in Fig. 6. The axial displacement from the equilibrium point along the z-axis, z, can be detected by the gap sensor. The detected axial position is compared with the axial position command z ref , then the error is inserted in the axial position controller R z . The output of the axial position controller is used for calculating d-axis reference current with compensation procedure from (15). Position command z ref is always set to zero to make sure the rotor is right in the midpoint between the two stators. The d-axis reference currents for the two stator windings i d1ref and i d2ref can be generated by using the offset current i d0 subtracting and adding i dref respectively. In this paper, the value of the offset current is zero. The rotor speed detected from encoder is compared to the reference speed, then, the difference is input of the speed controller R ω . The output of the speed controller is used for calculating the q-axis reference current by using (14), the q-axis reference currents for the two stator windings are same with this current. The motor currents in the two-phase stator reference frame α,β are calculated by the measurement of two actual phase currents. Therefore, the d,q components are obtained using the rotor position from encoder. The quadrate components are controlled to the reference value which is given by the speed controller, while the direct components are controlled to the reference value which is given by the axial position controller. The outputs of the current controllers, representing the voltage references, are afterward directed to the motor through inverters using the Pulse Width Modulation (PWM) technique, once an inverse transformation from the rotating to the three phase stator referent frame has been performed. All controllers are standard PI controllers except axial position one (PID). 3. Implementation and Results 3.1 Hardware In order to confirm the proposed control method for the PM type ASBM, an experimental setup was set up which is shown schematically in Fig. 7. The rotor disc has a diameter of 50 mm and two neodymium iron magnets with the thickness of 1mm for each side are inserted into its surfaces to create one pole pair. For experimental simplicity, the rotor is supported by two radial ball bearings in order to restrict the radial motion of the rotor. The stator has a diameter of core 50 mm and six concentrated wound poles, each with 200 coil turns. The stators can slide on linear guide to ensure the same desired air gap between rotor and two stators. A DC generator (Sanyo T402) is installed to give the load torque. In order to measure the rotor angle and the axial position, a rotary encoder (Copal RE30D) and an eddy- Fig. 8. Picture of the experiment setup. Tuyển tập công trình Hội nghị Cơ điện tử toàn quốc lần thứ 6 839 Mã bài: 177 current-type displacement sensor (Sentec HA- 101S) are installed, respectively. The control hardware of the ASBM drive is based on a dSpace1104 board dedicated to control of electrical drives, which includes PWM units, general purpose input/output units (8 ADC and 8 DAC) and encoder interface. The DSP reads the displacement signal from the displacement sensor via an A/D converter, and the rotor angle position and speed from the encoder via an encoder interface. Two motor phase currents are sensed, rescaled, and converted to digital values via an A/D converter. Then, the dSpace1104 calculates reference currents using the rotation control and axial position control algorithms and send its commands to three-phase inverter board. The ASBM is supplied by two three-phase PWM inverters with switching frequency of 40 kHz. The image of the experimental setup is presented in Fig. 8 and the parameters of the ASBM is shown in table 1. Table 1 Parameters of the ASBM Stator phase resistor Rs = 2.6Ω Stator phase d- axis inductance per unit air gap 6 8.2 10 Hm sd0 L     Stator phase q- axis inductance per unit air gap 6 9.6 10 Hm sq0 L     Leakage inductance 3 6 10 H sl L    Air gap at equilibrium point 0 1.7 g mm  Rotor mass m = 0.235 kg Rotor inertia J = 0.000086kgm 2 Rotor flux Pole pair 1 3.2 Experimental Results Fig. 9 shows the response of axial displacement and speed when the ASBM starts Figure 7. Overview of control hardware of the ASBM. Fig. 9. Response of displacement and speed at start Fig. 10 Response of displacement when speed changed 840 Nguyen Quang Dich and Nguyen Huy Phuong VCM2012 to work. First, the displacement error is 0.32mm. When the controllers is on, the displacement jumps immediately to zero and the rotor speed reaches 1500 rpm after 0.5s without influence of each other. In the second experiment, the influence of rotor speed to the displacement is conducted by changing speed from 1500rpm to 1000 rpm and vice versa. The result is shown in Fig. 10. Obviously, the displacement controller and speed controller work independently with each other. 4. Conclusion The axial gap self bearing motor was fabricated with salient PM type rotor and the vector control was implemented. The results confirm that the motor can perform both functions of motor and axial bearing without any additional windings. Furthermore, by using this proposed control method, the axial displacement and speed are independently controlled. Thank to these advantages, the ASBM can be used for many kind of applications, which require small size, high speed and levitation force such as liquid pumps, compressors and machine tools. Tài liệu tham khảo [1] M. Dussaux, “The industrial application of the active magnetic bearing technology,” in Proc. 2nd Int. Symp. Magnetic Bearings, Tokyo, Japan, July 12–14, 1990. [2] A. Chiba, T. Deido, T. Fukao and M. A. Rahman. “An analysis of bearingless AC motors”, IEEE Trans. Energy Conversion, vol. 9, pp. 61-67, Mar. 1994. [3] Y. Okada, K. Dejima and T. Ohishi, “Analysis and comparison of PM synchronous motor and induction motor type magnetic bearing”, IEEE Trans. Industry Applications, vol. 32, pp. 1047-1053, Sept./Oct. 1995. [4] Y. Okada, S. Ueno, T. Ohishi, T. Yamane and C. C. Tan, “Axial type self bearing motor for axial flow blood pump”, Int. Society for Artificial Organs vol. 27, pp. 887-891, 2003. [5] S. Ueno and Y. Okada, “Vector control of an induction type axial gap combined motor- bearing”, in Proc. of the IEEE Int. Conf. on Advanced Intelligent Mechatronics, Sept. 19- 23, 1999, Atlanta, USA, pp. 794-799. [6] S. Ueno and Y. Okada, “Characteristics and control of a bidirectional axial gap combined motor-bearing”, IEEE Transactions on Mechatronics, Vol. 5, No. 3, Sept. 2000, pp. 310-318. [7] D. Q. Nguyen and S. Ueno “A study on axial gap self bearing motor drives”, Proc. of the Int. Symposium on Micro/Nano system technology, CD Rom, Dec. 2008. [8] D. Q. Nguyen and S. Ueno “Sensorless speed control of a permanent magnet type axial gap self bearing motor”, Journal of System Design and Dynamics, Vol. 3, No. 4, July 2009, pp. 494-505. [9] A. E. Fitzgerald, C. Kingsley Jr., and S. D. Uman, Electric Machinery, 5 th edition, McGraw-Hill, New York,1992. [10] A. Chiba, et. al., Magnetic Bearings and Bearingless Drives, 1 st edition, Elsevier, Great Britain, 2005. Quang Dich Nguyen was born in Bac Ninh, Viet Nam. He received the B.S. degree in electrical engineering in 1997 from Hanoi University of Technology, Ha Noi, Viet Nam, M.S. degree in electrical engineering in 2003 from Dresden University of Technology, Dresden, Germany and Ph.D. degree in Mechatronics at Ritsumeikan University, Shiga, Japan. From 2000 he joined the Department of Industrial Automation, Hanoi University of Technology. His main interests include magnetic bearings, self- bearing motor, sensorless motor control. Huy Phuong Nguyen was born in Hanoi, Vietnam. He received the B.Sc (1996), M.Sc (1997) and Ph.D (2000) degree in Automaion Industry from Moscow Power Engineering Institute of Russian Federation. From 2002 he joined the Department of Industrial Automation, Hanoi University of Science and Technology. His main interests include automatic control and process control in power plant. . Quang Dich and Nguyen Huy Phuong VCM2 012 Development of Vector Control System for a Novel Self-Bearing Motor Xây dựng hệ điều khiển véc tơ cho động cơ tự nâng kiểu mới Nguyen Quang Dich and Nguyen. biến hiện nay do chúng thường có kích thước lớn, hệ điều khiển phức tạp và giá thành cao. Để giải quyết những vấn đề này, động cơ tự nâng động cơ điện có tích hợp chức năng của ổ từ - đang được. phương pháp điều khiển được giới thiệu. Để minh chứng cho phương pháp điều khiển được giới thiệu ở trên, động cơ ASBM được chế tạo và thử nghiệm. Kết quả thực nghiệm chỉ ra rằng ASBM hoạt động ổn