教育资料（2021-2022年收藏的）英文固定框架的横向磁通永磁机电流控制策略

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1、Stationary-frame current control strategy for transverse flux permanent-magnet machine.Wang Jian kuan(王建宽)，CUI Wei(崔巍)，JIANG JianZhong(江建中）School of Electromechanical Engineering and Automation, Shanghai University, Shanghai 200072, P. R. ChinaAbstract A new stationary-frame AC current control strat

2、egy that can eKminate steady-state errors is discussed and applied to the control of transverse flux permanent-magnet machine (TFPM). Based on the principle of modulation and demodulation, this AC controller can achieve the same frequency response characteristic as the equivalent DC controller. VaHd

3、ity of the TFPM control system using this current control strategy is confirmed with simulation results.Keywords transverse flux permanent-magnet machine (TFPM), current controller, stationary frame, modulation.1. IntroductionOver the last decades, with the rapid developments in power electronics, p

4、ermanent magnetic materials, and manufacturing and applications of modern permanent magnet motors have been made significant progress. Among them, transverse flux permanent-magnet machine (TFPM) with relatively high torque density and low speed, which can avoid gearing configurations, is especially

5、suited for direct drive such as full electric ship, electric vehicle, and industrial robots. Compared with conventional machines, TFPM has a number of favorable featurest: (1) It has unique three-dimensional flux pattern leading to decoupling of space requirements of the flux carrying core iron path

6、 and the space occupied by armature winding. This permits applications of small pole pitches， leading to high current loading and high force density.(2) Each of the machine phases is entirely separated, and therefore does not couple electromagnetically with other phases.(3) Low vibration signature a

7、nd high reliability are achieved by increasing the number of machine phases.Due to these advantages, design work is carried out to maximize the torque density for these machines. However, in order to make full use of these machines, their control also needs to be optimized.As a novel invert-fed sync

8、hronous permanent-magnet (PM) machine, the design of current controller is an important issue for high-performance motor drivers. Over the iast few decades research on current control for power inverters has been intensive. When the reference current is a direct signal as in DC motor drives, zero st

9、eady-state error can be secured by using a conventional proportional-integral (PI) controller. When the reference current is a sinusoidal signal as in AC motor drives, however, straightforward use of the conventional PI controller would lead to steady-state errors due to finite gain at the operating

10、 frequency. Appling the Park transform, a synchronous-frarae PI controller was then proposed which guarantees zero steady-state error in a three-phase system.However, transverse flux PM machine can not meet the Park transform due to the fact that the machine phases axe entirely decoupled. To solve t

11、he problem, this paper introduces and applies a new P+Resonant stationary frame current controller in the TFPM control system which achieves zero steady-state error since it has an infinite gain at the resonant frequency. The resonant frequency is adjusted in term of the output current fundamental f

12、requency. In the TFPM control system, control error between the input current and its reference is applied to this current controller and its output signal is applied to the pulse width modulation (PWM) pattern generator as the reference signal for input phase voltage of the transverse flux PM machi

13、ne.2. Model of transverse flux PM machineA single phase TFPM proposed by Weh is illustrated in Fig.l. The stator is composed of several U-shape cores. The stator windings lie transverse to the axial length in parallel with rotor, whereas in the conventional machines the windings lie in the longitudi

14、nal plane. The rotor is composed of several vertical blades and PM with opposite polarity.Modeling is one of the most important steps in analytical analysis and control design in TFPM. BecauseTFPM phases are entirely separated, the per-phase voltage equation is the same and given as follows, from wh

15、ich the saturation effect and loss of the iron are excluded: （1）where x is phase number, ux is phase voltage, R is armature resistance, ix is armature current, Xpx is armature flux linkage. where Lx and are armature inductance and PM flux linkage respectively.Suppose that the predominant component o

16、f the PM flux linkage is very close to a cosine shape and the rotor position 0 with respect to the aligned position of stator. Thus, the armature flux linkage equation becomes (2)where and are the maximum PM flux linkage value and the electrical angle of rotor respectively.When the armature inductan

17、ce Lx is not change with the rotor position, substitute (2) into (1). The voltage equation can be expressed as (3)With the rotor rotating at synchronous speed, the electrical angle of rotor can be written where w is the electrical angular frequency of the rotor. The back electromotive force (EMF) ca

18、n be expressed as (4)The pre-phase input power of TFPM is calculated: (5)According to the above energy balance equation，the first item in the right side of (5) represents the power dissipated in the stator resistance. The second item corresponds to the rate change of magnetic emergy stored in the in

19、ductance, which does not contribute to output power being converted from electrical to mechanical form. Dividing (5) by the mechanical speed ，the instantaneous electromagnetic torque can be obtained: (6) where p is the number of pole pairs.Under the steady-state condition, to a TFPM prototype with t

20、wo-phase axially arranged and radically shifted by 90 electrical angle, sinusoidal armature current of the two phases is applied. Suppose the instantaneous armature current is given as(7)where Im is the amplitude of the armature current, and S the initial phase angle between The total torque is prod

21、uced by the sum torque of two phases respectively, (8)According to (6)(8)，the torque equation can be express as (9)The dynamic equation governing the speed of the machine is (10)where is the load torque, the damping coefficient, and J the moment of inertia.3. Principles of stationary frame current c

22、ontrollerFor an AC control system, the key limitation of most stationary frame linear current control system such as the PI control system is their inability to eliminate steady-state error. In 5，a stationary frame AC current controller was proposed, which does achieve zero steady-state error withou

23、t the complex transformation of a synchronous frame controller and can be directJy applied to single system. This control strategy is based on the technique of modulation and demodulation, and obtained by transforming the DC type controller into an equivalent AC controller.3.1 Modulation and demodul

24、ation techniqueFVom the modulation and demodulation theory, the modulating signal is multiplied by reference sine and cosine waveforms that shift the harmonic content at that frequency to DC and double-frequency:Taking Fourier transform, these become Now if ，the real and imaginary components have in

25、formation present at DC and at the double- frequency, if these signals are low-pass filtered the output signals becomeFig.2 illustrates how the modulation and demodulation principle defined by (11)(16) can be implemented to achieve an AC current controller for a single-phase sinusoidal system. The t

26、ransfer function plays dual roles of providing regulation action and filtering the double-frequency.The modulation and demodulation process illustrated in Fig.2 can be express in the time-domain bywhere “*” denotes convolution, The process in this form can be ako represented byThus, (18) becomes ( 1

27、9 )The Laplace transforms of the expressions in the braces of (18) areThe Laplace transform of the demodulation theorem can be expressed asFinally the transfer function of this system is produced by summing A and B:Equation (25) allows generation of the AC transfer function for any given DC transfer

28、 function and these transfer functions have the same frequency response characteristic in their bandwidth of concern.3.2 Realization of the stationary frame controller for TFPMA major objective for stationary frame AC current controller is to achieve zero steady-state error. Prom the above analysis,

29、 the stationary frame current controller with zero steady-state error will be obtained by transforming a DC controller that achieves this goal into the equivalent AC controller.For a DC system, a conventional PI transfer function can achieve the desired objective of zero steady-state error. Hence, u

30、sing the transform of (25), an equivalent stationary frame AC current controller has the transfer function ofwhere fcp， are the gains of proportional controller, integral controller and resonant controller respectively, and u;o denotes the resonant frequency of the AC current regulator. Fig.3 shows

31、the control block diagram of this stationary frame AC current controller for the TFPM. In Fig.3, R and Lx are the resistance and inductance of the TFPM, and Exo is the back electromotive force (EMF). is the transfer function of.the PWM inverter and assumed to be unity, = 1, From Fig.3, the transfer

32、function from the reference signal of the AC input current to its actual value Ix is given bywhere is the transfer function of the stationary frame AC current controller given by (27). Substituting into (28)，we can obtain the control characteristics at the resonant frequency : From the above equatio

33、n we can see that the AC input current Ix coincides exactly with its reference in steady-state. This means that the steady-state control error in AC system can be eliminated completely. We also note that regardless of the values of the control parameters and and the TFPM parameters Lx and R.4.Simula

34、tion investigationUsing the MATLAB/Simulink packages, the control system of TFPM based on this stationary frame current controller discussed in this paper has been simulated. Fig.4 shows the model, where /ref is current reference， Ia, Ib are two phase output current, W is angular frequency, Te is el

35、ectromagnetic torque, Ts is the sample period of the model, Thea is the angular frequency, V is the DC voltage. In Fig.4 the machine induction Lx is 16 mH, the resistance R is 0.064，the number of pole pairs is 15，and the DC bus voltage is 300 V.Fig.5 shows the steady-state and transient simulated wa

36、veforms of one phase current ix and the reference current i* when P，PI and P+resonant controller were used for driving the TFPM. Fig.5(a) shows that there is steady-state magnitude error and no phase error when only P controller was used. Fig.5(b) shows that thereare both magnitude and phase steady-

37、state error when the PI controller was used. Fig.5(c) shows that there is almost no steady-state error when the stationary frame P+resonant controller was used. From the simulation results, we can conclude that the application of t,his new stationary frame current controller to TFPM is satisfactory.

38、 Compared to the conventional stationary frame P and PI controller the improvement in steady-state performance is clear.5.ConclusionIn this paper, a new stationary frame current controller for driving TFPM has been discussed. Simulation model of this control system was established. Effectiveness of

39、the current control strategy has been confirmed by theoretical investigation and simulation results. Due to the infinite gain at the resonant frequency, the control strategy can completely eliminate the steady-state error of AC current. As a new type PM synchronous machine, the current frequency of

40、TFPM varies with the machine rotate speed. Thus the resonant frequency must adjust according to the rotate speed of the TFPM.References1 Lu K Y, RlTCHIE E，RASMUSSEN P O，SANDHOLDT P. Modeling a single phase surface mounted permanent magnet transverse flux machine based on Fourier series method C/IEEE

41、 Covference on Electric Machines and Drives, IEMDC03, Madison, Wisconsin, USA. Piscataway: Institute of Electrical and Electronics Engineers, Inc., 2003, 2: 1609-1613.FRENCH C D，HODGE C, HuSBAND M. Optimized torque control of marine transverse-flux propukion machines C/IEE International Conference o

42、n Power Electronics, Machines and Drives, Edinburgh. S.L: IEEE, 2002: 16.MARIAN P K, LuiGl M. Current control techniques for three-phase voltage-source PWM converters: a survey J. IEEE Transaction on Industrial Electronics 1998，45(5): 691-702.WEH H. Transversal Flow Machine in Accumulator Arrangemen

43、t: United States America, 5051641 P. 1991， 1-8.ZMOOD D N. Stationary frame current regulation of PWM inverters with zero steady-state error Jj. IEEE Transactions on Power Electronics, 2003, 18(3): 814- 822.FUKUDA S. A novel current-tracking method for active filters based on a sinusoidal internal model J. IEEE Transactions on Industry Applications, 2001, 37(3): 888-895.WANG JlAN-KUAN, SHI JlN-HAO1 JlANG JlAN-ZHONG. Model and simulation of transverse flux permanent- magnet machine and control system J. Smail and Special Electrical Machine, 2006, 34(4): 5-7