A Special Flux-weakening Control Scheme of

PMSM - Incorporating and Adaptive to Wide-Range Speed Regulation

Song Chi, Student Member, and Longya Xu, Fellow IEEEDept. of Electrical and Computer Engineering

The Ohio State University2015 Neil Avenue

Columbus, OH 43210 USA

Abstract- This paper presents a special flux-weakeningcontrol scheme for permanent magnet synchronousmachines (PMSM) over wide speed range. In contrast toconventional two-loop (d-, q-axis) control methods, theproposed control scheme achieves both flux-weakening andspeed control simultaneously using only one speed/flux-weakening controller. The controller automaticallygenerates both the required demagnetizing and torque-producing currents based on the crossing-coupling effectsbetween d- and q-axes. Additional futures of the proposedcontroller include 1) not requiring knowledge of motorparameters and dc bus voltage of power inverter, and 2)preventing saturation of the current regulators under anyload conditions. Therefore, this scheme is adaptive to thevariation of motor parameters and load levels. Theeffectiveness of the proposed control scheme is verified byboth computer simulation and experimental results.

Keywords-flux weakening; PMSM; adaptive

I. INTRODUCTION

Permanent magnet synchronous machine (PMSM)drives have been increasingly used in a wide variety ofindustrial applications due to their high power density andefficiency, high torque to inertia ratio and high reliability.In high-performance applications, PMSM can readilymeet sophisticated requirements such as fast dynamicresponse, high power. Recently, the continuous costreduction of magnetic materials with high energy densityand coercitivity makes the ac drives based on PMSMmore attractive and competitive. This has opened up newpossibilities for large-scale application of PMSM. Acontinuous increase in the use of PMSM drives will bewitnessed in the near future [1-3].The advantages of PMSM recently make them highly

attractive candidates for traction and residential driveapplications, such as hybrid electrical vehicles (HEV) orelectrical vehicles (EV) and washing machines. ThePMSM drive systems for such applications normallyrequire high starting torque and wide speed range as wellas high efficiency and power density. In order to satisfy

these requirements, PMSMs are operated not only in theconstant torque region when the speed is below the basespeed but also in the constant power region over a widespeed range. In this way, the cost and size of the motordrive can be significantly reduced. The constant torqueoperation can be easily achieved in PMSM drives byconventional vector control. However, when the speed isabove the base speed, the back-EMF of PMSM is muchlarger than the line voltage so that the PMSM suffers fromthe difficulty to produce torque due to the voltageconstraints. Thanks to the flux-weakening technology, theoperating speed range can be extended by applyingnegative field stator current component to weaken the air-gap flux [4, 5].

In general, permanent magnet synchronous machineswith approximate sinusoidal back-EMF (electromotiveforce) can be broadly categorized into two types [5]: 1)interior (or buried) permanent motors (IPM) with saliencyand 2) surface-mounted permanent motors (SPM) withoutsaliency. Both IPM and SPM can be operated in theconstant power region by flux-weakening technologies toan extended speed range. Various control algorithms forflux weakening have been published.Macminn and Jahns presented two control techniques to

enhance the performance of the IPM drive over anextended speed range. Although the proposed feed-forward compensation and flux-weakening algorithmswere combined to improve the torque productioncapability of the IPM in high speeds, full effectiveness ofthe techniques heavily depended on accurate machineparameters, and the performance degraded noticeably aserrors between the programmed and actual parametersincreased [6].

Dhaoudi and Mohan researched a current-regulatedflux-weakening method by introducing a negative currentcomponent to create a d-axis flux in opposition to that ofthe rotor permanent magnets, resulting in a decreased air-gap flux. This armature reaction was used to extend theoperating speed range of a PMSM and relieve the currentregulator from saturation in high speeds [7]. Similarly, a

1-4244-0449-5/06/$20.00 ©2006 IEEE IPEMC 2006

current vector control to expand the operating limits underthe constant inverter capacity and the improvement bydecoupling feed forward compensation were proposed in[8, 9] respectively by Morimoto et al. With these flux-weakening schemes, the required demagnetizing currentcomponent was calculated based on the mathematicalmodel of PMSMs and, consequently, the performance ofthe PMSM drive system was seriously affected by thesystem parameters and sensitive to operating conditions.

Sozer and Torrey [10] presented an approach foradaptive control of the surface mounted PM motor over itsentire speed range. The adaptive flux-weakening schemewas able to determine the right amount of direct-axiscurrent at any operating conditions without knowing theload torque and inverter parameters. The level ofdemagnetizing current was obtained by using the currenterror between the actual and reference currents.Integration of the error with a proper forgetting factor wasused to drive the direct-axis current.

Y. S. Kim et al, J. M. Kim et al and J. H. Song et alrespectively proposed a flux-weakening control algorithmbased on a voltage regulator using the voltage errorsignals between the maximum voltage and the voltagecommand [11-13]. The output of the voltage regulatordetermined the required mount of the demagnetizingcurrent. In addition, the onset of flux weakening could beadjusted to prevent the saturation of the current regulatorsrequired by the vector control of PMSM.

Both current-error- and voltage-error-based flux-weakening methods require an additional PI regulator orintegrator to generate the demagnetizing currentcommand. However, the added regulator could onlyoperate properly in the tuned conditions, which is noteasily reached, resulting in the increased complexity of theoverall control system.

Conventionally, two current regulators are alwaysrequired to achieve torque (q-axis current) and flux (d-axiscurrent) control as in [14]. Unfortunately the d- and q-axis currents cannot be truly controlled independently dueto the cross-coupling effects inside the PMSM. The cross-coupling effects increase with the speed and becomedominant in the high-speed flux-weakening region. As aresult, the performance of current and torque response isdegraded without good decoupling control.

In the paper, a novel flux-weakening control of PMSMincorporating wide-range speed regulation is presented.The cross-coupling effect between d- and q-axis current isre-examined and a speed/flux-weakening controllerproposed. The controller is able to achieve the closed-loopspeed control and flux weakening control simultaneously,which simplifies the control algorithm by using only onecurrent regulator. The proposed control scheme does notrequire the knowledge of motor parameters and dc busvoltage of the power inverter. In addition, saturation ofcurrent regulation is prevented under any load conditions,showing control robustness in high speeds. Computersimulation results are presented to show the control

performance and robustness with respect to disturbancesfrom load and dc bus voltage. An experimental setup isbuilt based on a PMSM without saliency. Experimentalresults are used to demonstrate the effectiveness of theproposed approach.

II. MATHEMATICAL MODEL OF PMSM IN THESYNCHRONOUS REFERENCE FRAME

The dynamic equations of a PMSM in the synchronousreference frame with d-axis aligned to the actual rotormagnets can be expressed in the matrix form as

Fvds1FRs+PLs -Or *Lq 1 Fids lK FOl110SjL hi) .R + p ) sLs 0) d Rs pL s lqs

(1)

In steady state, the equations are reduced to

kds s CO Ry q ds +K r

whereVds, Vqs d-axis, q-axis stator voltage;ids, iqs d-axis, q-axis stator current;Ld, Lq d-axis, q-axis stator inductance;Rs stator resistance;Ke back-EMF constant, or magnetic flux

linkage per phase;(Or rotor speed.

The developed electromagnetic torque Te in terms ofstator currents is expressed as

Te =2 P [Ke iqs +(Ld -Lq)'qsdds] (3)

where p is the number of pole pairs.From (2), we can find the cross coupling effect between

ids and iqs~which is expressed in

Ci-_ Ld i+vqs-Ke Mr- r dRs

Equation (4) clearly shows that the iqsJids cross couplingbecomes stronger when the rotor speed, Wir, is higher.When Lq = Ld = Ls, referring to surface-mounted

PMSM without saliency, (3) and (4) can be rewritten as

Te =2 P Ke iqs

_ _ ()r Ls . + Vqs-Ke*Orqs - R ds R+

(5)

(6)

As shown in (3), Te consists of the torque componentscontributed by the permanent magnets and reluctance.When only the magnet-contributed torque is produced as

(4)

in SPM, (5) applies. In order to increase the efficiency ofoverall PMSM drive system, it is obvious that themaximum torque per ampere can always be achievedunder the current and voltage constraints.

III. CURRENT AND VOLTAGE CONSTRAINTS IN FLUX-WEAKENING REGION

In general, the required terminal voltage of a PMSMincreases as its speed goes high. However, the maximumavailable voltage VsmaX applied to the PMSM is alwayslimited by the fixed dc bus voltage. Also the maximumcurrent hmax is limited by the thermal ratings of both theinverter and the stator windings of the PMSM. Suchconstraints can be expressed in

2 2 2

qs c/Vs - Vsmaxi 2 i 2 < I 2

liqs +dis s max

a control strategy that the q-axis current iqs, or torque, canbe controlled by means of controlling ids, adaptive to theload and operating speed. Fig.2 shows a speed controlblock diagram including an adaptive speed/flux-weakening controller based on the above control concept.The speed/flux-weakening controller is but not limited toa PI regulator. The input signals are actual speed andspeed error. And the outputs are ids command and anenabling signal to the FWC Mux. The actual speeddetermines the onset of flux weakening, while the speederror determines the id command.

M-xlmu Torque per --

/Voltage Limit //Ellipse~VLMT1 ./

w.r.tw .' L_ \(w 1< w2) \(7)

Neglecting the stator resistance, we can rewrite thevoltage limit equation as

2 Ld 2 Ke )2 Vs max ) 2iq5 + ( ) (ids + <).( m )Lq Ld COrLq

(8)(a) IPM

Maximu Torque perAmp. Trajector

,1 Voltage Lim..itCircle VLMTI

w.r.t ,I(,,I < w2)From (7) and (8), we can see that the current limit

equation determines a circle with a radius of hmax whilethe voltage limit equation determines a series of nestedcircles (Lq = Ld) or ellipses (Lq > Ld).

Fig. 1 shows the current-limit circle CLMT and thevoltage-limit ellipses/circles VLMT1, 2 in the id-iq plane.The voltage-limit circles centering at Point "A" (-Ke/L, 0)with the radius become smaller as the speed .), increases.The maximum torque-per-ampere trajectory is alsoillustrated by a bold and piecewise curve from Origin "O"to Point "A". When a PMSM is operated from the start upto the base speed CoJ in the constant torque region, thevoltage limit ellipse/circle meets the intersection of themaximum torque-per-ampere curve and the current limitcircle CLMT. The PMSM cannot be operated beyond thebase speed without flux-weakening control. To extend thespeed range, a proper demagnetizing current has to beapplied according to its operating speed so that the currentvector trajectory can move along the maximum torque-per-ampere curve from B to A, corresponding to the speedchanging from CoJ to infinite, assuming K/Ls < ismax.

IV. ADAPTIVE FLUX-WEAKENING CONTROLLER

Define VFWC= vqs = const., and consider (4), we get

i=_rO)Ldi VFWC KeOir (9)qs RS RS

Examining (9), we can see that at the specific speed cor.there exists a linear relationship between iqs and ids,

showing the iqs-ids cross coupling. This equation suggests

(b) SPM

Figure 1. Current-limit CLMT, voltage-limit ellipse/circle VLMT1,VLMT2 and maximum torque per ampere trajectory in the id-iq plane.

In the constant torque region, one speed regulator andtwo current regulators (referring to iqs-and id5-regulator)are used in the synchronous reference frame. The threeregulators work together for the speed control below thebase speed as in conventional vector control systems [6]-[8]. When the speed increases near but still less than thebase speed, the system starts to smoothly switch into flux-weakening operation using the proposed adaptivecontroller. Thereafter, speed control is achieved by thespeed/flux-weakening controller and the ids currentregulator. The ids current command (i.e. id in Fig. 2)generated by the speed/flux-weakening controllercomprises not only the required demagnetizing currentcomponent but also the torque-related component definedby (9). In this way, the cross-coupling effect is utilized tocontrol the torque as well as flux weakening, instead ofbeing purposely eliminated in conventional systems.

It should be noticed that there is a tradeoff between themaximum torque capability and efficiency of the PMSMas using the proposed flux-weakening controller.

f A

CurretLimit Circ]lCLMT

VLMT'w.r.t w'

:- Ke lIL,

C-retLi .. t Circle\CLMT

VLMT~w.r.t w~

According to the load torque profile, VFWC can beproperly selected to meet the requirements of torque andefficiency.

In the paper, VFWC = 0.5 (p.u.) is selected for thecomputer simulation and experimental testing.

Vd*

nSpeedjb

tdjb

Figure 2. Block diagram of the adaptive flux-weakening control

V. SIMULATION AND EXPERIMENTAL RESULTS

A. Simulation resultsA PMSM drive system has been simulated by

Simulink/MatLab. The parameters of PMSM were: R, =

16 ohm, Ls= 60 mH and Ke = 0.22 Vs/rad. The base speedwas 250 rpm. The onset of the flux-weakening operationwas 0.2 in per unit. The speed base was 1250 rpm andcurrent base was 7A.

Figs.3 and Fig.4 show the simulation results when themotor was running up from 0 to 1000 rpm and stayed for0.5 s and then slowed down to 0 with a constant load of 1

Nm.

&5 1 1.5 2 2.5

0.3

0.2

0.1

M-0

-02

:03

Current Trajectory in the Synchronous Frame

-05 -0A4 -03 -0.2 -01 0 01

id (p u)

Figure 4. Current vector trajectory in the synchronous id-iq planeduring speeding up

The dc bus voltage was 3 10V. We can observe theautomatically generated demagnetizing current id, andgood performance of speed control within the entire speedrange.

Fig.5 shows the robustness of the system with respect tothe disturbances from load and dc bus voltage. In thesimulation the motor was accelerated from 0 to 500 rpm

and stayed after. The dc bus voltage was initially 310Vand ramped to 320V in 2 s. and then down from 320V to280V. The load was initially 0 Nm and stepped to 1 Nm.in 2.5 s. We can observe that the speed regulation in theflux-weakening region functioned very well. It shows thatthe proposed scheme is adaptive to the variation of dc busvoltage and load condition.

0 0.5 1,6 2 25 3 3.5 4 4

0 0.5 t.5 2 25 3 1.5 4 4.5 5- 1

co-l

nu r =

OUSE 1 1.5 2 25E65li

6_

65 L

0 05 1 15 2 25Time (s)

Figure 3. Speed command and feedback (up), ids (2nd), iqs (3rd) andstator phase current ias (5.0 A/div, bottom)

Figure 5. Speed command and feedback (up), Vdc (2nd), zoomed speedcommand and feedback (3rd), ids (4th), iqs (5th) and stator phase current

ias (5.0 A/div, bottom)

4 4b

03 1.5 2 25 3 3.5 4 43 5

UA4

-n 4,

B. Experimental resultsThe proposed flux-weakening control scheme was

verified by an experimental PMSM drive systemincluding: 1) a 48-pole non-saliency outer-rotor PMSMwith its base speed of 250 rpm, 2) a DSP controller basedon an eZdspF2812 DSP board, 3) a three-phase powerinverter and 4) a dynamometer coupled with the shaft ofthe PMSM as load. The switching frequency of powerinverter was 20kHz. Space vector PWM was used for thePWM generation. The dc bus voltage of the powerinverter was 3 10V and the maximum current was 7A. Thesampling frequency of the current and voltagemeasurement was 20 kHz. The parameters of PMSMwere same as in the computer simulation.

Figs.6 and 7 show the experimental results when themotor was accelerated from 50 to 1025 rpm and stayed for25 s and then down to 50 rpm. The dc bus voltage variedbetween 320V and 280V due to operating conditions. Theload was 0.5 Nm. We can observe the automaticallygenerated demagnetizing current ids and the goodperformance of speed control within the wide speed rangeincluding flux-weakening region. Comparing the resultsof computer simulation and those of experimental testing,it is clearly seen that the experimental results agree withthe simulation results very well, indicating that theproposed adaptive flux-weakening control scheme is validand the real-time implementation of the speed/flux-weakening controller is successful.

OS05/09/18 1 7:37 :5 1lOk

n1 n

oIUPptU I vn/U' 0/ OO

Figure 6. Speed command and feedback (757 rpm/div, up), ids (1.7A/div, 2nd), iqs (1.7 A/div, 3rd) and stator phase current ias (1.0 A/div,

bottom), 10 s/div

Current Trajectory in the d-q plane

X. 04 2 0.2

X4 X ~~~~~~~~~~~~~~0.4

(p ui

Figure 7. Current vector trajectory in the synchronous id-iq planeduring speeding up

VI. CONCLUSIONS

In this paper, a special adaptive flux-weakening controlscheme incorporating wide-range speed regulation ispresented. No knowledge of motor parameters and dc busvoltage of power inverter is required, indicating that thisscheme is adaptive to the variation of system parametersand load levels. The automatically generateddemagnetizing current by the proposed speed/flux-weakening controller satisfies both flux-weakeningoperation and torque control based on the cross-couplinginherent to PMSMs. The robustness and stability of thesystem has been demonstrated. In addition, the two-controller structure for both flux and speed controlreduces computation time in real-time implementation.The effectiveness of the proposed flux-weakening controlscheme and the speed control performance of thespeed/flux-weakening controller have been verified byboth computer simulation and experimental results.

ACKNOWLEDGMENT

This work was supported by the Research andEngineering Center of Whirlpool.

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