advanced torque and current control techniques for pmsms

IEEJ Journal of Industry ApplicationsVol.5 No.2 pp.167–173 DOI: 10.1541/ieejjia.5.167

Paper

Advanced Torque and Current Control Techniques for PMSMs with aReal-time Simulator Installed Behavior Motor Model

Ryo Tanabe∗ Student Member, Kan Akatsu∗ Member

(Manuscript received May 18, 2015, revised Oct. 2, 2015)

This paper presents advanced torque and current control techniques for Permanent Magnet Synchronous Motors(PMSMs) with a real-time simulator which has a nonlinear motor model. This model is called “Behavior motormodel”, and it is developed based on finite element analysis results considering non-linear characteristics that includespatial harmonics and magnetic saturation. The real-time simulator is implemented within a circuit simulator that cou-ples the behavior motor model with switching circuits in real-time, and it can be applied to torque and current control asan advanced controller. In this paper, the torque and current control of a PMSM with the proposed system is presented.Effectiveness of this technique is verified by performing simulations and experiments.

Keywords: Behavior motor model, PMSMs drive system, real time simulator

1. Introduction

Permanent Magnet Synchronous Motors (PMSMs) havebeen widely used in various industrial applications due totheir high efficiency and high power density characteristics.

In general, PMSMs drive systems are developed based onsimplified mathematical model. In this model, the distribu-tions of the inductance and linkage flux density due to ro-tor magnets are assumed as sinusoidal. Consequently, thedq transformation method gives simple voltage and torqueequation expressed with constant motor parameters. Be-cause of this modeling, PMSMs drive system can be eas-ily constructed by controller design techniques for DC ma-chines. However, PMSMs typically have nonlinear char-acteristics such as the spatial harmonics and magnetic sat-uration (1) (2). The nonlinear characteristics degrade the per-formance of torque and current control based on simplifiedmathematical model because this drive system is controlledas a linear system.

In PMSMs which have the nonlinear characteristics, thepulsating torque is caused by interaction between excitationcurrent and spatial harmonics in the linkage flux. Torqueripples may degrade speed and position control and causelarge acoustic noises and vibrations. In previous researches,the optimal current command for the torque smoothness areachieved by developing torque controllers with mathematicalmodel which has spatially dependent machine parameters hasbeen proposed (3)–(5). However, this technique requires amountof off line data for look up tables. If the magnetic saturationis also taken into account the machine parameters depend onnot only the position but also current amplitude. This maycause the model construction to be complicated.

Furthermore, the realization of the optimal excitation cur-rent to achieve torque smoothness requires high performance∗ Shibaura Institute of Technology (M & E Energy Conversion

Lab.)3-7-5, Toyosu, Koto-ku, Tokyo 135-8548, Japan

current controller. The current feed-forward control gives op-timal voltage commands to achieve desired current based oninverse PMSMs model. The current feed-forward controllerhas already been developed in the linear system (6)–(8). How-ever, in the case of nonlinear machine, the inverse model can-not give optimal voltage commands because of the nonlinear-ity of the machine. Precise voltage equation model can be ob-tained by considering the nonlinear characteristics (9). How-ever, as previously noted, the model construction is muchcomplicated.

This paper presents advanced torque and current controltechniques by using a real time simulator (high speed calcu-lator) which has a precise PMSMs model. Precise PMSMsmodel is created by Finite Element Analysis (FEA) whichcan take into account the spatial harmonics and magnetic sat-uration. In the previous research, this model is called as a“behavior motor model” and this model is applied to a cir-cuit simulator such as MATLAB/Simulink. In this paper, thecoupling analysis between the behavior motor model and thecircuit simulator is installed in the real time simulator as acontroller of PMSM drive system. Therefore, the controllerenables to achieve the advanced control method by using theinstantaneous analysis results. In this paper, torque ripplecontrol and high performance current control based on a feedforward control of PMSM by using the proposed techniqueis presented. Effectiveness of this technique is verified byperforming some experiments.

2. Conventional PMSM Control System

In this section, the linear model of PMSM is firstly intro-duced. In general, the control system is developed by sim-plified mathematical model which is presented linear charac-teristics of PMSM in dq synchronized rotor reference frame.The torque equation is described as follow:

Te = Pn{Ψd + (Ld − Lq)id}iq · · · · · · · · · · · · · · · · · · · · · · (1)

where Te, Pn, Ψd, Ld, Lq, id and iq, are torque, the number

c© 2016 The Institute of Electrical Engineers of Japan. 167

PMSM Control Using Real-time Simulator Installed Behavior Model（Ryo Tanabe et al.）

Fig. 1. Conventional PMSM control system

of pole pairs, d-axis linkage flux due to the rotor magnets,d-axis inductance, q-axis inductance, d-axis armature currentand q-axis armature current, respectively. In case the d-axiscurrent is a constant value, the torque has a linear character-istic with q-axis current.

The voltage differential equation is described as follow:[vd

vq

]=R

[idiq

]+

[Ld 00 Lq

]ddt

[idiq

]+ωe

([0 − Lq

Ld 0

] [idiq

]+

[0Ψd

])

· · · · · · · · · · · · · · · · · · · · · (2)

where R and ωe are the armature resistance, and angularelectrical velocity, respectively. The current dynamics is de-scribed by differential equation based on (2) as follow:

ddt

[idiq

]=

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣− R

Ld

ωeLq

Ld

−ωeLd

Lq− R

Lq

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦[idiq

]+

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣1Ld

0

01Lq

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦[vd

vq

]−⎡⎢⎢⎢⎢⎢⎢⎢⎣

0ωeΨd

Lq

⎤⎥⎥⎥⎥⎥⎥⎥⎦· · · · · · · · · · · · · · · · · · · · (3)

Figure 1 shows the block diagram of PMSMs control sys-tem which has torque and current controller based on (1) and(3).2.1 Conventional Torque Control The torque con-

trol generates current command due to torque constant un-der an assumption that the relationship between torque andcurrent is a linear characteristic (if d-axis current is zero).Therefore, the current command is generated as constantvalue according to torque command. However, in this con-trol, the pulsating torque is caused because the relationshipbetween current and torque is not linear by spatial harmonicsof PMSM.2.2 Conventional Current Control The current con-

trol works to achieve the current command. In general, the PIcontroller and decoupling controller are designed based on(2) is used as current controller. However, this controller mayexhibit bandwidth limit and is not suited to cover the full crit-ical range of harmonics frequencies. Therefore, the desiredcurrent is not completely excited. Adding that, this controlcannot achieve a fast response because of its bandwidth lim-itation.

3. Proposed Nonlinear Control System

In this section, a proposed nonlinear control system basedon FEA is described. The proposed control system is devel-oped based on a behavior motor model which presents non-linear characteristics of PMSMs. The behavior motor modelhas 3-D table data of inductance, magnet flux and torque asthe function based on current amplitude, current phase androtor position (10).

In general, the construction of 3D-table data requires somecomplex processes such as the data interpolation. How-ever, in this research, acquisition, interpolation, and construc-tion of the machine parameter data are automatically imple-mented by computer software with the FEA (JMAG-RT pro-duced by JSOL Corporation is used in this research). Inaddition, the behavior motor model is easily applied to thecircuit simulator such as MATLAB/Simulink. This couplingmethod is implemented as a controller of PMSM drive sys-tem by using a real time simulator. This controller can takeinto account nonlinearities of not only tested machines butalso external drive circuits.

In the proposed method, the sampling period is requiredas fast as possible because the FEA motor model uses rotorposition signal to consider spatial harmonics. The accuracyof rotor position signal brings effectiveness of the spatial har-monics information. The sampling time should be decideddepend on the data amount of the coupling circuit.3.1 Drive System Setup Figure 2 shows the ex-

perimental set up. Drive system developed by MAT-LAB/Simulink with the behavior motor model is installed inthe real time simulator (LT-RTSimII produced by DSP Tech-nology Co. Ltd is used in this research). The real time simula-tor communicates with fast A/D converter to take the analogsignal of actual system into the real time simulator. The realtime simulator outputs the PWM pulses to the voltage sourceinverter. The tested motor is rotated at a constant speed bya servo motor system. In addition, the behavior motor mod-els and tested motor are synchronized each other by detectingthe rotor position.3.2 Verification of the Behavior Motor Model Fig-

ure 3 shows tested motor models. Specifications of the tested

168 IEEJ Journal IA, Vol.5, No.2, 2016


Fig. 2. Drive system setup

(a) Model A (b) Model B

Fig. 3. Test motor models

Table 1. Specification of test motor model

(a) Cogging torque waveforms and FFT results

(b) Load torque waveforms and FFT results (d-axis current is0 A, q-axis current is 4 A, and rotation speed is 300 min−1)

Fig. 4. Characteristics comparison of Model A

motors are shown in Table 1. Model A and Model B are usedfor torque ripple control and current control tests.

Figure 4 shows the characteristics comparison betweenthe behavior motor model and tested motor of model A. Asshown in Fig. 4(a), the cogging torque waveform and FFTresults calculated by the behavior motor model correspondswith the tested motor output. As shown in Fig. 4(b), thebehavior motor model can simulates 24th and 48th harmon-ics component which are main component of torque ripples.

(a) U phase back EMF waveforms and FFT results (Rotationspeed is 500 min−1)

(b) U phase current waveforms and FFT results (Current is 2 A,Current phase is 30 degree and rotation speed is 1000 min−1)

(c) d, q-axis inductance

Fig. 5. Characteristics comparison of Model B

From these results, the behavior motor model can calculateprecise output torque includes ripples. Therefore, this modelgives accurate estimated instantaneous torque.

Figure 5 shows the characteristics comparison betweenthe behavior motor model and tested motor of model B. Asshown in Fig. 5(a), the U-phase back EMF waveform andFFT results calculated by the behavior motor model corre-sponds with output of tested motor. In Fig. 5(b), the U-phasecurrent waveform calculated by the behavior motor model isalmost identical with excitation current of the tested motor. InFig. 5(c), q-axis inductance which is calculated by behaviormotor model corresponds with inductance which is measuredfrom tested motor includes magnetic saturation characteris-tics. From these results, the behavior motor model can calcu-late precise instantaneous motor behavior including nonlinearcharacteristics. Therefore, this model enables to design theinverse model and to estimation of the instantaneous currentof the tested motor in the current control.

4. Proposed Torque Control

In this section, a proposed torque control is described. Fig-ure 6 shows the system of the proposed torque ripple con-trol. In the proposed torque ripple control, the instantaneoustorque is estimated by the behavior motor model from thesimulated excitation current. This estimated torque includescharacteristics of torque ripple. The current command gener-ated by the torque controller is the optimal current to achievetorque smoothness. Therefore, the torque ripple is reducedcompared with the conventional one. In addition, the excita-tion current which is applied the behavior motor model is es-timated in the real time simulator. Hence, the gain of torquePI controller can be high because noises which are gener-ated by sensors are not included in the system. In the sim-ulation, the voltage signal is output by ideal voltage source.



Fig. 6. Proposed torque control system

(a) Conventional method (Without torque ripple control)

(b) Proposed method (With torque ripple control)

(c) FFT results

Fig. 7. Experimental results of torque ripple control(Output torque is shown in left side and q-axis currentis shown in right side)

In fact, the output voltage is generated by voltage source in-verter. Therefore, the output includes 6th harmonics due todead time and voltage drops witch is not considered in sim-ulation. However, the 6th harmonics of the torque ripple dueto the inverter is much smaller than the torque ripple due tospatial harmonics. Thus, the 6th harmonics generated by in-verter is negligible in this paper. In the proposed method,optimal current command is just calculated in the simulation.Then, current control works to achieve excited current of the

Table 2. Experimental condition of torque control

actual motor with current reference. It means the effects ofthe voltage drops of the device can be ignored.

Figure 7 shows the experimental results of the conventionaltorque control and the proposed torque ripple control. Thecondition of this verification is shown in Table 2 and mo-tor model A is used for the experimental test. As shownin Figs. 7(a) and (b), it is confirmed that the torque rippleis compensated by the proposed torque ripple control. Espe-cially in Fig. 7(c), the 24th and 48th harmonics componentsare greatly reduced. As shown in Fig. 7(b), the pulsating cur-rent as the optimal current to achieve torque smoothness isconfirmed.

Therefore, using the estimated instantaneous torque by thebehavior motor model enables to reduce the torque ripple.From these results, the proposed torque ripple control whichuses the real time simulator installed behavior motor modelis verified to be reducing the torque ripple of PMSM.

Even in the case of using reluctance torque, the d-axis cur-rent reference should be given, the q-axis current reference iscalculated by the PI regulator as optimal current reference toreduce torque ripple include the reluctance torque.

5. Proposed Current Control

In this section, a proposed current control is described.Figure 8(a) shows the control system of the proposed cur-rent control which is consisted of the inverse model designpart, voltage limit compensation part and PI feed-back con-trol part. Figure 8(b) shows a block diagram of the volt-age limit compensation part. The inverse model design partworks for generating optimal voltage command to achievedesired current using precise motor parameters obtained fromFEA. In this research, this system is called as an “inverse



(a) Perspective of proposed current control system

(b) Voltage limit compensation part

Fig. 8. Proposed current control system

behavior motor model”. The feed forward voltage commandis calculated using precise motor parameters obtained fromFEA and (2) as follow:[

v∗dFFv∗qFF

]= R

[i∗di∗q

]+

[Ld(i∗ ,θ) 0

0 Lq(i∗ ,θ)

]ddt

[i∗di∗q

]

+ ωe

([0 − Lq(i∗ ,θ)

Ld(i∗ ,θ) 0

] [i∗di∗q

]+

[0

Ψd(i∗ ,θ)

])

· · · · · · · · · · · · · · · · · · · (4)

where v∗d, v∗q, i∗d, i∗q, Ld(i∗ ,θ), Lq(i∗ ,θ) and Ψd(i∗,θ) are the d-axisvoltage command, q-axis voltage command, d-axis currentcommand, q-axis current command, d-axis inductance ac-cording to d-axis, q-axis current and rotor position, q-axisinductance according to d-axis, q-axis current and rotor posi-tion, and d-axis linkage flux due to rotor magnets accordingd-axis, q-axis current and rotor position, respectively. Thoseparameters have influence of magnetic saturation and spatialharmonics because of dependence of current and rotor posi-tion. Therefore, this part can generate optimal voltage com-mand without modeling errors.

However, the inverse behavior motor model cannot con-sider the voltage limitation due to DC link voltage. Becauseof the voltage limitation, the ideal current response in tran-sient state is not achieved and the controller does not cor-rectly work. The inverse behavior model calculates optimalvoltage command under the assumption that instantaneouscurrent before sampling accordance with current reference.In the case of the voltage saturation, this assumption is notachieved. To be correct operation, the compensation part

makes accordance instantaneous current with current refer-ence.

In the proposed controller, the compensation voltage com-mand is generated from the error of between current refer-ence and estimation instantaneous current in the voltage limitcompensation part. The compensation voltage command iswritten in discrete system as follow:

[v∗d comp[k+1]v∗q comp[k+1]

]=

[Ld(i∗ ,θ)[k+1] 0

0 Lq(i∗ ,θ)[k+1]

]1Ts

[i∗d[k] − idMB[k]

i∗q[k] − iqMB[k]

]

· · · · · · · · · · · · · · · · · · · · (5)

where v∗d comp, v∗q comp, Ts, and k are d-axis compensationvoltage command, q-axis compensation voltage command,sampling time, and number of sampling, respectively. If DClink voltage is enough, this compensation part does not work.

In general, using the differential operation is usually diffi-cult to calculate because of noises of sensors. However, in theproposed current controller, the differential operation of thecurrent is estimated by the behavior motor model, the actualcurrent detected by the current sensor is not used for this al-gorithm. Therefore, the voltage limit compensation part doesnot effect to the stability by using the signal generated in thereal time simulator. Hence, the desired current can be excitedand this control achieves fast response. In addition, the cur-rent PI controller part will work to compensate disturbanceswhich are not considered in the real time simulator such asthe error of the modeling due to temperature variation.

The voltage command is calculated based on feed forwardvoltage command, compensation voltage command and feed



(a) Convention method (Current feedback control)

(b) Proposed method (Current feed forward control with currentfeedback control)

(c) FFT results

Fig. 9. Experimental results of current control in steadystate (U-phase voltage waveform is shown in left side andU-phase current waveform is shown in right side)

back voltage command are expressed as follow:[v∗d[k+1]v∗q[k+1]

]=

[v∗dFF[k+1]v∗qFF[k+1]

]+

[v∗d comp[k+1]v∗q comp[k+1]

]+

[v∗dFB[k+1]v∗qFB[k+1]

]

· · · · · · · · · · · · · · · · · · · · (6)

where, v∗dFB and v∗qFB are d-axis feed back voltage commandand q-axis feed back voltage command, respectively.

Figure 9 shows the experimental results of the conventionalcurrent control and the proposed current control in the steadystate. The condition of this verification is shown in Table 3and the motor model B is used for the experimental test. Asshown in Figs. 9(a), (b) and (c), in the conventional currentcontrol, U-phase current is distorted by spatial harmonics.In the proposed current control, the harmonics in U-phasecurrent are reduced in comparison with conventional one.Also in the proposed current control, the voltage commandis pulsating because the voltage commands are generated toachieve the desired current.

Figure 10 shows the experimental results of the conven-tional current control and proposed current control in thetransient state. The condition of this verification is shown inTable 3. As shown in Fig. 10(a), the proposed current controlcan achieve the fast response in comparison with the conven-tional one. In Fig. 10(b), the proposed current control utilizesthe maximum level of the limited voltage until the currentagrees with the command to achieve the fast response be-cause the voltage limit compensation part gives maximum

Table 3. Experimental condition of current control

(a) q-axis current response (b) dq-axis voltage

Fig. 10. Experimental results of current control in tran-sient state

voltage command to correspond with the command on nextsampling step.

From these results, the proposed current control which usesthe real time simulator installed the inverse behavior motormodel can achieve good tracking performance in the steadystate, and can achieve fast response in the transient state.

6. Conclusion

This paper presented the advanced torque ripple controland current control based on precise motor model called as“behavior motor model”. The circuit simulator installed thebehavior model is applied in the real time simulator to de-velop the advanced PMSM drive system. This system canrealize these advanced controls taking the nonlinear charac-teristics of tested motor into account. The proposed torqueripple control based on the instantaneous torque estimationby the behavior motor model can give the optimal currentcommand to achieve smooth torque because the behavior mo-tor model can estimate the instantaneous torque including thetorque ripples according to spatial harmonics. The proposedcurrent control based on the inverse behavior motor modelcan achieve the desired current because the inverse modeluses precise motor parameters to generate the optimal voltagecommands. In addition, this control achieved fast current re-sponse with consideration of the voltage limitation. Based onthe experimental verification, the proposed advanced torqueripple control and current control implemented by the realtime simulator proved higher performance than the conven-tional ones.

References

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Ryo Tanabe (Student Member) was born Ishikawa, Japan in 1991.He received the B.S. degrees in electrical engineeringfrom Shibaura Institute of technology, Tokyo, Japan,in 2014. His research interests include the advancedcontrol system and method of Permanent magnet syn-chronous motors.

Kan Akatsu (Member) received the B.S., M.S., and Ph.D. degreesfrom Yokohama National University, Japan, in 1995,1997, and 2000, respectively, all in electrical engi-neering. In 2000, he joined the Nissan Research Cen-ter, Yokosuka, Japan, where he contributed to thedesign and analysis of the new concept permanent-magnet machines. In 2003, he joined the Departmentof Electrical and electric Engineering, Tokyo Univer-sity of Agriculture and technology, Tokyo, Japan, asan Assistant Professor. From 2005 to 2007, he was

the recipient of a Japan Society for the Promotion of Science PostdoctoralFellowship for Research Abroad and was a Visiting Professor with the Wis-consin, Electric Machines and Power Electrics Consortium, University ofWisconsin, Madison. Since 2009, he was an Associate Professor and from2015 he is a professor with Shibaura Institute of Technology, Tokyo. Hisresearch interests are motor control, motor design, and power electronics.Dr. Akatsu is a member of the IEEE Power electronics, IEEE Industry Ap-plications, and IEEE Industrial Electronics Societies, and the Institute ofElectrical engineers of Japan.


advanced torque and current control techniques for pmsms

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