control method suitable for direct-torque-control-based...

970 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 48, NO. 3, MAY/JUNE 2012

Control Method Suitable forDirect-Torque-Control-Based Motor Drive System

Satisfying Voltage and Current LimitationsYukinori Inoue, Member, IEEE, Shigeo Morimoto, Member, IEEE, and Masayuki Sanada, Member, IEEE

Abstract—This paper proposes a control method suitable forlimited armature voltage and current in a permanent-magnetsynchronous motor drive system based on direct torque con-trol (DTC). First, this paper proposes torque-limiting and flux-weakening controls that are suitable for a DTC-based motor drivesystem. The proposed method utilizes a mathematical model ina rotating reference frame synchronized to the stator flux link-age. Second, this paper proposes an antiwindup scheme for thetorque controller of the DTC system. Windup of the controllerdegrades the performances of torque-limiting (current-limiting)control and of torque control. Applying the antiwindup resultsimproves the performance of the proposed torque-limiting methodin the transient state. This paper presents a DTC-based drivesystem combined with a speed controller. The proposed systemcan achieve stable control, and its effectiveness is confirmedexperimentally.

Index Terms—Antiwindup, direct torque control (DTC),permanent-magnet synchronous motor (PMSM), wide-speed-range operation.

I. INTRODUCTION

D IRECT-TORQUE-CONTROLLED permanent-magnetsynchronous motor (PMSM) drive systems have severaladvantages. For example, an accurate motor model is notrequired to estimate the torque and the stator flux linkage [1],[2]. In addition, no rotor position sensor is needed becausedirect torque control (DTC) operates in a stationary referenceframe [3], [4].

Optimal controls, such as maximum torque per ampere(MTPA) control and flux-weakening (FW) control, and voltageand current limitations are important for high-performancemotor drives [5]. A DTC system can achieve optimal controlby providing the reference torque and the reference flux basedon the operating conditions. However, in most cases, DTC-based motor drives utilize control laws based on a mathematical

Manuscript received August 7, 2011; revised October 31, 2011; acceptedDecember 3, 2011. Date of publication March 15, 2012; date of currentversion May 15, 2012. Paper 2011-IDC-435.R1, presented at the 2010 In-ternational Power Electronics Conference, Sapporo, Japan, June 21–24, andapproved for publication in the IEEE TRANSACTIONS ON INDUSTRY APPLI-CATIONS by the Industrial Drives Committee of the IEEE Industry ApplicationsSociety.

The authors are with Osaka Prefecture University, Sakai 599-8531, Japan(e-mail: [email protected]; [email protected]; [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TIA.2012.2191170

model in the rotating d–q reference frame, which is synchro-nized to the rotor magnet [6]–[8]. Thus, it is necessary tocalculate the d- and q-axis currents to determine the relationshipbetween the torque and the flux. In addition, motor parameters,such as the inductance and magnet flux, are required for thesecontrols.

A control law based on the mathematical model in thed–q frame does not appear to be suitable for DTC and flux-oriented control. It is expected to be possible to derive a simpleexpression for the control law by using a novel mathematicalmodel. Several studies have investigated the control laws de-fined in a rotating reference frame that is synchronized with thestator flux linkage [9]–[12]. In [9], a control method for unitypower factor operation of the rotating-field-type synchronousmachine is proposed. In [10], a control method is proposed forthe flux and the current component orthogonal to the flux. In[11] and [12], a control method for the flux and the torqueis proposed, and torque limiting utilizes the reactive torque,which is calculated by taking the product of the flux and thecurrent.

This paper proposes a novel method for calculating thereference torque and the reference flux that are suitable forDTC-based motor drive systems. The proposed method consistsof torque limiting that is capable of current limiting and FWcontrol for limiting the voltage. These control laws are derivedfrom mathematical equations in a rotating reference frame thatis synchronized to the stator flux linkage. The proposed methodfor the FW and the torque limiting has several advantages, in-cluding simplicity of calculation and insensitivity to parametervariation because it does not require the values of the magnetflux and inductance.

This paper also proposes an antiwindup scheme for thetorque controller of a DTC system that is based on proportionaland integral (PI) control. Windup of the controller generallyoccurs when the terminal output voltage of the inverter is sat-urated. Windup degrades the performances of torque-limiting(current-limiting) control and torque control. In the proposedantiwindup scheme, the controller gain is changed accordingto the degree of voltage saturation, which is detected usingthe estimated flux linkage. Consequently, the proposed torque-limiting method is confirmed to be valid for both steady andtransient states.

This paper proposes a DTC-based drive system combinedwith a speed controller, and the effectiveness of the proposedmethod is confirmed from experimental results.

0093-9994/$31.00 © 2012 IEEE

INOUE et al.: CONTROL METHOD SUITABLE FOR DTC-BASED MOTOR DRIVE SYSTEM 971

Fig. 1. DTC-based PMSM drive system.

II. DTC MOTOR DRIVE SYSTEM

Fig. 1 shows a block diagram of the direct-torque-controlledPMSM drive system. This system is equipped with a speedcontroller based on PI control. The DTC system requires appro-priate reference values for the torque and the stator flux linkagefor high-performance control.

The DTC system is based on control of the stator fluxlinkage, which is estimated using the following equations [1]–[4], [6], [7]: {

ψ̂α =∫

(vα − Raiα) dtψ̂β =

∫(vβ − Raiβ) dt

(1)

Ψ̂ s =√

ψ̂2α + ψ̂2β (2)

θ̂s = tan−1ψ̂β

ψ̂α. (3)

Here, vα and vβ are the armature voltages, iα and iβ are thearmature currents in the stationary α–β reference frame, Rais the armature resistance, Ψ̂α and Ψ̂β are the α- and β-axiscomponents of the estimated stator flux linkage, respectively,Ψ̂ s is the estimated stator flux linkage, and θ̂s is the estimatedposition of the stator flux linkage in the α–β frame.

It is generally difficult for inverter-fed motor drives to mea-sure the armature voltages in the motor terminals (vα and vβ).Instead, the reference voltages (v∗α and v

∗β) are used to estimate

the flux, as shown in Fig. 1.Various compositions of the torque and flux controller shown

in Fig. 1 have been proposed (e.g., [1]–[4]). The DTC methodused to evaluate the method proposed in this paper is describedin Section IV.

III. CONTROL METHOD OF TORQUE AND FLUX

A. Mathematical Model in M–T Frame

Fig. 2 shows the vector diagram and coordinate axes understeady-state operating condition. The α–β reference frame is astationary reference frame, whereas the d–q reference frame is arotating frame that is synchronized to the rotor. The α-axis cor-responds to the direction of the u-phase of the stator windings,

Fig. 2. Vector diagram of PMSM and coordinate axes.

and the d-axis corresponds to the direction of the stator fluxlinkage of the rotor magnet (Ψa). The M–T reference frameis a rotating reference frame that is synchronized to the stator-flux-linkage vector (ψs) [9]. The angle θs indicates the positionof the stator-flux-linkage vector.

In the steady state, the voltage equation of the PMSM in theM–T frame is given by[

vMvT

]= Ra

[iMiT

]+

[0

ωΨ s

](4)

where vM and vT are the armature voltages, iM and iT are thearmature currents in the M–T frame, and ω is the electricalrotor angular velocity.

The electromagnetic torque is given by

Te = PnΨ siT (5)

where Pn is the number of pole pairs.

B. Calculator of Reference Torque and Reference Flux

Fig. 3 shows the proposed reference torque and referenceflux calculator. In this paper, the torque limiting required forcurrent limitation and the FW required for voltage limitation areimplemented as limiters. The control laws for torque limitingand FW are obtained using equations in the M–T frame, as de-scribed later. However, for MTPA control only, the relationshipbetween the torque and the flux is calculated from equations


Fig. 3. Proposed calculator for reference torque and reference flux.

in the d–q frame. The control law for MTPA control [5] isgiven by

id =Ψa

2(Lq − Ld)−

√Ψ2a

4(Lq − Ld)2+ i2q (6)

where id and iq are the d- and q-axis currents, respectively, Ψais the stator flux linkage due to the rotor magnet, and Ld and Lqare the d- and q-axis inductances, respectively.

The relationship between the torque and the flux can becalculated using the following equations to satisfy (6):[

ψdψq

]=

[Ld 00 Lq

] [idiq

]+

[Ψa0

](7)

Ψ s =√

ψ2d + ψ2q (8)

Te =Pn(ψdiq − ψqid). (9)

Since this calculation for MTPA control is complicated, alookup table is used in Fig. 3. The effect of the parametervariation should be considered when the magnetic saturationis significant. For example, the q-axis inductance is modeled asa function of the q-axis current.

C. Torque Limiting

The torque is restricted to satisfy the current limiting, whichis determined by the capabilities of the inverter and the motor.For interior PMSMs, which can utilize the reluctance torque,the relationship between the torque and the current is nonlinear,and thus, deriving this relationship is complicated. In the M–Tframe, however, the limiting torque can be calculated using (5)as follows:

Tlim = PnΨ siTm (10)

where iTm is the limiting value of the T -axis current. When thelimiting current is Iam, iTm is given by

iTm =√

I2am − i2M . (11)

This control law can be applied in both the MTPA and theFW regions.

In [11] and [12], the limiting torque is calculated using

Tlim =√

(PnΨ sIam)2 − T 2r (12)

Fig. 4. Torque and flux controller for RFVC DTC (PI-controller-based DTC).

where Tr is termed the reactive torque and is defined by

Tr = PnΨ siM . (13)

Substituting (13) into (12) gives control laws that are equiv-alent to (10) and (12).

D. FW Control

In contrast to the conventional control method in the d–qframe, it is easy for a DTC system to accomplish FW controlbecause DTC directly controls the stator flux linkage. Theproposed system uses an FW control method to maintain thearmature voltage Va at its limiting value Vam. The proposedmethod is derived from the voltage equation in the M–T frame.

Using Va =√

v2M + v2T and solving (4) for the variable Ψ s

yield the stator flux linkage Ψ s−FW for the case when Va =Vam, as follows:

Ψ s−FW =1ω

{−RaiT +

√V 2am − (RaiM )2

}. (14)

IV. ANTIWINDUP SCHEME OF TORQUE CONTROLLER

This study adopts a DTC method using a reference fluxvector calculator (referred to hereafter as RFVC DTC) [3], [4],[7]. The torque and flux controller used by this method is shownin Fig. 4. The RFVC DTC system has several advantages,including a fixed switching frequency and a low torque ripple.

The RFVC DTC system has a PI controller for torquecontrol. Windup of the PI controller generally occurs whenthe terminal output voltage of the inverter is saturated. Theperformance of the current limitation based on torque limitingdepends on the response characteristic of the torque controlsystem. This paper proposes an antiwindup scheme for thetorque controller.

Fig. 5 shows a vector diagram for voltage saturation. Here,the voltage drop in the resistance is neglected. ψ̂s[k] is the vec-tor of the estimated stator flux linkage. In the DTC system, thisvector is controlled to obtain the torque and the flux based onthe reference values. ψ∗s[k] is the reference vector of the statorflux linkage, and it corresponds to the reference flux (Ψ ∗s) andthe reference position (θ∗s), which are shown in Fig. 4. In theRFVC DTC system, the reference voltage calculation is based


Fig. 5. Vector diagram for voltage saturation.

Fig. 6. Antiwindup implementation for torque controller.

on time subtraction of the flux. Hence, the desired armaturevoltage is (ψ∗s[k] − ψ̂s[k])/ts, where ts is the sampling period.In Fig. 5, the desired voltage vector exceeds the voltage-limitingcircle, which corresponds to the maximum available voltage ofthe inverter. Thus, voltage saturation occurs, and v∗[k] is theactual voltage vector applied to the motor. In the torque and fluxcontroller shown in Fig. 4, the reference voltage vector v∗[k] isgenerated in the reference voltage vector calculator, and then,voltage limiting according to the available output voltage of theinverter is applied.

The estimated vector of the stator flux linkage in the nextcontrol period is ψ̂s[k + 1]. When voltage saturation occurs,the estimated position θ̂s[k + 1] differs from the reference po-sition θ∗s[k], as shown in Fig. 5. The angular difference betweenthe reference and estimated positions of the stator flux linkageis defined by

θε = θ∗s[k − 1] − θ̂s[k]. (15)

An antiwindup scheme utilizing the value θε is proposedto improve the torque control performance. Fig. 6 shows themodified PI controller with antiwindup. In the proposed an-tiwindup scheme, the gain of the integral element is variedaccording to the variable γi. Consequently, the input quantity tothe integrator becomes suppressed. The variable γi should havea value of unity for an angular difference θε of zero. It shouldalso approach zero as θε increases. A function that satisfiesthese conditions is given by

γi =1

1 + Ka|θε|(16)

where Ka is the antiwindup gain, and it satisfies Ka > 0.

TABLE IEXPERIMENTAL SYSTEM PARAMETERS

Ka is determined through performing simulation and exper-iment. Note that the antiwindup is disabled when Ka = 0.

Details regarding the torque controller and the gain design inthe RFVC DTC system have been reported in [13]. The PI gainsof the torque controller can be determined from the dampingfactor and the natural angular frequency of the quadratic trans-fer function.

V. EXPERIMENTAL RESULTS

A. Experimental Setup

The effectiveness of the proposed system is evaluated experi-mentally. Table I lists the parameters of the PMSM drive systemconsidered in this study. All the controls are processed througha digital signal processor (Texas Instruments, TMS320C6713).The speed control period is 5 ms, and the sampling period ofthe other control is 100 μs. An insulated-gate bipolar transistormodule is used for the inverter, and the pulsewidth-modulationcarrier frequency is 10 kHz.

The rotor speed is detected by an incremental encoder at-tached to the tested motor. Flux estimation is based on a first-order low-pass filter instead of a pure integrator to reduce theeffects of the dc offset of the experimental system and the errorof the initial value used to estimate the flux.

B. Effectiveness of Antiwindup Scheme

Fig. 7 shows the characteristics of the torque step responseto confirm the effectiveness of the antiwindup scheme. Theoperating speed is 500 r/min, and no load is applied. In this case,neither the proposed methods for torque limiting nor the FW isapplied. A large torque overshoot appears when antiwindup isnot applied. In contrast, the torque overshoot becomes smallwhen antiwindup is applied. This is because voltage saturationincreases the angular difference θε and, thus, the gain variationγi decreases.

This confirms that the antiwindup scheme proposed inSection IV is effective for the torque controller of the RFVCDTC system.

C. Acceleration Characteristics

To confirm the effectiveness of the torque limiting and theFW control proposed in Section III-C and D, respectively,


Fig. 7. Comparison of torque step response (operating conditions: 500 r/minand no load).

the acceleration characteristics are investigated. In this section,antiwindup is applied to the torque controller.

Fig. 8 shows the speed response characteristics when therotor speed is increased from 500 to 3500 r/min when no loadis applied. The results in Fig. 8(a) show that the rotor speedincreases stably. When torque limiting and FW are applied, theproposed scheme satisfies the limiting values of the voltage andcurrent, as shown in Fig. 8(a) and (b). Fig. 8(c) shows that theM -axis current decreases as the rotor speed increases duringFW.

Fig. 9 shows the torque trajectory for the same operatingconditions as those in Fig. 8. Torque limiting is applied betweenpoints B and D, and FW control is applied between points Cand E. These results confirm that the proposed system achievesmaximum power operation and stable control.

Fig. 10 shows the acceleration characteristics when the rotorspeed is increased from 500 to 2500 r/min when no load isapplied. In Fig. 10(a), the trajectory moves from the FW regionto the MTPA region at the operating point E. The proposed sys-tem can change smoothly between control methods. Fig. 10(b)shows that the armature voltage is below its limiting value afterpoint E. In the proposed system, both torque limiting and FWare achieved by the limiter. Thus, it is unnecessary to calculatethe rotor speed when the control method changes.

In the conventional method, the limiting torque is calculatedbased on the PMSM model in the d–q frame [6]. In the MTPAcontrol region, the maximum torque is constant. In the FWcontrol region, the limiting torque is variable and is a functionof the rotor speed. Therefore, an approximate value of thelimiting torque Tlim is given by (17), shown at the bottom ofthe page, which is an example of the conventional method,where Tlim−MTPA is the limiting torque calculated using thePMSM model and Ktl4, Ktl3, Ktl2, Ktl1, and Ktl0 are thecoefficients of the approximating polynomial. In this case,

Fig. 8. Acceleration characteristics (ω∗m = 500 to 3500 r/min; no load).(a) Rotor speed, torque, and stator flux linkage. (b) Armature voltage andcurrent. (c) M - and T -axis currents.

motor parameters such as the inductance and magnet flux arerequired.

When the PMSM model has the parameters shown in Table I,Tlim−MTPA is 1.9 N · m. The coefficients Ktl4, Ktl3, Ktl2,Ktl1, and Ktl0 are −1.019 × 10−10, 2.045 × 10−7, −1.490 ×10−4, 4.431 × 10−2, and −2.670, respectively.

Fig. 11 shows the armature voltage and current for theconventional method, where the limiting torque is given by

Tlim ={

Tlim−MTPA, for MTPA control regionKtl4ω

4 + Ktl3ω3 + Ktl2ω2 + Ktl1ω + Ktl0, for FW control region(17)


Fig. 9. Torque trajectory in torque/rotor speed plane (ω∗m = 500 to3500 r/min; no load).

Fig. 10. Acceleration characteristics (ω∗m = 500 to 2500 r/min; no load).(a) Torque trajectory in torque/rotor speed plane. (b) Armature voltage andcurrent.

(17). The plots exhibit almost the same characteristics as thoseshown in Fig. 8(b) for which the proposed method was applied.However, calculating torque limiting based on the motor modelin the d–q frame is complicated. In addition, when parametervariation (e.g., variation in the inductance due to magneticsaturation) is considered, parameters should be determined forseveral operating conditions.

Therefore, the proposed control laws have several advan-tages, including insensitivity to parameter variation and sim-plicity of calculation.

D. Transient Performance of Torque Limiting

Fig. 12 shows the transient characteristics of the proposedtorque limiting. Fig. 12(a) shows that, when antiwindup is notapplied, the estimated torque does not follow the referencetorque. Fig. 12(b) reveals that good torque control performanceis achieved when antiwindup is applied. Consequently, the

Fig. 11. Armature voltage and current for torque limiting based on motormodel in the d–q frame (acceleration characteristics: ω∗m = 500 to 3500 r/minand no load).

Fig. 12. Effect of torque response improvement on current limitation (operat-ing condition: 500 r/min and no load). (a) Torque response without antiwindup.(b) Torque response with antiwindup. (c) Comparison of armature current.

armature current is maintained at the limiting value for bothsteady and transient states, as shown in Fig. 12(c).

Fig. 13 shows the transient performance of the torque limit-ing when the parameter error exists. In this case, the resistancevalue used in the proposed controller is 0.4 Ω, which is about50% of the nominal value, and thus, the estimation error occurs.However, in the proposed method for the FW and the torquelimiting, the flux estimation error does not affect the voltage andcurrent limitations as long as the torque follows the referencevalue. This is because both the proposed method and the DTC


Fig. 13. Transient characteristic of the torque limiting under the parametervariation. (The resistance error is 50% of the nominal value, and antiwindup isapplied. Operating condition is the same as that in Fig. 12.) (a) Torque response.(b) Armature current.

are based on the same mathematical model, as shown in (4) and(5). Hence, the errors of the estimated and the reference valuesare canceled out.

VI. CONCLUSION

In this paper, control laws for torque limiting and FWsuitable for a DTC system have been proposed. Experimentsconfirm that the proposed method for the FW and the torquelimiting can accomplish maximum power operation satisfyingthe limitations of the voltage and the current without the needto determine any motor parameters except for the resistance.In addition, the proposed antiwindup scheme for the torquecontroller was applied, and it was confirmed that the proposedtorque-limiting method is valid for both steady and transientstates. Consequently, the proposed system has several advan-tages, including insensitivity to parameter variation, simplicityof calculation, and stable control.

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Yukinori Inoue (S’07–M’10) was born in Japan in1982. He received the B.E., M.E., and Ph.D. degreesfrom Osaka Prefecture University, Sakai, Japan, in2005, 2007, and 2010, respectively.

Since 2010, he has been with the Graduate Schoolof Engineering, Osaka Prefecture University, wherehe is currently an Assistant Professor. His researchinterests include control of electrical drives, particu-larly the direct torque control of permanent-magnetsynchronous motors and position-sensorless controlof these motors.

Dr. Inoue is a member of the Institute of Electrical Engineers of Japan andthe Japan Institute of Power Electronics.

Shigeo Morimoto (M’93) was born in Japan in1959. He received the B.E., M.E., and Ph.D. degreesfrom Osaka Prefecture University, Sakai, Japan, in1982, 1984, and 1990, respectively.

In 1984, he joined Mitsubishi Electric Corpora-tion, Tokyo, Japan. Since 1988, he has been withthe Graduate School of Engineering, Osaka Prefec-ture University, where he is currently a Professor.His main areas of research interest are permanent-magnet synchronous machines, reluctance machines,and their control systems.

Dr. Morimoto is a member of the Institute of Electrical Engineers of Japan,the Society of Instrument and Control Engineers of Japan, the Institute ofSystems, Control and Information Engineers, and the Japan Institute of PowerElectronics.

Masayuki Sanada (M’94) was born in Japan in1966. He received the B.E., M.E., and Ph.D. degreesfrom Osaka Prefecture University, Sakai, Japan, in1989, 1991, and 1994, respectively.

Since 1994, he has been with the Graduate Schoolof Engineering, Osaka Prefecture University, wherehe is currently an Associate Professor. His main areasof research interest are permanent-magnet motors fordirect-drive applications, their control systems, andmagnetic field analysis.

Dr. Sanada is a member of the Institute of Electri-cal Engineers of Japan, the Japan Institute of Power Electronics, and the JapanSociety of Applied Electromagnetics and Mechanics.

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