Abstract- An improved and modified Direct Torque Control (DTC) algorithms for permanent magnet synchronous motor (PMSM) drive is investigated in this paper, which features low torque and flux ripple and almost fixed switching frequency. Indeed, a first algorithm uses DTC with Space Vector Modulation (SVM), which is called DTC-SVM, improves greatly the torque and flux ripples compared to the basic DTC reported in the literature. To minimise the calculation time of this modified DTC strategy and guarantee almost the same advantages of DTC-SVM, a novel algorithm uses DTC with Sinusoidal Pulse With Modulation (SPWM), which is named DTC-SPWM, is proposed in this study and compared to the basic and modified DTC. Simulation results, in Matlab/Simulink, demonstrate well the performance of the basic DTC and DTC-SVM and the effectiveness of the proposed control schemes.

I. INTRODUCTION Permanent Magnet Synchronous Motors (PMSM’s) are

used in many applications that require a rapid torque response and a high-performance operation. DTC which was initially developed for induction-motor drives [5]–[10], has also been investigated in PMSM drives recently [11]–[13]; although for some applications the DTC becomes unusable, however it significantly improves the dynamic performance of the drive compared to the vector control due to torque and flux ripples. Indeed, hysteresis controllers used in the conventional structure of the DTC, generate a variable switching frequency causing electromagnetic torque oscillations [4]. This frequency is also varies with speed, load torque and hysteresis bands selected [2]. In addition, a high sampling frequency is needed for the digital implementation of hysteresis comparators and also a current and torque distortion are caused by sectors changes [1].

In recent years, several authors have addressed the problem of improving the behavior of a direct torque controlled induction machine and also of PMSM, especially by reducing the torque and flux ripples and/or by imposing the average switching frequency of the Voltage-Source Inverter (VSI). As reported in [20] a multilevel VSI can be used to overcome DTC drawbacks, but more power switches are needed to achieve a lower ripple and almost fixed switching frequency, which increases the system cost and complexity. Also in [18], the authors propose a new DTC for induction machines with imposed switching frequency by using a multicell (flying capacitors) inverter with whatever number of levels, lower ripples in torque and flux were achieved but at the cost of power switches and system complexity. In [2], [4], [11], [13], [17] and [20] a modified DTC for PMSM has been proposed to improve basic DTC performances by replacing the hysteresis controllers and the commutation table by a PI

regulator, predictive controller and Space Vector Modulation (SVM). Indeed, both torque and flux linkage ripples are greatly reduced when compared to those of the basic DTC, while the switching frequency of the modified DTC is almost fixed.

A PMSM DTC using SVM based on the subdivision of space voltage vectors has been presented in [16], in which the calculation of objective space voltage vector has been realized by introducing the thought of prediction. Instead of using six sectors in the basic SVM, this technique uses SVM with twelve sectors in the whole space and twelve effective vectors with the same amplitude in order to reduce the flux and torque ripples more and more with a constant switching frequency. However, a robust digital signal processing (DSP) card is needed to carry out the real-time algorithms because more calculations are needed.

In this paper, a novel and simple DTC algorithm with fixed switching frequency for PMSM based on SPWM technique is proposed to reduce the flux and torque ripples and minimize the computation time and the need for a processor powerful enough to carry out the real-time algorithm. By contrast, DTC-SVM greatly improves the PMSM DTC performances, but it requires significant computation time due to SVM algorithm complexity, then a powerful processor is needed.

The remaining sections of the paper are arranged as follows. Section II contains the comparison of the basic DTC and the DTC-SVM scheme. Section III explains the DTC-SPWM scheme. Section IV demonstrates the simulation results for speed, torque, flux linkage, and current under the three schemes, and Section V concludes the paper.

II. DTC AND DTC-SVM COMPARISON Figure 1 and Figure 3 present two systems configuration of

DTC controlled PMSM drives; both of them use the same flux vector and torque estimators. However, torque and flux hysteresis controllers and the switching table used in basic DTC are replaced by a PI torque controller and a predictive calculator of vector voltage reference to be applied to stator coils of the PMSM (Fig.3).

In the proposed scheme of DTC-SVM with speed loop control, shown in Figure.3, after correction of the mechanical speed through a PI controller, the torque PI controller delivers Vsq voltage to the predictive controller and also receives, more the reference amplitude of stator flux Ψsr, information from the torque and flux estimator namely, the amplitude and position θs of the actual stator flux and measured current vector. After calculation, the predictive controller determinates the polar coordinates of stator voltage command vector V _

A Novel Fixed-Switching-Frequency DTC for PMSM Drive with Low Torque and Flux Ripple Based on Sinusoidal Pulse With Modulation and Predictive Controller

(1) Khalid Chikh, (1) Mohamed Khafallah, (1) Abdallah Saad, (2) Driss Yousfi and (1) Hamid Chaikhy (1) Hassan ΙΙ University-ENSEM, Casablanca, Morocco (2) Cadi Ayyad University-ENSA, Marrakech, Morocco

ENSEM. Route d'El Jadida. BP 8118 Oasis Casablanca, Morocco chikh_khalid@hotmail.com / genielectrique@gmail.com

978-1-4673-1520-3/12/$31.00 ©2012 IEEE

V , θ for space vector modulatorgenerates the pulses S1, S3 and S5 to control th

Fig.1. Basic DTC scheme for PMSM drive with

The vector diagram of PMSM is shown in fig

Fig.2. (a) Different coordinate of PMSM, (b) Flux, vectors. (A-B-C) 3-phase coordinates. (α,β) stator orieoriented coordinates.

The voltage and flux equations for a PM

oriented coordinates d-q can be expressed as: U R . I P. ω . Ψ U R . I P. ω . Ψ Ψ L . I ΨPM Ψ L . I

Where Isd and Isq are the d - q axis stator cstator resistance, ΨPM is the flux linkage of tlinking the stator, Ld and Lq are the d inductances, p is the number of pole pairs mechanical speed, Ψsd and Ψsq are d - q costator flux linkage. And the electromagnetic tthe rotor oriented coordinates d-q can be eГ P Ψ I Ψ P ΨPMI L

r, which finally he inverter.

h speed loop.

gure 3.

current and voltage ented and (d,q) rotor

MSM in the rotor

currents, Rs is the the rotor magnets

- q axis stator and is the

omponents of the torque equation in expressed as (5): L I I 5

Fig.3. Modified DTC scheme for PMSM

Finally, the motion equation J Г Г f ω

Where J moment of inertia, Гr m

constant.

From the vector diagram of figwe demonstrate that expression of given by: Г P L L ΨPML sin δ Ψ

Above equation consist of twexcitation torque, which is producflux and the second term is the reluc

In the case where Ld = electromagnetic torque becomes:

Г P L ΨPM sin δ From equation 8 we can see th

amplitude and flux produced by torque can be changed by control othe angle between the stator and rostator resistance is neglected. The tobe changed by changing position respect to PM vector using the actuby PWM inverter [1]. When the PMSM drive, we distin- Steady state: the angle δ is constatorque of the machine, while the stathe same speed is the - The transient state, the angle δ is vrotor flux rotate at different speeds (The change of the angle δ is done the stator flux vector relative to thevector Vs-réf provided by the predictof the SVM.

The figure.4 shows the evolutioat the beginning and the end of a pethe beginning, stator flux vector is

(1)

(2)

(3)

(4)

(6)

(7)

(8)

M drive with speed loop.

is expressed as:

motor load and fr damping

gure.2b, equations 3 and 4 f electromagnetic torque is L L sin δ

wo terms, the first is the ced by permanent magnet ctance torque.

Lq, the expression of

hat for constant stator flux PM, the electromagnetic

of the torque angle. This is otor flux linkage, when the orque angle δ, in turn, can

of stator flux vector in ual voltage vector supplied

nguish between two cases: nt and its value is the load

ator flux and rotor rotate at synchronous speed.

variable then the stator and (Figure.4). by varying the position of

e rotor flux vector with the tive controller to the power

on of the stator flux vector eriod vector modulation. At s at the position δ with an

amplitude Ψs , it’s at this moment that the precalculated the variation Δδ of the stator flux this same moment that the space vector modunew position and amplitude of the voltage veachieved at the end of the modulation periodthis vector will allow the stator flux to transit defined by the predictive controller to afluctuations, and this by calculating the time the adjacent vectors V1, V2 and V0 as well athat depends on the symmetry of the modulati

Fig.4. Vector diagram of illustrating torque and flux c

The objective of the DTC is to maintain thtorque within the hysteresis bands of Regulatreference values by selecting the output inverter. And when the torque or the modulreaches the upper or lower limit of the hystea single vector suitable voltage is applisampling step to bring the quantity invohysteresis band.

Fig.5. Stator flux vector evolution in the fir The stator voltage equation of PMSM is givrelation: V R . I dΨdt This equation can be represented as discrete a Ψ k 1 Ψ k T . V k 1

If the voltage drop across the stator resista

compared with the stator voltage, while there + Ts], the end of the vector Ψs moves on a stdirection is given by the vector VS selected d

ΨPM

∆δ

α

β q

Ψsr Ψs

δ

Θm

Θs réf Θs

edictive controller angle, it’s also at

ulator receives the ector that must be d, and of course it

to the location as adjust the torque

of application of as their sequence ion vector.

control conditions.

he stator flux and tors close to their

voltage of the lus of stator flux

eresis comparator, ied during each olved within its

rst sector

ven by the vector

as follows: R . T . I k

ance is negligible is an interval [t, t

traight line whose during Ts. Indeed,

this vector with two components, oand the other control the torque.

The block diagram of flux equations 3 and 4 is shown in figure

The estimation of flow requires thcurrents and rotor position.

The block scheme of the investiwith space vector modulation (DTCinverter (VSI) fed PMSM is presentstructure of the predictive torque anin figure.7.

From equation we can write: I 1R U dΨdt P.

So the average change Δδ of theequation 9 and figure.3.b, which giv∆δ Te ddt Arcsin ΨL

Te is the sampling time.

From equation 10, the relation bincrement of load angle Δδ is ncontroller, which generates the loadto minimize the instantaneous erroactual estimated torque, has been apΔ δ that corresponds to the torque erposition θs of the stator flux vectposition of this vector.

d

Fig.6. Current model for fl

Fig.7. Internal structure of predictive

(9)

(10)

one for controlling the flux

estimator based on the e 6.

he measurement of stator

gated direct torque control C-SVM) for voltage source ed in figure.3. The internal

nd flux controller is shown

ω . Ψ

e angle δ is calculated from ves: Ψ _I

between error of torque and non linear. Therefore PI d angel increment required or between reference and pplied [1]. The step change rror is added to the current tor to determine the new

lux vector estimator

controller used in DTC-SVM

(11)

(12)

(13)

(13)

The module and argument of the reference vector of the stator voltage is calculated by the following equations, based on stator resistance Rs, Δ δ signal, actual: V é V _ é V _ é θ _ é arctan V _ éV _ é

Where: V _ é Ψ _ cos θs ∆δ Ψ cos θs _ T R . I V _ é _ ∆ _T R . I

The figure.8 below, shows the sequence of application of the two adjacent vectors and zero vector in the first sector of vector Vsréf. Indeed, after the vector modulation algorithm computation times T1, T2 and T0 successively apply the voltage vectors V1, V2 and V0, we choose the symmetry in the schematic figure.8 of dividing each modulation period Tp into two sequences and transistor control of the upper arms of the VSI, in the second half of the period are an image of themselves in relation to the vertical axis passing through the point Ts / 2. Fig.8. Time sequences and applications of adjacent vectors in the first sector

So to have a fast transit of stator flux vector, very low flux

ripple and fast torque response, the space vector modulator generates a voltage vector V _ é governed by the following law: V _ é 1T T2 V T2 V T2 V T2 V T2 V T2 V

So at each modulation period and in this case, the sequence

of adjacent vectors in the first sector is applied (V1-V2-V7-V7-V2-V1) respectively during the time T , T , T , T , T , T to rebuild the better rotating vector.

III. DTC-SPWM FOR PMSM DTC-SPWM for PMSM is based on the same algorithm

used in DTC-SVM (see figure 2), but instead of using SVM pulses generator, a simple and fast SPWM pulses generator is investigated to control the VSI. Indeed, after transformation of V _ é and V _ é produced by the predictive controller (see figure 7): from the stator flux reference frame (α-β) to the (a-b-c) frame. These three signals, used as reference signals, will be compared with a triangular signal (figure 9). Then the inverter is controlled by the SPWM.

Fig.9. Sinusoidal PWM pulses generator scheme.

In this proposed technique, the same flux and torque

estimators and the predictive torque and flux controller as for the DTC-SVM are still used. Instead of the SVM generator, a SPWM technique is used to determine reference stator flux linkage vector.

It is seen that the proposed scheme retains almost all the advantages of the DTC-SVM, such as no current control loop, constant switching frequency, low torque and flux ripple, etc. But, the main advantage of the DTC-SPWM is the simple algorithm of PWM (SPWM) used to control the VSI. Of course, the SVM algorithm needs more calculation time than SPWM and the same advantages of DTC-SVM will be obtained by using DTC-SPWM. Whatever is the load torque and speed variation, SPWM guarantees a constant switching frequency, which greatly improves the flux and torque ripples.

In this work, the feasibility and the effectiveness of PMSM DTC-SPWM will be presented in simulation results; also a comparison of this new technique with basic DTC and essentially with DTC-SVM will be discussed in the next section.

Ts/2 T2/2 T1/2

V1 V2 V7 V7 V2 V1

S1

S3

S5

T1/2 T2/2 T0

Ts/2

time

time

time

IV. SIMULATION RESULTS IN MATLAB/SIMULINK We developed in Matlab/Simulink, the models of the

PMSM, voltage inverter, basic DTC, DTC-SVM and DTC-SPWM algorithms to examine and to compare the complete behavior of these tree techniques. In the simulation, the sampling time is 50 µs (20 KHz) for the basic DTC and 100 µs (10 kHz) for DTC-SVM and DTC-SPWM. The switching delays and the forward drop of the power switches, the dead time of the inverter and the nonideal effects of the PM machine are all neglected in the models. Note, that in the simulation, the DC voltage is Vdc=60 Volts. The parameters of PMSM are shown in Table I.

TABLE I. MOTOR PARAMETRS:

In order to examine and to compare the robustness of these

tree strategies, the same operating conditions of speed and torque variation were applied to control the PMSM. The simulation results of basic DTC , DTC-SVM and DTC-SPWM are presented in figures 10-11-12-13-14. In the beginning the machine starts under a speed set-point of 1000 rpm at no load (DC machine inertia corresponds to 0.12 Nm load torque). In this phase the flux and torque ripple under the basic DTC are 0.0052 Wb and 0.16 Nm, respectively; as shown in figures 14(a) and 11(a). However, the flux and torque ripple under the modified DTC is almost 0.001 Wb and 0.05 N m, respectively, as shown in figures 14(b) and 11(b). Also, figures 11(c) and 14(c) shows that the torque and flux ripples under DTC-SPWM are greatly reduced in comparison with figures 14(a) and 11(a). Figure 10 and 11 shows that DTC-SVM and DTC-SPWM preserves the fast torque and speed reponse such as conventionnel DTC.

Figures 12(a), 12(b) and 12(c) shows the steady-sate phase currents under basic, DTC-SVM and DTC-SPWM, respectively, at 800 rd/min. Note that in spite of smaller sampling time used to simulate DTC algorithm compared to DTC-SVM and DTC-SPWM algorithms, low distorsion in current can be observed in these two modifieds DTC currents compared to basic DTC current. This is mainly because in SVM algorithm and SPWM, contrary to hysterisis controller and the switching table, the switching frequency is constant and also because, in SVM and SPWM, many vectors (IGBT states) are selected to adjust the torque and flux ripple in each sample time, whereas in basic DTC just one vector is selected

to adjust ripple inside hysteresis bands of torque and flux regulators. From figure 12(c), a high order-harmonics can be observed in DTC-SPWM phase current waveform, whereas the DTC-SVM phase current waveform contains too few high order-harmonics. This is due to the SVM capability to alleviate the amplitude of the high order-harmonics and to remove the uneven high order-harmonics.

Figures 13(a), 13(b) and 13(c) shows the stator phase current spectrums under basic DTC, DTC-SVM and DTC-SPWM, respectively. Indeed, spectral analysis of current presented in figure 13(a) shows that the total harmonic distortion (THD) of the phase current waveform under basic DTC is 13.93% , it’s seen that there are dominant harmonics: 6.18% and 6.14% of the fundamental current at the frequency of 680 Hz and 76O Hz, respectively. In addition, there are also other low- order harmonics scattered from fundamental to 2 kHz, which are not desirable. The THD of the current waveform of DTC-SVM is 3.5% (figure 13(b)), it is smoother than that of the basic DTC, which is around 1/4 of the basic DTC. This is, because the amplitude of the dominant harmonic is around 1.35% at 280 Hz and the amplitudes of the other harmonics are less than 0.5% except haromics 5 and 8 wich their amplitudes are also less than 1.2%. Note that the sampling frequency of the DTC-SVM is only half of that of the basic DTC. The reason for the high distortion in the basic DTC is mainly due to the fact that the switching function of the inverter is only updated at the sampling instant and also the number of vectors applied to adjust the torque and flux ripple. Although the switching frequency of the basic DTC (varying from 6.3 to 7.9 KHz) is lower than that of the DTC-SVM (10 KHz), which means a lower switching loss, however, the distortion of the basic DTC is too high. Figure 14(c) shows that the THD of the current waveform under DTC-SPWM is 3.85% , which is almost the same as DTC-SVM. This small difference is mainly due to:

- The number and the amplitude of low-order harmonics in current waveform under DTC-SVM are too small than those of DTC-SPWM.

- the use of SPWM generates many harmonics around the even and uneven multiple of switching frequency. Indeed, figure 13(c) shows that there are many harmonics around 10 KHz, 20 KHz, 30 KHz, 40 KHz, etc. It’s seen, in figure 13(b), that SVM generates harmonics just around the even multiple of switching frequency: 20 KHz, 40 KHz, etc.

- The amplitude of harmonics around 20 KHz in DTC-SVM current spectrum is smoother than that of DTC-SPWM.

Brief, the total harmonic distortion (THD) of the current waveform under DTC-SPWM is almost the same as DTC-SVM and the calculation time needed is to smoother than DTC-SVM. In addition, these two fixed switching frequency strategies were presented, in simulation results, the same torque and speed dynamic performance.

The dynamic performances for basic DTC and fixed switching frequency strategies under the same operating conditions are very similar (compare mechanical speeds and electromagnetic torques in figures 10 and 11). Whereas, the steady-state performance of these two modiefied schemes is much better than the basic DTC.

Rated output power (Watt) 500 Rated phase voltage (Volt) 190

Magnetic flux linkage (Wb) 0.052

Poles 3

Rated torque (Nm) 0.8

Rated speed (r/min) 1000

Rated speed (r/min) 6000

Stator resistance (Ω) 1.59

d-axis inductance (mH) 3.3

q-axis inductance (mH) 3.3

Inertia (Kg.m2) 0.003573

Fig.10. Speed tracking performance under load variations in case of: (a) basic DTC ; (b) DTC-SVM and (c) DTC-SPWM

Fig.11. Speed tracking performance: (a) in case of basic DTC ; (b) DTC-SVM and (c) DTC-SPWM

Fig.12. Stator current waveform at 800 rd/min with nominal load under : (a) basic DTC ; (b) DTC-SVM and (c) DTC-SPWM

Fig.13. Stator current spectrum at 800 rd/min with nominal load under: (a) basic DTC ; (b) DTC-SVM and (c) DTC-SPWM

Fig.14. Stator flux in (α,β) axes under load variations in caese of: (a) basic DTC ; (b) DTC-SVM and (c) DTC-SPWM (a) (b) (c)

(c) (b) (a)

(a) (b) (c)

(c) (b) (a)

(a) (b) (c)

V. CONCLUSION

In this paper, a novel Direct Torque Control strategy with

predictive controller and Sinusoidal Pulse With Modulation (DTC-SPWM) has been proposed and validated in Matlab/Simulink. On the one hand, the modeling results confirm that in spite of the lower sampling interval, under DTC-SPWM and DTC-SVM which can reduce the requirement of the real-time software, both torque and flux linkage ripples are greatly reduced under these two starategies when compared to those of the basic DTC, because the application of the SPWM and SVM guarantees a lower harmonics current by the elimination of the distorsion caused by sector changes in case of conventional DTC switching table and by fixing the switching frequency.

On the other hand, this paper confirms that the performances of DTC-SPWM and DTC-SVM are approximately the same with regard to torque and flux ripples in steady state, while they are exactly the same concerning the torque and speed response. Furthermore, the calculation time of the novel technique is much inferior to the DTC-SVM.

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