1. INTRODUCTION

Permanent magnet (PM) synchronous motors are widely used in high-performance drives such as industrial robots and machine tools. These motors have many advantages as: high efficiency and power density, high-torque/inertia ratio. The fast development of power-and microelectronics and computer science opened a new way of investigation for PMSM with vector control strategies [1]-[2]. Firstly DTC was proposed for IM [3], however now is applied also for PMSM [4]. Direct Torque Control (DTC) seems to be a good performance alternative to the classical vector control drives. After its implementation on induction motor drives, this control method in recent years has been proposed for permanent magnet synchronous motor with good results. DTC is able to produce fast torque and stator flux response with a well designed flux, torque and speed estimator. In order to reduce the torque and current pulsations, in steady state a mixed DTC- SVM control method seems more suitable. SVM techniques [5-6] offer better DC link utilization and they lower the torque ripple. Lower THD in the motor current is also obtained. The method is different from standard PWM techniques, such as sinusoidal PWM or 3rd

The variation of stator resistance due to changes in temperature or frequency deteriorates the performance of DTC controller by introducing errors in the estimated flux linkage and the electromagnetic torque [13-14-15-16]. A novel stator resistance estimator during the operation of the motor is proposed.

harmonic PWM methods recently, the emphasis of research on PMSM has been on sensorless drive [7-8-9-10], which eliminates flux and speed sensors mounted on the motor. In addition, the development of effective speed and flux estimators has allowed good rotor flux-oriented (RFO) performance at all speeds except those close to zero. Sensorless control has improved the motor performance, compared to the Volts/Hertz (or constant flux) controls .The EKF is considered to be suitable for use in high-performance PMSM

drives , and it can provide accurate speed estimates in a wide speed-range, including very low speed [11-12].

The contribution of this study is the development of an EKF based speed sensorless DTC-SVM system for an improved performance. The developed EKF algorithm involves the estimation of speed, rotor position, load torque and stator resistance.

2. MODELING OF THE PMSM The electrical and mechanical equations of the PMSM in the rotor reference (d,q) frame as follows:

qd sr q d

d d d

q s d fr d r q

q q q q

rd q q d f q r r

LdI R 1= - + pω I + Udt L L L

dI R L 1= - - pω I - pω + Udt L L L L

dω 3p 1 f= [(L - L )I I + I ] - T -ωdt 2J J J

Φ Φ

(1)

The space-state equations of the PMSM can be written as:

[ ] [ ] [ ] [ ] [ ]d X = A X + B Udt

(2)

Defining:

[ ][ ]

Td q

Td q f

X = I I

U = U U Φ

(3)

Robust Direct Torque and Flux Control of Adjustable Speed Sensorless PMSM

Abstract: Direct torque control (DTC) is known to produce fast response and robust control in ac adjustable-speed drives. However, in the steady-state operation, notable torque, flux, and current pulsations occur. a new sensorless direct torque control method for voltage inverter – fed PMSM is presented. The control method is used a modified direct torque control scheme with constant inverter switching frequency using space vector modulation (DTC-SVM). The variation of stator resistance due to changes in temperature or frequency deteriorates the performance of DTC controller by introducing errors in the estimated flux linkage and the electromagnetic torque. As a result, this approach will not be suitable for high power drives such as those used in tractions, as they require good torque control performance at considerably lower frequency. A novel stator resistance estimator during the operation of the motor is proposed. The estimation method is implemented using the Extended Kalman Filter (EKF) schemes. . Finally extensive simulation results are presented to validate the proposed technique and a very satisfactory performance has been achieved.

Sebti Belkacem,Bouakaz Ouahid ,Boubaker Zegueb, Farid naceri

Department of electrical engineering, university of batna

belkacem_sebti@yahoo.fr

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[ ]

qsr

d d

d sr

q q

LR- ω

L LA =

L R-ω -

L L

[ ] dr

q q

1 0 0LB = ω10 -

L L

The equation of the electromagnetic torque is given by:

L d q q d f q

L r

3pT = [(L - L )I I + I ]2

dΩJ = T - T - f Ωdt

Φ

(4)

3. DTC SPACE VECTOR MODULATION (DTC-SVM)

The principle of Direct Torque Control (DTC) is to directly select voltage vectors according to the difference between reference and actual value of torque and flux linkage. Torque and flux errors are compared in hysteresis comparators. Depending on the comparators a voltage vector is selected from a table. In the DTC system the same active voltage vectors is applied during the whole sample period, and possibly several consecutive sample intervals which give rise to relatively high ripple levels in stator current, flux linkage and torque. One of proposals to minimize these problems is to introduce Space Vector Modulation; SVM is a pulse width modulation technique able to synthesize any voltage vector lying inside the sextant spanned by the six PWM voltage vectors. In the DTC–SVM scheme the hysteresis comparators are replaced by an estimator which calculates an appropriate voltage vector to compensate for torque and flux errors. This method has proved to generate very low torque and flux ripples while showing almost as good dynamic performance as the DTC system. The block scheme of the investigated direct torque control with space vector modulation (DTC-SVM) for a voltage source PWM inverter fed PMSM is presented in Fig. 1.

The internal structure of the predictive torque and flux controller is shown in Fig.2.

Fig. 2 Predictive controller.

The objective of the DTC-SVM scheme, and the main difference between the classic DTC, is to estimate a reference stator voltage vector *

sV in order to drive the power gates of the inerter with a constant switching frequency. Although, the basic principle of the DTC is that the electromagnetic torque of the motor can be adjusted by controlling the angle δ∆ between the stator and rotor magnetic flux vectors generally, the torque of a PMSM can be calculated by the following equation.

( ) ( ) ( )s_réfL m q s_réf d q

d q

Φ3 1T = pΦ L sin δ + Φ L - L sin 2δ2 L L 2

(5)

Fig. 3 Vector diagram of illustrating torque control.

The change in torque can be given by the following formula,

f s sL

d

Φ Φ + ΔΦpΔT = 3 sinΔδ2 L

(6)

Where the change in the stator flux vector, if we neglect the voltage drop in the stator resistance, can be given by the following equation,

s s sΔΦ = V T (7) The predictive controller determinates the stator voltage command vector in polar coordinates *

sV [ *

sV , *sγ ] for space vector modulator; witch finally

generates the pulses a b cS , S , S . Sampled torque error eΔT and reference stator flux amplitude *

sΦ are delivered to the predictive controller. The relation between error of torque and increment of load and angel δ∆ is nonlinear .

*sΦ

sγ

sV α Voltage Vector

Calculation e∆Γ

PI

δ∆ *s∆γ sV β

sΦ sI

+ -

δ mΦ

sΦ

δ sγ

*sΦ

ac power supply

Inverter

dcu

as

cs

bs

load

PMSM

SVPWM

Flux and Torque Estimation

+

Predictive Controller *

LΓ LT

-

sΦ

sΦ sI sγ

sV α

sV β +

Fig. 1 DTC-SVM for PMSM.

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Therefore PI controller, witch generates the load angle increment required to minimize the instantaneous error between reference *

eT and actual

eT torque, has been applied. The reference values of the stator voltage *

sV [ *sV , *

sγ ] is calculated based on stator resistance sR , Δδ signal, actual stator current vector Is, actual stator flux amplitude sΦ and position sγ as:

( ) ( )

( ) ( )

*s*

sα

*s*

sβ

s s ss sα

s

s s ss sβ

s

Φ cos γ + Δδ - Φ cos γ ˆV = + R IT

Φ sin γ + Δδ - Φ sin γ ˆV = + R IT

* * *s

*sβ*

s *sα

2 2sα sV = V + V β

Vγ = arctan

V

(9)

Where, Ts

is sampling time.

4. VOLTAGE SPACE VECTOR MODULATION TECHNOLOGY

The voltage vectors, produced by a 3-phase inverter, divide the space vector plane into six sectors as shown in Fig. 4

Fig. 4 The diagram of voltage space vector which is exported by inverter

In every sector, the arbitrary voltage vector is synthesized by basic space voltage vector of the two side of sector and one zero vector. For example, in the first sector, *

sV is a synthesized voltage space vector the equation is:

*s s 0 0 1 1 2 2V T = V T + V T + V T (10)

s 0 1 2T = T + T + T (11)

Where, sT is the sample time of system, 0T , 1T ,

2T is the work time of basic space voltage vector

0V , 1V , 1V respectively.

Fig. 5 Projection of the reference voltage vector.

The determination of the amount of times 1T and 2T is given by simple projections:

*s1

*s2

*sαsβ

sβ

TT = 6.V - 2.V

2ET

T = 2 VE

(12)

The rest of the period spent in applying the null-vector. For every sector, commutation duration is calculated. The amount of times of vector application can all be related to the following variables:

*ssβ

* *s

* *s

ssβ

ssβ

TX = 2.V

ET 2 6Y = .V + .VE 2 2

T 2 6Z = .V - .VE 2 2

α

α

(13)

Table 1. Application durations of the sector boundary vectors

SECTOR T1 T2 1 Z Y 2 Y -X 3 -Z X 4 -X Z 5 X -Y 6 -Y -Z

The third step is to compute the three necessary duty cycles as;

(8)

Sector 1

Sector 2

Sector 3

Sector 4

Sector 5

Sector 6

α

β

1(100)V

srefV

0 (000)V

7 (111)V

6 (101)V

5 (001)V

4 (011)V

3 (010)V

2 (110)V

α

sβ refV s refV

22

s

TV

T

2V

1V

sα refV 11

s

TV

T

60°

β

X

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s 1 2aon

bon aon 1

con bon 2

T - T - TT =

2T = T + TT = T + T

(14)

The last step is to assign the right duty cycle ( xonT ) to the right motor phase according to the sector Table 2. Assigned duty cycles to the PWM outputs.

5. DEVELOPMENT OF THE EKF ALGORITHM

In this study, EKF, is used for the estimation of, dsI , qsI , rω ,δ , rT and Rs.

Fig. 6 shows the structure of a Kalman filter .

Fig. 6. Simulink model of EKF speed estimation. The discrete model of the PMSM can be given as follows:

+=+=+

v(k)c(x(k))y(k)w(k)u(k))f(x(k),1)x(k

(15)

With: w(k) is the measurement noise and v (k): is the process noise and

6. APPLICATION OF THE EXTENDED KALMAN FILTER

The speed estimation algorithm of the extended Kalman filter can be simulated by the MATLAB/Simulink software

6.1. Prediction of the state vector Prediction of the state vector at sampling time (k+1), from the input u (k), state vector at previous sampling time x(k/k) .

ˆ ˆ ˆx(k +1/k) = F(x(k/k), u(k)) (16)

6.2. Prediction covariance computation

The prediction covariance is updated by:

TP(k +1/k) = F(k)P(k)F(k) + Q (17

fF(k)

x x(k) x(k / k)

∂=∂ =

(18)

6.3. Kalman gain computation The Kalman filter gain (correction matrix) is computed as;

+T T -1L(k +1) = P(k +1/k)C(k) (C(k)P(k +1/k)C(k) R)

With:(k)xx(k)x(k)

c(x(k))C(k)=∂

∂= (19)

6.4. State vector estimation The predicted state-vector is added to the innovation term multiplied by Kalman gain to compute state-estimation vector. The state-vector estimation (filtering) at time (k) is determined by

ˆ ˆ ˆx(k +1/k +1) = x(k +1/k) + L(k +1)(y(k +1) - Cx(k +1/k)) (20)

7. PROPOSED SENSORLESS PMSM DRIVE

The proposed sensorless PMSM drive is depicted in Fig. 7. The stator flux is estimated by the EKF and used in the DTC control the parameters are listed in Table 3. 8. SENSITIVITY STUDY AND SIMULATION

RESULTS Computer simulations have been carried out in order to validate the effectiveness of the proposed scheme. The speed, current, rotor position, and load torque responses are observed under various operating conditions, the stator flux is estimated by the EKF and used in the DTC control the parameters are listed in Table 3. During the simulations, the torque set value is limited to 5 N.m (rated torque), In order to show the performances and the robustness of the combined DTC-SVM-EKF algorithm, we simulated different cases, which are presented thereafter. Fig. 8 shows the actual and estimated responses of the proposed sensorless scheme. The machine is started from rest and assumed to follow a certain speed trajectory. A load torque of 5 N.m. is assumed to be applied at time 0.15s. Current ripple has also a notable reduction in DTC-SVM compared to classic DTC. DTC-SVM has a significantly lower ripple level both in torque, flux and stator current, a lower current ripple advantageous because the machine will have less EMI noise. Fig. 9 show the trajectory of the estimated stator flux components DTC-SVM has as good dynamic response as the classical DTC.

Sector 1 2 3 4 5 6 Ta T Tbon Taon Taon Tcon Tbon con Tb T Taon Tcon Tbon Tbon Tcon aon Tc T Tcon Tbon Tcon Taon Taon bon

2

2

Voltage

Current

Kalman Filter

Estimated speed

S-Function

Isd

Isq

Tr

δ

rω

states

Rs

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Torq

ue (N

m)

t (s)

Spee

d (r

ad /s

ec)

Actual value

Estimated value

Reference value

t (s)

Cur

ent (

A)

sdI

sqI t (s)

||Ψs|

(Wb)

^ Estimated value

Reference value

t (s)

Fig.8 Simulation results: A load torque of 5 N.m is applied at t = 0.15 sec Classical DTC-EKF DTC-SVM-EKF

Spee

d (r

ad /s

ec)

t (s)

Actual value

Estimated value

Reference value

Torq

ue (N

m)

t (s)

t (s)

Cur

ent (

A)

sdI

sqI

||Ψs|

(Wb)

^ Estimated value

Reference value

t (s)

load

PMSM

SVM

su

si

Inverter a

s

cs

bs

α, β d,q

si

sv

Fig. 7. DTC-SVM for sensorless PMSM using the EKF

EKF

sdI

rT

sR

sqI

δ

rω

Flux and Torque

Estimation

Predictive Controller

*LΓ

LT

-

sΦ

sΦ sI sγ

sV α

sV β +

PI

refω

rω

sR

+ -

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Table. 3. PMSM parameters

Parameters of the PMSM Rated torque 5 Nm d-Axis inductance Ld=0.0066 H q-Axis inductance Lq=0.0058 H Stator resistance Rs Ω=1.4 Moment of rotor inertia J=0.00176 kgm2 Magnetic flux linkage fΦ =0.1546 Wb Viscous friction coefficient f=0.00038Kg.m²/s Numbers of pole pairs P=3

9. CONCLUSIONS

In this paper an extended Kalman filter (EKF) algorithm is developed for the speed sensorless direct torque control strategy combined with space vector modulation. The complete sensorless solution is presented with the combined DTC-SVM-EKF strategy; low torque ripple operation has been

obtained with PMSM. In spite of lower switching frequency, the DTC-SVM scheme has lower harmonic current, and consequently lower ripple than conventional hysteresis based DTC. Simulation results obtained clearly demonstrate the effectiveness of the estimator in estimating the stator resistance and improving performance of DTC. Additionally, the application of SVM guarantee:

• Inverter switching frequency is constant; • Distortion caused by sector changes is

delimited; • Low sampling frequency is required; • High robustness; • Good dynamic response; • Low complexity.

REFERENCES

[1] I. Takahashi and T. Noguchi, “A new quick-response and high efficiency control strategy of an induction machine,” IEEE Trans. Industry

Load

Tor

que

(Nm

)

Estimated value

Reference value

t (s)

rT rT

. (DTC-SVM-EKF)

Classical DTC-EKF

Ψsβ

(Wb)

^

Ψsα (Wb) ^

Ψsα (Wb) ^

Ψsβ

(Wb)

^

Fig. 9. Simulation results

Load

Tor

que

(Nm

)

Estimated value

Reference value

t (s)

Reference value

t (s)

sR

sR

Estimated value A t l l

Stat

or re

sist

ance

(Ω)

Stat

or re

sist

ance

(Ω)

Estimated value

Reference value

sR

sR

t (s)

rT rT

Stat

or re

sist

ance

(Ω)

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[3] T. Vyncke, K. Boel and A. Melkebeek, “direct torque control of permanent magnet synchronous motors – an overview,” IEEE symposium in electrical power engineering 27-28 April 2006, belgium.

[4] B. Akin A , State Estimation Techniques for Speed Sensorless Field Oriented Control of induction Motor, Thesis submitted to the graduate school of the middle east technical university, August 2003.

[5] Z. hilmi bin ismail, “Direct torque control of induction motor drives using space vector modulation (dtc-svm),” Master of Engineering Faculty of Electrical Engineering Malaysia, November, 2005.

[6] M. P. Kazmierkowski, M. Zelechowski, D. Swierczynski, “ Simple DTC-SVM Control Scheme for Induction and PM Synchronous Motor,” XVII International Conference on Electrical Machines, ICEM 2006 September 2-5, 2006 Chania,.

[7] S.Baris Ozturk, Modelling, “simulation and analysis of low-cost direct torque control of PMSM using hall-effect sensors,” Master of Science, Texas University. December 2007.

[8] A. Paladugu, H. Chowdhury, “ Sensorless control of inverter-fed induction motor drives" Electric Power Systems Research, Vol. 77, Issues 5-6, April 2007, pp. 619-629.

[9] C. Bian Shuangyan, R. Liangyu, “Sensorless “DTC of Super High-speed PMSM,” Proceedings of the IEEE International Conference on Automation and Logistics August 18 - 21 Jinan, China, 2007,

[10] S. Benaggoune, S. Belkacem and R. Abdessemed, “Sensorless direct torque control of PMSM drive with EKF estimation of speed, rotor position and load torque observer,” Al-Azhar University Engineering Journal, JAUES, Egypt, Vol. 2, No. 5 Apr. 2007,pp.469-479.

[11] M. Barut, S. Bogosyan and M. Gokasan, “Switching EKF technique for rotor and stator resistance estimation in speed sensorless control of IMs “Energy Conversion and Management, Vo.48, Issue 12, December 2007, pp 3120-3134.

[12] M. Kosaka and H. Uda “Sensorless IPMSM drive with EKF estimation of speed and rotor

position,” Journal of low frequency noise, vibration and active control, Vol. 22. No. 4, 2004. pp.59-70.

[13] M. Kadjoudj, N. Goléa and M.E.H Benbouzid " “Problems of Stator Flux Estimation in DTC of PMSM Drives,” Journal of Electrical Engineering & Technology, Vol. 2, No. 4, 2007,pp. 468-477.

[14] M. E. Haque and M. F. Rahman “Influence of stator resistance variation on direct torque controlled interior permanent magnet synchronous motor drive performance and its compensation”, IEEE Industry Application Society Annual Meeting, Chicago, USA, vol. 4, pp. 2563 -2569, 2001.

[15] Yanping Xu, Yanru Zhong, Jie Li, “Fuzzy Stator Resistance Estimator for a Direct Torque Controlled Interior Permanent Magnet Synchronous Motor ,” ICEMS 2005. Proceedings of the Eighth International Conference on Electrical Machines and Systems, 27-29 Sept. pp.438- 441, 2005.

[16] C. Yongjun1, H. Shenghua1, W. Shanming1, W. Fang, "Direct Torque Controlled Permanent Magnetic Synchronous Motor System Based on the New Rotor Position Estimation,” Proceedings of the 26th Chinese Control Conference July 26-31, Zhangjiajie, Hunan, China,2007.

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