fuzzy mras pmsm

TRANSACTION ON CONTROL AND MECHANICAL SYSTEMS, VOL. 2, NO. 7, PP. 321-326, JUL., 2013.

RECEIVED: 3, FEB., 2013; REVISED: 16, MAY, 2013; ACCEPTED: 22, MAY, 2013; PUBLISHED: 4, JUN., 2013. ISSN: 2345-234X

Abstract: In this paper, a sensorless Direct Torque control

(DTC) for Permanent Magnet Synchronous Motor (PMSM)

drive based on Adaptive Model Reference (MRAS) algorithm

and PI with adapted gains fuzzy logic (FL) are presented. The

MRAS is utilized to estimate speed and stator resistance and

compensate the effects of parameter variation on (stator

resistance variation introduce errors flux and torque

estimation and affect the performance of DTC). In other hand,

speed regulation by PI with two adaptive FLC is investigated

and compared with classical PI controller. Simulation results

are presented and show the effectiveness of the proposed

method.

Keywords: MRAS, PMSM, Speed and Resistance Estimation,

Sensorless Drive, FLC, DTC. 1

1. INTRODUCTION

High dynamic performance of servo motor drives is

indispensable in many applications of today’s automatically

controlled machines. AC motor control has attracted much

attention recently in the power electronics field [1]

.

Progress in the field of power electronics and

micro-electronics, software engineering, and materials,

enables the application the PMSM, based on modern rare

earth variety, becomes serious competitor to the induction

motor and conventional wound rotor synchronous motor

and DC motor. PMSM drives are used in many applications.

They are used more in the variable speed applications due to

some advantages like: more simplicity, low maintenance,

low dependency on the motor parameters, good dynamic

torque response, high rate torque/inertia and simplicity of

design [2]

.

Direct Torque control (DTC) for induction motor

synchronous machines was introduced about more than

twenty years by Takahashi and Depenbrock [3-4]

. The main

advantages of DTC are the simple control scheme, a very

good torque dynamic response, as well as the fact that it

does not need the rotor speed or position to realize the

torque and flux control, moreover DTC is not sensitive to

parameters variations (except stator resistor) [1, 5]

.

However, it still has some disadvantages: high torque

ripples and variable switching frequency, which is varying

1,3 A. Ameur and B. Mokhtari are in LeDMaSD Laboratory, Electrical

Engineering Department, Laghouat University, Email: [email protected] 2 K. Ameur are in La LACoSERE Laboratory, Electrical Engineering

Department, Laghouat University, Email: [email protected].

Please refer to the Nomenclature at the end of the paper!

with speed, load torque, selected hysteresis bands and

difficulty to control torque and flux at very low speed [5-6]

.

The high performance speed or position control requires

an accurate knowledge of rotor shaft position and velocity

in order to synchronize the phase excitation pulses to the

rotor position. This implies the need for speed or a shaft

position sensor such as an optical encoder or a resolver [6]

.

However, the speed controller design of such systems plays

a crucial role on these performances [7]

. The speed controller

PI compensator based torque-load angle and speed control

scheme have a simple structure and it can offer a

satisfactory performance over a wide range of operation but

fixed gain PI controllers does not provide satisfactory

control performance in the presence of parameter variations

and disturbances under a wide range of driving conditions [8]

.

The FLC is seemed an ultimate solution in terms of high

dynamic response and best disturbance rejection. The

special merit of this controller is that it does not require the

knowledge of a mathematical model of the plant for the

adaptation mechanism, and it can be easily implemented [7-9]

.

This technique proposes the tuning online adaptive gains of

classical PI controller based on Self tuning FL.

In other hand, the presence of this sensor (expensive and

fragile and require special treatment of captured signals),

causes several disadvantages from the standpoint of drive

cost, encumbrance, reliability and noise problem [10-12]

.

A variety of different solutions for sensorless ac drives

have been proposed in the past few years. Their merits and

limits are reviewed based on a survey of the available

literature. These techniques are generally based on sliding

mode observer [6]

or Luenberger observer, MRAS method [10-11]

and extended Kalman filters [12]

. The PMSM speed

sensorless DTC schemes are sensitive to motor parameters

variation, especially to the stator resistances that change

with temperature. In addition, the error in the PMSM stator

flux estimation is mainly because of stator resistance

variation. This error influences the stator flux as well as the

electromagnetic torque, which means significant error on

the position which causes a bad selection of state of the

switches and generates instability of the machine operation [6]

. So far many methods such as MRAS-based and observer

based have been proposed for stator resistance estimation.

MRAS for Speed Sensorless Direct Torque Control of a

PMSM Drive Based on PI Fuzzy Logic and Stator

Resistance Estimator

Ameur Aissa 1, , K. Ameur

2, and B. Mokhtari

3


TRANSACTION SERIES ON ENGINEERING SCIENCES AND TECHNOLOGIES (TSEST) ©

322

Adaptive Model Reference system (MRAS) algorithm

provide an effective way of improving the robustness of the

control system against parameter variation, load disturbance

due to its simple structure and fast response [10]

.

This paper presents MRAS for a speed sensorless DTC

of PMSM based stator resistance estimator and Fuzzy Logic

PI controller. The improvements and the effectiveness of

the proposed even against DTC key parameter deviation is

demonstrated by some simulation results.

2. PMSM MODEL

The stator and rotor flux equation of PMSM can be

written in the reference frame of Park in the following form [3]

:

00

0 e

sq

sd

q

d

q

d

I

I

L

L

(1)

While the equations of the stator voltages are written in

this same reference frame in the following form:

0

0

0 0

0

d ds d ds

s

q qs d qs

d ds

r r

d qs e

v I L Id

rdt

v I L I

L I

p p

L I

(2)

In addition the electromagnetic torque can be expressed:

e

3

2d q sd sq e sqT p L L I I I

(3)

The mechanical equation of the motor can be expressed

as flows:

.

e rlJ T T f (4)

3. CONVENTIONAL DTC

The methods of direct torque control (DTC) as shown in

Fig. 1 consist of directly controlling the turn off or turn on

of the inverter switches on calculated values of stator flux

and torque from relation (6). The changes of state of the

switches are linked to the changes in electromagnetic state

motor. They are no longer controlled based on voltage and

frequency references given to the commutation control of a

pulse width voltage modulation inverter [1, 3]

. The reference

frame related to the stator makes it possible to estimate flux

and the torque, and the position of flux stator. The aim of

the switches control is to give the vector representing the

stator flux the direction determined by the reference value

0

0

( )

( )

t

s s s s

t

s s s s

v r I dt

v r I dt

(5)

The DTC is deduced based on the two approximations

described by the formulas (6) and (7) [4]

:

( 1) ( ) s s s E s s Ek k V T V T (6)

' '( ) sine s r s rT k k (7)

More over:

2 2ˆ ˆ ˆ

ˆˆ

ˆ

s s s

s

ss

arctg

(8)

A two levels classical voltage inverter can achieve seven

separate positions in the phase corresponding to the eight

sequences of the voltage inverter.

Fig. 1. Diagram of DTC control applied for PMSM supplied with a

three-phase inverter with PMW.

Fig. 2. Different vectors of stator voltages provided by a two levels inverter.

Where:

I(D)F : Increase (Decrease) of Flux amplitude.

I(D)T : Increase (Decrease) of Torque.

Tables 1 have the sequences corresponding to the

position of the stator flux vector in different sectors

(see Fig. 1).

AISSA et al.: MRAS FOR SPEED SENSORLESS DIRECT TORQUE CONTROL OF A PMSM DRIVE BASED ON PI FUZZY LOGIC AND STATOR RESISTANCE ESTIMATOR.


323

TABLE 1

VECTORS VOLTAGE LOCALIZATION

The flux and torque are controlled by two comparators

with hysteresis illustrated in Fig. 3. The dynamics torque

are generally faster than the flux then using a comparator

hysteresis of several levels, is then justified to adjust the

torque and minimize the switching frequency average [4]

.

Fig. 3. Comparators with hysteresis used to regulate flux and torque.

4. FUZZY LOGIC SPEED CONTROLLER

A proportional-integral controller (PI controller) is a

generic control loop feedback mechanism (controller). A PI

controller calculates an "error" value as the difference

between a measured process variable (speed) and a desired

setpoint. The controller attempts to minimize the error by

adjusting the process control inputs[9]

.

s

KKcontrollerPI i

p (9)

Fig. 4. Fuzzy controller input and output membership functions.

Two fuzzy logics searched the gains of the PI speed

controller. Each FL has two inputs and one output. The

inputs to the gains of the PI are the normalized error

between the reference and actual rotor speed, e(k) =wr*(k)-

wr(k), and the normalized change in Flux error

e(k)=e(k)-e(k-1). The selected inputs and output

memberships for the fuzzy estimator are given in Fig. 4, the

centroid defuzzification algorithm is used, in which the

output fuzzy variable value is calculated as the centre of

gravity of the membership function. In addition, the rule

base controlling the defuzzified output according to the

fuzzified input values is given in Table 2.

TABLE 2

LINGUISTIC RULE BASE FOR TWO PI- FUZZY LOGIC CONTROLLER

de e NB NM NS ZE PS PM PB

N P NS ZE PS PM PB PB

ZE PB P NS ZE PS PM PB

P PB PB PS NS ZE PS PM

5. MODEL REFERENCE ADAPTIVE

SYSTEM

Accurate and robust estimation of motor variables which

are not measured is crucial for high performance sensorless

drives. Multitude observers have been proposed, but only a

few [6, 10-12]

are able to sustain persistent and accurate wide

speed range sensorless operation.

The model reference adaptive system (MRAS) is an

important adaptive controller [10]

. The MRAS for estimating

rotor position angle and speed is based on a stator current

estimator using discontinuous control. Due to the fact that

only stator currents are directly measurable in a PMSM

drive. In this way, when the estimated currents, i.e., state,

reach the manifold. Comparing to other adaptation

techniques, this method is simple and needs a low

computation power and has a high speed adaptation even at

zero speeds. This method is more stable and robust because

it eliminates the error generated in the adjustment of the

speed [10]

. The rotor speed and the stator resistance are

reconstructed using the model reference adaptive system

(MRAS). The MRAS principle is based on the comparaison

of the outputs of two estimators. The first is independent of

the observed variable named as model reference. The

second is the adjustable one. The error between the two

models feed an adaptive mechanism to turn out the

observed variable.

From (2) the state space axis stator currents of PMSM

designed as reference model is given by:

s Ce S1 S2 S3 S4 S5 S6

1

1 110 010 011 001 101 100

0 000 000 000 000 000 000

-1 101 100 110 010 011 001

0

1 010 011 001 101 100 110

0 000 000 000 000 000 000

-1 001 101 100 110 010 011

0

+1

0

+1

-1



324

CBUAXX

(10)

Where

Tqsds

T

qsds v vU , I IX

,

10

011

d

d

r

r

d

lB ,

l

rp

pl

r

A

r

d

e pl

C

0

In this work, the actual system is considered as the

model reference and the observer is used as the adjustable

one. The rotor speed is included in the (10) that present

current model are relevant to rotor speed. So the state space

axis stator current model is chosen as the state variable:

CBUXAX ˆˆ

(11)

Where

qsds

T

qsds v vU , I IX ˆˆˆ

,

10

011

ˆˆ

ˆˆ

ˆ

d

d

r

r

d

lB ,

l

rp

pl

r

A

r

d

e pl

C

ˆ

0

The adaptation mechanism is designed in a way to

generate the value of estimated speed used so as to

minimize the error between the estimated and reference axis

stator currents. By adjusting the estimated rotational speed,

the error between the reference and the estimated axis stator

currents from (11) is reduced [13]

. The error between the

estimated and reference axis stator currents are defined as:

qsqsqsdsdsds IIeIIe ˆ;ˆ (12)

The value of the rotor speed error and resistance stator

error are given as:

rrrrrr rrr ˆ;ˆ (13)

The state error model of the PMSM expressed in the

synchronous reference frame (d_q) is given as follow:

WeAe

(14)

Where

Tqsds e ee is the error state vector, AΔ is the state

matrix and is the output vector of the feedback block

defined as follow:

,ˆˆ

ˆˆ

d

ed

q

d

r

r

d

lI

I

W ,

l

rp

pl

r

A

According to [14]

, to ensure the hyperstability of the

system can be achieved, two criterions must be established.

Firstly, the linear time-invariant forward path transfer

matrix, 1)()(

ApIpH must be strictly positive real

and secondly, the nonlinear feedback (which includes the

adaptation mechanism) must satisfies the following Popov’s

criterion for stability.

2

0

0

Wdte

t

T (15)

Where t0 ≥ 0, γ is a finite positive real constant, which is

independent of t0.

By using the Popov's theory, we obtain: limε→∞=eT (∞)=0

and therefore, the system of the MRAS speed and resistance

estimations is asymptotically stable.

Finally, the stator resistance and the rotor speed are built

around the following adaptive mechanisms:

t

ipr

qsqs

t

dsds

d

s

edtkekp

dtIeIel

r

0

0

)(1ˆ

)ˆˆ(1

ˆ (16)

qs

d

eqsqsdsds e

l

qIIIIe ˆˆ (17)

qsqsqsdsdsds IIeIIe ˆ;ˆ (18)

Where kp and ki are the proportional and integral

constants respectively. The tracking performance of the

speed estimation and the sensivity to noise are depending on

proportional and integral coefficient gains. The integral gain

ki is chosen to be high for fast tracking of speed. While, a

low proportional kp gain is needed to attenuate high

frequency signals denoted as noises [10]

.

Fig. 5. Basic MRAS structure.

+

-

vds,vqs, Ids, Iqs

Reference

Model

Adaptation

Mechanism

Adaptive

Model

AISSA et al.: MRAS FOR SPEED SENSORLESS DIRECT TORQUE CONTROL OF A PMSM DRIVE BASED ON PI FUZZY LOGIC AND STATOR RESISTANCE ESTIMATOR.


325

6. RESULTS OF SIMULATION

Table 3, summarizes the PMSM parameters used in this

simulation[6]

.

We simulated the system drive for a reference speed of

100 (rd / s) load at startup. At t = 0.1(s), the PMSM is

tracking load equal to 5 (Nm), then from t = 0.02 (s), we

assumed a variation of the stator resistance (see Fig. 6).

The results are obtained using a PI speed controller and PI

controller based on Self tuning FL.

Figure 6 illustrates the evolution of stator resistance,

actual and estimated (delivered by the propose MRAS). The

two quantities are combined in practice, in steady state. As

in Fig. 7, it illustrates estimated speed (rad / s) issued by

MRAS, the speed response is achieved without dip and with

a shorter recovery time which is almost similar with the

actual speed motor.

TABLE 3 PMSM PARAMETERS

Pole pairs 3

Rated power KW (at 50 Hz) 1.5

Rated voltage (V) 220/380

Rated Flux (Wb) 0.30

Rated torque (Nm) 5

Rs (Ω) 1.4

Ld ; Lq (H) 0.0066; 0.0058

Flux magnet (Wb) 0.15

J(Kg.m²) 0.00176

fr (Nm/(rad/s)) 0.0038

Figure 8 shows the stator flux estimation using the

MRAS. We notice that it is not affected by these changes.

Electromagnetic torque follows his rate as shown in Fig. 9.

It can be seen that a rapid and non-overshoot speed response

is obtained show the robustness of the proposed PI

controller based on Self tuning FL (Fig. 7).

Fig. 6. Stator Resistance.

7. CONCLUSIONS

In this paper, a model reference adaptive system has

been presented for estimating the stator resistance and speed

of a PMSM in order to achieve a robust speed sensorless

DTC.

Fig. 7. Rotor speed.

Fig. 8. Stator Flux.

Fig. 9. Electromagnetic Torque.

The effect of the variations of motor parameters such as

stator resistance on speed estimation has been studied. A

novel design of a PI controller with fuzzy adapted gains

applied to the speed regulation of DTC motor is fully

presented.

The obtained simulation results were satisfactory in

terms of estimation errors, robustness and global stability of

the drive electrical system for different operating

conditions.

0 0.05 0.1 0.15 0.21

1.5

2

2.5

3

Time (s)

Sta

tor

Resis

tance (

Ohm

)

Actual Resistance

Estimated Resistance

0 0.05 0.1 0.15 0.20

20

40

60

80

100

Time (s)

Roto

r S

peed (

rd/s

)

Actual Speed

Estmated Speed with FLC

Estmated Speed

0 0.05 0.1 0.15 0.20

0.05

0.1

0.15

0.2

0.25

0.3

Time (s)

Sta

tor

Flu

x (

Wb)

0 0.05 0.1 0.15 0.2-5

0

5

10

15

Time (s)

Ele

ctr

om

ag

neti

c T

orq

ue (

N.m

)

Torque with classical PI

Torque with FLC



326

NOMENCLATURE

dq Synchronously rotating frame.

,sd sqI I dq stator current components.

sd sq, dq stator flux components.

e Flux magnet.

M Mutual inductance.

ld , lq Stator d and q axis inductances.

Rs Stator resistance.

J, fr Rotor inertia, friction coefficient.

Tem Electromagnetic torque.

Tl Load Torque

p Number of pole pairs.

r Rotor angular

Te Sampling Period

ki, kp Integral and proportional (IP) speed controller.

I Identity matrix

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Available online at: http://tsest.org/index.php/TCMS/article/view/140

Download full text article at: http://tsest.org/index.php/TCMS/article/download/140/106

Cite this work as:

Ameur Aissa, K. Ameur, and B. Mokhtari, "MRAS for

Speed Sensorless Direct Torque Control of a PMSM

Drive Based on PI Fuzzy Logic and Stator Resistance

Estimator," TSEST Transaction on Control and

Mechanical Systems, Vol. 2, No. 7, Pp. 321-326, Jul.,

2013.

http://en.wikipedia.org/wiki/Identity_matrix

fuzzy mras pmsm

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