attou. neuro-fuzzy msap

7/27/2019 Attou. Neuro-fuzzy Msap

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Neuro-Fuzzy Control of an Input Output

Linearization of a Permanent Magnet

Synchronous Machine fed by a Three LevelsInverter

Ahmed Massoum

Faculty of

Technology Sidi Bel-

Abbes, Algeria

[email protected]

El Mehdi Chiali

Faculty of


Abbes, Algeria

e.chiali @hotmail.fr

Sarra Massoum

Faculty of


Abbes, Algeria

[email protected]

Amine Attou

Faculty of


Abbes, Algeria

[email protected]

Abdelkader Meroufel

Faculty of


Abbes, Algeria

[email protected]

AbstractIn this paper, we present the linearizing control

technique controlled by a neuro-fuzzy regulator applied to the

permanent magnet synchronous machine (PMSM). It permits

decoupling and linearizing the system without taking into

accounts the flux orientation. The nonlinear control (NLC)

applied to the PMSM decompose the system into two mono

variable, linear and independent subsystems. The neuro-fuzzy

control permits to the speed and the Id current control is

carried out by neuro-fuzzy regulators (ANFIS). The analysis

of the results obtained by this type of nonlinear regulator

shows the robustness characteristic with respect to the load

perturbations and the parametric variations. A qualitative

analysis of the evolution of the principal variables describing

the behaviour of the global system (PMSM-Inverter (PWM)-Control) is developed by several tests of digital simulation in

last stage.

Keywords: PMSM, nonlinear control, Neuro-fuzzy control,

three levels inverter

I. INTRODUCTIONThe vector control technique permits to compare the

PMSM to the separate excitation D.C machine. The vectorflux must be concentrated on the D axis with Id current null.However the exact knowledge of the rotoric flux positionposes a precision problem [1]. The nonlinear controltechnique which makes abstraction with the flux orientationpermits to solve this problem. It also allows, by a nonlinear

state negative feedback, to completely decouple the systemin two linear and mono variable subsystems [2,3]. Thus, itis possible to control independently the speed and theforward current Id. The traditional control algorithms (PI orPID) prove to be insufficient where the requirements inperformances are very severe. Several methods of controlare proposed in the technical literature, among them, theNeuro-fuzzy control which held our attention by thesimplicity of its adjustment algorithm and which is theobjective of our work. The work is composed by a PMSMmodelisation in the Park frame and an overview of thenonlinear control technique in order to decouple themachine model. Then, a brief outline on the Neuro-fuzzy

control and its application to the speed and the I d currentcontrol of the PMSM supplied with the three levels inverter.In the last step, a comment on the results obtained insimulation and a conclusion where we emphasize theinterest and the contribution of this method of control.

II. THEPMSMNONLINEARMODELWith the simplifying assumptions relating to the

PMSM, the model of the machine expressed in thereference frame of Park, in the form of state is written as[2,3].

+==

m

1i ii(x)UgF(x)x (1)

With

=

=

=

=

=

=

0

L

10

g;

0

0

L

1

g

U

U

U

UU;

I

I

x

x

x

x

q2

d

1

q

d

2

1

iq

d

3

2

1

(2)

( )

( )

( )

( )

+

+

+

=

=

J

Cx

J

pxx

J

LLp

xJ

f

xL

pxxL

pLxL

R

xxL

pL

xL

R

xf

xf

xf

xF

r

2

f

21

qd

3

3q

f

31q

d

2q

32d

q

1d

3

2

1(3)

The variables to be controlled are the current Id and the

mechanical speed

( )( )

( )

( )

( )

=

=

=

=

I

x

x

xh

xh

xy

xyxY d

2

1

2

1

2

1 (4)

,(((

WK,QWHUQDWLRQDO&RQIHUHQFHRQ3RZHU(QJLQHHULQJ(QHUJ\DQG(OHFWULFDO'ULYHV ,VWDQEXO7XUNH\0D\

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III. THEPMSMINPUT-OUTPUTLINEARIZATIONThe linearization condition that permits to verify if a

nonlinear system admits an input output linearization is therelative degree order of the system [1,4].

Relative degreeThe relative degree of an output is the number of times

that it is necessary to derive the output to reveal the inputU.

Relative degree of the Id current:d11g1f1 U).x(hL)x(hL)x(y += (5)

With

]0g[)x(hL

)x(f)x(hL

111g

11f

=

=(6)

The relative degree of )x(y1 is r1 =1.

Relative Degree of the mechanical speed :

qU)x(hLL)x(hL)x(y

)x(hL)x(y

2fg22f2

2f2

+=

=

(7)

With

[ ])xcc(ggxc)x(hLL

)x(fc)xcc)(x(f)x(fxc)x(hL

)x(f)x(hL

12321222fg

31123212222f

32f

+=

+++=

=

(8)

The relative degree of )x(y2 is r2 =2

Relative Degree of the system:The total degree of the system is equal to order N

(r=r1+r2 = N =3). The system is exactly linearisable.

Decoupling matrix

The matrix defining the relation between the physical

input (U) and the output derivative (Y (x)) is given by the

expression (9).

+=

=

q

d

2

2

d

2

1

U

U)x(D)x(A

dt

d

Idt

d

)x(y

)x(y

(9)

With

+

=

++

=

21qdf

2qd

1

1

3r

21qdf

12qd

1

g)xJ

)LL(p

J

pQ(x

J

)LL(pg

0g

)x(D

)x(fJ

f

)x(f)xJ

)LL(p

J

pQ()x(fx

J

)LL(p

)x(f

)x(A

10)

The model linearization

To linearize the behaviour input-output of the machine

in closed loop, one applies the nonlinear state feedback

given by equation (11) [1,4]:

=

)x(A

V

V)x(D

U

U

2

11

q

d(11)

The decoupling matrix determinant D-1 (X) is no null

(permanent magnet machine). The application of the

linearizing law (11) on the system (10) led to two

decoupled linear systems.

=

=

2V

1V

2dt

2d

dIdt

d

)x(2y

)x(1y

(12)

IV. NEURO-FUZYCONTROLThe fuzzy inference controller based on the neuronal

networks adaptation (ANFIS), uses an optimization trainingmethod of his parameters [9].

A first order Sugeno model of with two inputs x and y ,

five layers and only one output z is considered. The

architecture of the equivalent Neuro-Fuzzy model is givenat fig.1, where the nodes of the same layer have similar

functions, as explained below [6,8,9]:

Fig. 1 The first order ANFIS Architecture

y;x : Input vectors

With

A,B: Membership functions matrices of each input variable.

)y();x( BA : Memberships degrees of input

x associated to set A, or of the input y associated to set B.

kw : is the k th rule weight.

ANFIS training Method

The ANFIS architecture depends on two parameters

sets which are:1. The previous membership functions (A and B

matrices elements).

2. The consequence parameters (p, q, r)

The ANFIS training algorithm is summarized asfollows: Layer 1:

Each node of this layer is adaptive whose outputs are

defined by:


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4,3i),y(O

2,1i),x(O

2i

i

B1i

A1i

==

==

(13)

2ii B,A : Linguistic values associated to iA and

2iB .

iA Can be characterized by the function:

ib2

i

i

a

cx1

1

+

=[L$

(14)

iii c,b,a : Parameters of node i of layer 1. Layer 2:Composed of two fixed nodes (without parameters) which

fulfil the function prod, thus this node output is given by:

iBA2i w)y().x(O ii

== (15)

(Weights determination). Layer 3:Composed of two fixed nodes fulfilling the function:

.2,1i,www

wO i

21

i3i

==+

= (16)

(Standardization of the weights) Layer 4:Have two adaptive nodes which fulfil the function:

)ryqxp(wfwO iiiiii4i ++== (17)

giving the calculation rule of the output based on the

consequences parameters iii retq,p of the node i [8]. Layer 5:It has only one node which is used to calculate the

summation of all the inputs:

222222

111111ii5i

rwq).yw(p).xw(

r.wq).yw(p).xw(fwO

++

+++==

Rearranging the last equation in the following

form:

222222

1111115i

rwq).yw(p).xw(

rwq).yw(p).xw(zO

++

+++==(18)

T222111

222111

]rqprqp[

].wywxwwywxw[y =(19)

If the input-outputs data to be involved exist, the

weights vector W which contains the consequenceparameters can be solved starting from the preceding

equation.

Neuro-Fuzzy regulators implementation

For the Neuro-Fuzzy regulator implementation oneproceeds as follows:

a- The input variable choice:

o Speed regulator- The input variables selected are:

The error betwen the reference speed and the machine

speed )e( r*r = and the error derivative )de( .

o The Id current regulatorFor the Neuro-Fuzzy Id current regulator

implementation one proceeds as follows:

- The input variables selected are:

The error between the reference current and the machine

current )IIe( d*di = and the error derivative )de( i .

b- The training data base choice was based on the

results of the fuzzy controller.

c- The membership functions Choice

The membership functions associated to each input

variable )de,e( or )de,e( ii are of the sigmoid type.

d: The selected training technique is retro propagation

method

The architecture of the resulting controller is given by

fig.2 [6,9].

Fig. 2 The architecture of the resulting ANFIS

V. THELOADTORQUEESTIMATEThe load torque is hardly measurable what obliges us to

use its estimate in the qcI control expression. The method

suggested by le Pioufle permits to estimate in real time theload couple [2].The figure 3 illustrates the estimator

principle.

Fig. 3 The load torque Estimator

The error between measured speed and estimated speed

is presented as an input of a regulator PI whose output is:


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rC2s

2k

1s

2k

1k1

1

s2

k1

k1

rC~

++

+

+

=(20)

k1 and k2 are determined by the poles placement

method.

Fig. 4 The estimator Response characteristic

The estimated torque follows with a good precision the

load torque variations static mode while in dynamic mode itpresents a light shift due to the estimator reaction.

VI. THE THREE LEVELS INVERTER MODELISATIONThe NPC three levels inverter of tension consists of

twelve pairs of transistors - diodes that generate levels ofamplitude tension U,0,U . It is generally controlled by

the PWM. The simple tension of each phase is entirelydefined by the state of the four transistors (Switches)constituting each arm. The median diodes of each armpermits to have the zero level of the inverter outputvoltage. Only three sequences of operation are retainedand done in work. Each arm of the inverter is modelled by a

perfect switch with three positions [7] (- 1, 0, 1) (Fig.5).The operation of the converter is based on the PWMstrategy with two carriers. The intersections of these lastwith the modulating signals determine the instants and thedurations of closing or opening of the switches of each arm.The three-phase simple power provided by the inverter isdetermined by the following relation:

[ ] [ ] [ ]SC6

UV = (21)

With : ( ) [ ] ( ) [ ]SSSS;VVVV t321tcnbnan ==

[ ]

)3,2,1i(;TTTTS

211

121

112

C

4i3i2i1ii ==

= (22)

iS : Logic signals (Pwm), iF : Switching functions.

Fig. 5 Functional diagram of the Multilevel Inverter

VII. SIMULATIONThe decoupling based on the nonlinear control of the

PMSM supplied with a three levels inverter of tension

(PWM) and with the Neuro-fuzzy control (Fig.6), is tested

by digital simulation.

Fig. 6 General diagram of the Neuro-fuzzy control with NL decoupling of

the PMSM

The performance was verified by means of thenumerical simulation.

In order to valid the algorithm, the reference profileshown in figure 6 is used.

Figure7 represents the performances of the controldevice proposed for a speed level of 100rd/s followed by aninversion of speed rotation 100rd/s at 1s.

The control performances are very satisfactory. Thedynamics of continuation is not affected during theinversion of the speed. The NL decoupling is ensured wheninversing the speed.

The decoupling between the d and the q axis ismaintained under load and speed variation

One notices, for speed, a fast starting without anovershoot and static error. The Id current is maintained null


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and independent of the speed inversion (torque). The Iqcurrent is proportional to the torque. The fluctuationsrecorded on the currents are due to the inverter control.

Fig. 7 PMSM responses to a level speed of +100rd/s followed by an

inversion speed 100rd/s at 1s

VIII. CONCLUSIONWe presented in this paper the Neuro-fuzzy control

performances for a PMSM decoupled by a NL statefeedback and associated to a three levels inverter (PWM).The results obtained show the applicability of this controltechnique in the field of the electric drives. The objective ofcontinuation is very good.

The speed time response is very good with noovershoot.

Decoupling is maintained even with the inversion of thespeed. The input output linearization with NL statefeedback permits to bring the behaviour of the closed loopsystem of a NL system to a decoupled linear system withoutpassing by the exact knowledge of the rotoric flux position.This control strategy provided a stable system withsatisfactory performances with a good decoupling.

MACHINE PARAMETERS:

230rd/s;20AI;0.6R

;8.5NmeC;Nm/rds31.410f;kgm1.110J

;4P;0.12wb;2.8mHL;1.4mHL

nqn

123

fqd

===

===

====

REFERENCES[1] W. LEONHARD: Control of electrical drives. Springer Verlag

Berlin, 1985.

[2] B.K. BUMP: Power electronics and AC drive. Printice Hall New

York, 1986.

[3] G.A. KAPOLINO: Vector Numerical control of the current AC

machines,RGE, no.5, pp. 148-160, May 92.

[4] Makato Iwasaki Nobuyuki Matsui: Robust speed control of IM with

torque feed forward control, IEEE Trans Ind Elect, vol 40, no. 6,

pp553-560, Dec.93.

[5] B.HEMICI: Ordering of the position by the technique of the flow

directed for an inverter of current, Proceedings CEAV1, Algiers,

Nov.94.

[6] YANN MORERE: Neuro-Fuzzy Networks. May 17, 2001.

[7] A.RACHID: Regulation Systems. ED Masson 1996.

[8] J.F.JODOUIN: Neuronal Networks: Principles and Applications.

1998.

[9] A. ABRAHAM, B. NATH: Designing Optimal Neuro-Fuzzy

Systems for Intelligent Control, in proceedings off the

International Sixth Conference one Control..

BIOGRAPHIES

Ahmed MASSOUM was born in 1959 in Msirda Fouaga, Tlemcen,

Algeria. He received his BS degree in electrical engineering from theElectrical Engineering Institute (INELEC) of Boumerdes 1985 and the MS

degree from the Electrical Engineering Institute of Sidi Bel-Abbes

University in 2004 where he is currently Professor of electrical

engineering. He is a member in Intelligent Control Electrical Power

System Laboratory (ICEPS). His current research interest includes power

electronics and drives.

Abdelkader MEROUFEL was born in Sidi Bel-Abbes (Algeria) 1954.

He received his BS degree in electrical engineering from USTOran in

1979. He is a member in Intelligent Control Electrical Power System

Laboratory (ICEPS). His current research interest includes power

electronics and drives.


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attou. neuro-fuzzy msap

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