Artificial Intelligence Sensor Less Control Of Im

Artificial Intelligence Sensorless Control of Induction Motor Haithem Abu-Rub*, Abdel Karim Awwad**, Noreddin Motan* Electrical Engineering Department, Texas A&M University at Qatar, E-mail: haitham.abu-rub oqatar.tamu.edu *Institut fur Informatik, Friedrich-Alexander-Universitat, Erlangen-Nurenberg/Germany

Abstract In this paper a sensorless vector control system of induction motor using Artificial \intelligence is presented. The ANN and fuzzy logic solutions are discussed. A feed forward ANN with one input, two units in the hidden layer and one output is used for the speed controller. The tracking of the rotor speed is realized by adjusting the new weights of the network depending on the difference between the actual speed and the command speed.

A comparative study between the proposed controller and the conventional PI one will be presented and will show promising results. Also comparison between the conventional PI and fuzzy logic controllers will be shown. The rotor speed tracks the command one smoothly and rapidly, without overshoot and with very small steady state error. Computer simulation results are curried out Keywords: Artificial Neural Networks, fuzzy logic, vector control, induction motor, sensorless control.

IIntroduction: By using vector representation, it is possible to present the variables in an arbitrary coordinate system. If the coordinate system rotates together with a flux space vector, then we use different terminology: flux-oriented control. In this way, it was possible to represent the electromagnetic torque as a product of flux-producing current and a torqueproducing current. Keeping constant flux, an induction machine may be controlled, like a separately excited dc machine. Such method will be selected to control our machine. The new and real applications on the induction motor need more rapid and smooth without overshoot command speed track. The main problem during the use of PI controller is not best response of the system in the case of operating point variation. Artificial intelligence, such as the use of neural networks and fuzzy logic, can be used to identify and control the non-linear dynamic systems since they can approximate a wide range of non-linear functions to any desired degree of accuracy. The ANN have the advantages of that they can be implemented in parallel, which gives relatively fast computation. Also they have the immunity from harmonic ripples and fault tolerance. Since 1990s, there have appeared investigation approaches onto the applications of artificial intelligence to ac motors control [1-2]-[4-7,9].

1-4244-1055-X/07/$25.00 C2007 IEEE.

At the beginning of using ANN an off-line training was used [4], but this method needs to train the network with different patterns to accommodate the variation of the motor parameters, so it is not efficient. Another method was used at which perceptron (two layers NN) was used and the training is done online, [6] but this method was very sensitive to parameters changes. The new proposed ANN controller has three-layer feed forward network and depends only on the stator current. Its input value is the imaginary stator current component and it has one hidden layer (has two units only), and one output. So the system is simple and can be trained on line with very good response. The application of fuzzy logic is a good solution for motor control [12, 13]. The reason for this is the advantages over traditional methods particularly in fuzzy environment as in our case. The speed in sensorless drive system is not exactly obtained and represents a fuzzy condition. Therefore fuzzy logic controller (FLC) is a good solution for sensorless control. To obtain the motor model, which enables system control synthesis, it is necessary to realize variables transformation. The first step is to perform a transformation from three-phase to stationary coordinate system. This operation decreases the number of variables and differential equations in the motor model. For a quadrant coordinate system selected in arbitrary way, there are five non-linear differential equations in the motor model. The next step is to select a coordinate system, such that one of the selected vector components is equal to zero. This allows decreasing the number of differential equations to four, from which one is linear. The proposed ANN based and fuzzy logic controllers will be used in such control system (field oriented control method - FOC). Simulation results will be curried out.

II

INDUCTION MOTOR MODEL

The squirrel cage type of induction motor as differential equations for the stator current and rotor flux vector components presented in coordinate system XY rotating with arbitrary angular speed is: RL L disx RL2+RL2 L s r r mi +0i +j m ury ( Lr wsry+7sx drLrw r

di

RL L L sy= RL2+RL2 s r r mi + r myr -,i -c mlt + ru sy L wTry s sx r w wrx sy dr Lrw rr

cIis x d-

Rr Lrx L r rx

+(

dr

where

L1 M

Lr J

+R

L

mi r L r sx

(3)

mr i ~ +RrLSY )--mo 'frp i-yris sy rysx

(4)

dr dzLr L Wryy

dr 610)

(2)

s

(s

r

)f

-r

rx

6SLrL

ry

(5)

L2

and 'rx' l/IryixISx iSy are LrL s the rotor flux and stator current vectors in coordinate system XY rotating with arbitrary speed, cor is the angular speed of the rotor shaft. Rr, R(LrLs are rotor and stator resistance and inductances respectively, Lm is a mutual inductance, J is the w=

; 8 =1-

inertia, mO is the load torque.

system (stationary) to the rotating one. The produced torque Te in the machine has the next form:

L Tj Te mm(~

r

I -i/I) (vrdisq Vrq sd) -

(6)

where dq are the variables in rotating frame. If our coordinate system rotates with of rotor flux 1r then the electromagnetic torque could be controlled by only one component while the second one is kept constant. This happens because the imaginary component of rotor flux (Vrq=0) which gives the next form:

L

UL J r

rd sq

(7)

If we keep constant isd then the rotor flux will keep constant. By this way the produced torque will linearly depends on the imaginary component of stator current (isq). The vector control system with ANN controller is shown at Fig. 1.

III. VECTOR CONTROL SYSTEM The idea of vector control of AC machines depends on vector representation and transformation from one coordinate

Fig. 1. Control system of induction motor with Al controller (Artificial Intelligence controller)

IV. ROTOR ANGULAR SPEED CALCULATION Rotor angular speed in a presented control system may be determined by using the differential equations of stator current and rotor flux vectors products (equations 1 to 4). Rotor angular speed presents in deferent depends of stator and rotor deferential equations. In steady states the left-hand sides of equations (1 to 4) are equal to zero. This property, together with using new variables and power definitions, provides a lot of equations for rotor speed [10, 12-14]. For higher rotations the rotor speed can be calculated using the state variables as: -a2x 2-si +a4Q (8) r i2 + a3x22 where a2, a3, a4 are motor parameters, s, is the slip frequency and Q is the imaginary reactive power [11]. X12 and x22 are new variables defined below. The equations of used power is: Q=u s/ i sa -u i sf (9) sa where cx and ( denote a stationary frame. The slip frequency is: Si

=

Rr X12 Lr x22

(10)

(1 1)

'ra' s,/3 - 'r/3'soa

x22 Vraisaoc V/r,Z3s, A

disy

allsx + a2

rx

hidden layer output layer

input layer

Figure 2: Feed Forward ANN Figure 3 shows an artificial neuron, which is the processing unit in the artificial neural network, where xi: input and wji: weight from neuron i to neuron j.

wiO

xi

Oj

(12)

On the other hand the next observer system could be used for speed calculation at low speed region [2]: dt =

V- ARTIFICIAL NEURAL NETWORK CONTROLLER ANN is a system that tries to model the behavior of human brain, at which simple processing elements are connected to form the network. This network has the ability to lean nonlinear relations (Fig.2 shows a typical feed-forward artificial neural network).

xo

and the new variables are [3]:

12

signal obtained through experiments and Vf is the filtered signal V.

+ a3CariVry + a4UsX + k(isx -K

(3)

J Xn/

Figure 3: Artificial Neuron n

a2Vfry -+a3wr' au~+ ki~s drx = + a6VJrx y k2 (rry-Y) dzr a5sx ali

d

+

a4

-

-

diry d

a5lY + a6i/ry +

dX=

dzr-k

-

x

+k2(d)rWrx - (x)

_

-

is

)

+

(16)

(18)

,

k4(V 6tr=S4

Vtrx

(15)

(17)

S

dSy = _kl (i,,

i)1 (14yP'

Vf )

(19)

ry

where A denotes estimated variables, kl, k2k3 are the observer gains and S is the sign of speed. The values C, C, are the components of disturbance vector and V is the control

wI = Zxi*wj

(20)

i=1

Oj = g(WJ)

(21)

Where g is called activation function and it could be linear, unit-step, sigmoid etc. The proposed controller is shown in Figure 4 [2], it has one input (isq ) and one unit in the hidden layer and one output layer. The activation function in the input and output layers is the linear function while, for the hidden layer the activation function in equation 13 is used. The error between the current speed and the command speed should be back propagated to adjust the weights The input of the input-unit is isq, Because this unit has a linear activation function then its output is ai = isq . Assuming that INh is the input of the hidden unit h, then: INhi = a *Wi (22)

Ihl = I1*(3

INh2

=a i

*W 2

(23)

Therefore, the output of the hidden unit h (ah) is:

g(INh )

ah

=

W4

=W4 + a*ah2

(24)

where g is the activation function of the hidden units and it is: 1 (25) g(x) = l+x The input of the output unit o is: (26) INo = ahlIw3 + W4 *ah2 So that, the output (isqc) will be (27) isqc = INo The next two equations are used in back propagation to update the weights between the hidden unit h and the output unit o. (28) W W3 + a*ahl *AO

*AO

(29)

Ao= (rc Or ) (30) Where INo is the input of the output-unit, Xc is the command speed, w) is the current speed.

Figure 5: Speed response of the system when using AX controller

ANN controller

Wrc-Wr

Figure 4:the proposed ANN controller The next two equations are used in back propagation learning to update the weights between the input unit the hidden unit h andi: (31) WI = WI +a isq *A hi W2 =W2 where:

+a*is,q *Ah2

(32)

Ahl

g (IN hl) W3 *A (33) (34) Ah2 g (INh2) W4 *A, The proposed ANN controller is shown at Fig. 4. Figures 5-8 show the speed response of 4 kW induction

motor when PI and ANN controllers. The PI controller parameters are tuned using trial and error method. The gain of the controller is adjusted to 10 and the time constant is adjusted to 1. All results are presented in per-unit system. The learning rate is set to 0.3 which is get be trail and error, It is observed that when ANN controller is used the response is significantly better than when using PI one.

r igure o. )peeu response controller

o1

tUC systemil COnILFoi wrieni using

In the figures (5, 6) the command speed was changed from +1 pu. to 0. The learning rate is set by trial and error method. If the learning rate is set to the 0.05 instead of 0.3 the speed response will be worse as shown in figure 7 [2].

1

-4---= 0)-

1-------

Figure 7: Speed response for learning rate of 0.05

VI. FUZZY LOGIC CONTROLLER WITH FIELD WEAKENING Fuzzy logic controller (FLC) is a controlling system based on fuzzy logic concepts. It is a nonlinear mapping between inputs and outputs; it takes decisions depending on if-then rules and fuzzy sets. The control system of induction motors has difficulties in describing the analytical relationships caused by non-precise variable identification, in these situations FLC is the right choice for control [12-14]. Mamdani type of FLC is used for speed control. The input signals for the controller are: control error, 'e' and the change of error, 'Ae' and the output is the change of control signal, 'Au'. The controller consists of three elements: fuzzification block, block of rules (rules of inference) and defuzzification, which are related by proper relationships. On the basis of the values, 'e' and 'IAe', the fuzzy numbers are calculated in the fuzzification block using the membership function presented in Fig. 2. Simple membership functions for the three linguistic variables: 'N' negative, 'Z' - zero and 'P' - positive are used. Symbol "G" means great and symbol "S" means small. The resulting block consists of logic table like, 'If Then' which are described in Table 1. The results of the observer system at very low speed is shown on figure 8. The fuzzy controller requires less computation and design efforts than the ANN controller. The control system with fuzzy logic and PI controllers was investigated in the field weakening region. The investigated system is shown on figure 1.

wr

0.01 0.005

(pu)

.

Command: s::Observed :

-0 005

Acal

X

-0.01

_

-0 015

.

.. ...

... ... ...

-0.02

100

0

.. .. ...

200

300

400

500

600

000

700

101

900

Torquje (pu)

1.2.

1

. C.m: :omand ...

...

...

A

...

d

....1

..

.......a te

:::: :

.......................

04k

.

.

~~~~~d

0.20

-0.2

100

0

200

300

400

;00

500

Time

700

u00

900

1000

(sec)

Fig. 8. Response of the vector control system on torque change - operation at zero speed

...

I -1

L

I

-<

C~~~~~~~~~~~~~~~~~~~~~~,

0

0

10

20

30

40

L

I

30

40

50

60

d L -1

70

80

90

100

90

100

Tab. 1. Fuzzy logic controller rules of inference i'

-S 0.5 '

N

z

P

N

GN

SN

SP

Z

GN

Z

GP

P

SN

SP

GP

The simulation results of the control system with fuzzy logic and speed observer system at zero speed are shown on figure 8. The results for operation in the field weakening region using the voltage controller is shown on figure 9.

-

0

10

20

u

50 t [s]

60

.

d

70

80

Fig. 9. Response of the vector control system with fuzzy logic controller to speed change including field weakening region

VII CONCLUSION In the paper an ANN controller for sensorless control of induction motor was used. Fuzzy logic controller also was used and compared with a conventional PI one. The results obtained form simulation show that the ANN and the PI controller has significantly better performance than the classical PI controller. The controller has simple form and could be easily designed. The use of this controller caused

that the actual speed could track the command one rapidly, smoothly and with zero steady state error for the control system with speed sensor and without. [1] [2]

[3] [4] [5] [6]

[7] [8]

REFERENCES M. G. Simoes and B. K. Bose, "Neural network based estimation of feedback signals for a vector controlled induction motor drive," IEEE Trans. Ind. Applicat., vol. 31, pp. 620-629, May/June 1995. Awwad, A, Abu-Rub, H., Guzinski, J., Wlas, M. and Krzeminski, Z.: "Artificial neural network based sensorless control of induction motor". XVIII Symposium Electromagnetic Phenomena in Nonlinear Circuits. 28-30 June 2004, Poznan, Poland. Krzeminski Z.: Sensorless control of induction motor based on new observer. Int. Conf. on Intelligent Motion and Power Conversion, PCIM'2000, Nuremberg, 2000. T. Orlowska-Kowalska and C. T. Kowalski, 'Neural Network based flux observer for the induction motor drive:, Proc. of EPEPEMC'96, Budapest, Hungary, pp. 187-191, 1996. D. Fodor, J. P. Six, and D. Diana, "Neural networks applied for induc-tion motor speed sensorless estimation," in Proc. ISIE'95, 1995, pp. 181-186. Ben-Brahim and T. Kudor, "Implementation of an induction motor speed estimator using neural networks," in Proc. IPEC, 1995, pp. 52-57. Bose, Bimal K., "Artificial Neural Network Applications in Power Electronics" IEEE Trans pp 1631-1638, 2001 Russell, s. and Norvig, P. "Artificial Intelligent A modern Approach", Prentice Hall, 1995.

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[12].

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[15]

Kazmierkowski, M. and Sobczuk, D. "Investigation of neural network current regulator for VS-PWM inverters", Int. Con. on Power Electronics Motion Control PEMC'94, Warsaw, vol. II pp. 1009-1014, 1994. Abu-Rub H., Guzinski J., Krzeminski Z., Toliyat H., Speed Observer System for Advanced Sensorless Control of Induction Motor, (Accepted to IEEE Trans. On Energy Conversion). Abu-Rub H., Hashlamoun W., A comprehensive analysis and comparative study of several sensorless control system of asynchronous motor, accepted to ETEP journal (European Trans. On Electrical Power), Vol. 11, No. 3, May/June 2001. Akagi H., Kanazawa Y., Nabae A. (1983). "Generalised Theory of the Instantaneous Reactive Power in Three-Phase Circuits, IPEC, Tokyo. Batran, A., Abu-Rub, H. and. Guzinski, J.: "Wide Range Sensorless Control of Induction Motor Using Power Measurement and Speed Observer", 11th IEEE International Conference on Methods and in Models Automation and Robotics MMAR'05, Miendzyzdroje/Poland, 2005-published in Englis Abu-Rub, H. and Jafar Titi: "Comparative Analysis Of Fuzzy And PI Sensorless Control Systems Of Induction Motor Using Power Measurement" 4th International Workshop CPE 2005 Compatibility in Power Electronics, Gdynia, Poland, 2005, published in English. Batran, A, Abu-Rub, H., Guzinski, J.and Krzeminski, Z. "Fuzzy logic based sensorless control of induction motors". XVIII Symposium Electromagnetic Phenomena in Nonlinear Circuits. 2830 June 2004, Poznan, Poland.