of Induction Motor Using Artificial Neural Network and Implementation in MATLAB

8/2/2019 of Induction Motor Using Artificial Neural Network and Implementation in MATLAB

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Abstract: Motors play an important role in daily lifelike in industrial manufacturing and in many other applications. Induction motors are robust, simple, small

in size, low in cost, almost maintenancefree and possess a wide range of speedscompared to DC motors. However, complexity of signal processing and poor precision limits its usage. Speed estimation in an induction motor is very difficult because of its non-linear dynamic nature. Filed Oriented Control or Vector Control developed by Blaschke(1972) and Vas (1900) respectively is used in motor control. But it gives incorrect measurement of flux at low speed and lacks robustness. It has high drive cost, low reliability and noise immunity. Also these methodsemploy speed sensors. However, the algorithm of vector control theory requiresmanipulation of the electric parameters of the motor so that the governing equations in rectangular coordinates can be developed, prior knowledge of the state equations is necessary when the estimation theory is used to estimate the speed precisely. However, the values of the electric parameters may deviate from the de

signated values due to changes in the working environment, temperature, speed, external load and noise. The speed estimation technique employed here is dependent on expressions obtained from the induction motor dynamic equations. The equations have singularity therefore direct speed estimation cannot be employed. Two ANNs are used here to recover the speed from these two equations. The two equations are then combined and singularities are removed. This method is robust and iseasily implementable using commercially available ANN tools.

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LIST OF FIGURES FIGURE PAGE NO. FIG 1.1 Induction Motorcuit on Stationary Frame 14 FIG 1.4 Dynamic Equivalent Circuit on Arbitrary Fra

Axis Equation of Induction Motor..17 FIG 2.1 Numerator Curve

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Table of Contents CERTIFICATE02 ACKNOWLEDGEMENT..03 Anciple 1.1.3 Construction 1.2 Speed of Induction Motor 1.3 Speed Control of Indu

ction Motor 1.4 Dynamic Nature of Induction Motor 1.4.1 Per phase equivalent Circuit 1.4.2 Stationary Frame Circuit 1.4.3 Arbitrary Frame Circuit 1.5 d-q Axis Equation 1.6 Characteristic Equation 2. SPEED FUNCTION 2.1 Speed expression 2.2 Method of Singular Point 2.2.1 Non-Singularity 2.2.2 Continuity 2.2.3 Square integrable 223

08 08 08 08 09 09 11 12 14 15 17 17 19 19 21 21 21


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3. ARTIFICIAL NEURAL NETWORK 3.1 Neural Network 3.2 Definitions 3.3 Function Approximation 3.4 Data 3.5 Training 4. CONCLUSION 5. REFERENCES 6. APPENDIX

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A. MATLAB Command B. Plots

51 52

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CHAPTER 1

INDUCTION MOTOR

1.1 Introduction 1.1.1 Induction Motor Induction motor is the most popular typeof a.c. motor. It is very commonly used for industrial drives since it is cheap,robust, efficient and reliable. It has good speed regulation and high startingtorque. It has a reasonable overload capacity. Along with variable frequency ACinverters, induction motors are used in many adjustable speed applications whichdo not require fast dynamic response. 1.1.2 Principle: It works on the principle of electromagnetic induction. A rotating magnetic field is produced when a 3-phase supply is connected to the 3- phase winding of the stator. 1.1.3 Construction: A three phase induction motor consists of mainly two parts: 1. Stator 2. Rotor The stator is the stationary part and the rotor is the rotating part. The st

ator is built up of highgrade alloy steel laminations to reduce eddy current losses. The rotor is also built up of thin laminations of the same material as stator. The laminated cylindrical core is mounted directly on the shaft or a spidercarried by the shaft. There are two types of induction motor rotors: 1. Squirrelcage rotor 2. Wound rotor

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FIG 1.1

1.2 Speed of induction motor: Induction motor speed is given by following formula:

Where, v = speed of rotor f = frequency of rotor And, n = number of poles

1.3 Speed control of induction motor: The main method employed for speed controlof induction motor are as follows:

1. 2. 3. 4. 5.

Pole changing methods Stator voltage control Supply frequency control Rotor resistance control Slip energy recovery

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1. Pole changing methods: The number of stator poles can be changed by amultiple stator windings, bmethods of consequent poles cpole-amplitude modulation PAM. The met

ds of speed control by pole changing is suitable for cage motors only because the cage rotor automatically develops number of poles equal to the poles of the rotor winding.

2. Stator voltage control: The speed of a 3-phase induction motor can be variedby varying the supply voltage .Torque developed in induction motor is proportional to square of the supply voltage. Speed control is obtained by varying the supplying voltage until the torque required by the load is developed at the desiredspeed.

3. Variable-frequency control: The synchronous speed of an induction motor is given by: Ns=120f/P The synchronous speed and, therefore, the speed of the inducti

on motor can be controlled by varying the supply frequency.

4. Rotor resistance control: The speed of wound induction motor can be controlled by connecting external resistance in the rotor circuit through slip rings. This method is not applicable to cage motors.

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5. Supply energy frequency: In the rotor resistance control,the slip power in rotor circuit is wasted as I2 R Loss during the low speed operation. The efficienc

y of the drive system by this Method of speed control is, therefore, reduced. The slip power from the rotor Circuit can be recovered and fed back to the a.c. source so as to utilize it outside the motor. Thus, the overall efficiency of thedrive system can be increased. This method of speed control is used in large power applications where variation of speed over a wide range involves a large amount of slip power.

1.4 Dynamic model of induction motor: The concept of vector control has opened up a new possibility that induction motors can be controlled to achieve dynamic performance as good as that of DC or brushless DC motors. In order to understandan analyze vector control , the dynamic model of induction motor is necessary .it has been found that the dynamic model equations developed on a rotating refer

ence frame is easier to describe the characteristic of induction motors. It is the objective of the project to derive and explain induction motor model in relatively simple terms by using the concept of space vectors and d-q variables .whenwe choose a synchronous reference frame in which rotor flux lies on the d-axis,dynamic equations of induction motor is simplified and analogous to a DC motor.

1.4.1 CONVENTIONAL PER PHASE EQUIVALENT CIRCUIT :

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FIG 1.2 The inductance of rotor and stator is given by: Inductance of rotor circuit Lr = Llr + Lm Where, Inductance of stator circuit Ls = Lls + Lm, Where, Lr =

rotor inductance, Llr = rotor leakage inductance, Ls = stator inductance, Lls =stator leakage inductance, Lm = magnetizing inductance of motor. If the excitation frequency injected into the stator is e and the actual speed converted into electrical frequency unit is o, slip s is defined by,

s = e o e

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= r/ e Where r is called the slip frequency, hich is the frequency of actual rotor current. The po er consumption in stator circuit is given by, Is2Rs The po er

consumption in rotor circuit and load (output) is given by , Ir2Rs/s Torque produced is given by: T =Ir2Rr (P/2)(1-s)/s e =Ir2Rr(P/2 e) Where P is the no. of poles, although the per-phase equivalent circuit is useful in analyzing and predicting steady-state performance, it is not applicable to explain dynamic performance of the induction motor. In the next section, e ill develop dynamic model of induction motors in general frame ork and introduce several equivalent circuits as special cases. With space vector notation, voltage equations on the statorand rotor circuits of induction motors are, Vs s = Rs Is s + p s s Vr = Rr Ir + p r0 (1) (2)

It is very convenient to transform actual rotor variables (Vr, Ir,r) from eqs.2 . ona rotor reference frame into a ne variables ( Vr s, Ir s, r s) on a stator refe

rence frame as in the derivation of conventional steady-state equivalent circuit. Vs s = Rs Is s + p s s 0 = Rr Ir s + (p - jo) r s (3) (4)

Where o = p o, is the speed of the motor in electrical fre uency unit and s s = LsIs s + Lm Ir s r s = Lm Is s + Lr Ir s (5) (6)

1.4.2 DYNAMIC EQUIVALENT CIRCUIT ON STATIONARY REFERENCE FRAME:

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FIG 1.3 EQUATIONS: It is very convenient to transform actual rotor variables (Vr,Ir, r) from . on a rotor reference frame into a new variab

es ( Vr s, Ir s, r s) on

a stator reference frame as in the derivation of conventiona steady-state equiva

ent circuit. Let the stator to rotor winding turn ratio be n and the angu

ar

position of the rotor be , and define Ir s = (1/n) exp (j ) Ir, r s = n exp (j ) r)

Aso, by defining referred rotor impedances as Rr = n2 Rr, etc., we have Vs s = R

s Is s + p s s 0 = Rr Ir s + (p - jo) r s (8) (9)

Where o = p o, is the speed of the motor in electrical fre uency unit and s s = LsIs s + Lm Ir s r s = Lm Is s + Lr Ir s (10) (11)

The above 4 equations (8-11) constitute a dynamic modeof the induction motor o

n a stationary (stator) reference frame in space vector form. These mode

equations may be simp

ified by e

iminating f

ux

inkages as Vs s = (Rs + Ls p) Is s +Lm p Ir s 0 = (Rr + Lr (p - jo)) Irs + Lm (p - jo) Is s. (12) (13)

From (12-13) , The dynamic equivalent circuit model on a stationary reference frame can be dra n as in Fig.1.2 For steady-state operation ith excitation frequency e, p in may be replaced by je and after some algebraic manipulation, e get11


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Vs s = (Rs + je Ls ) Is s + Lm p Ir s 0 = (Rr/ s + je Lr) Ir s + je Lm Is s.

(14) (15)

hich exactly describes the conventional steady-state equivalent circuit of Fig.1.1.

1.4.3 DYNAMIC EQUIVALENT CIRCUIT ON ARBITRARY REFERENCE FRAME:

FIG 1.4

Equations: No , the previous procedure can be generalized so that the dynamic model is described on an arbitrary reference frame rotating at a speed a, here isa special case ith a,= 0 To do that, define the ne space vector on the arbitrar

y frame as Y a = exp(- ja ) Y s (16)

and reconstruct all the model equations in terms of the ne space vectors. In the arbitrary reference frame, Eqs are modified to Vs a = (Rs + Ls p) Is a + Lm pIr a + ja s a (17)12


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0 = (Rr + Lr p) Ir a + Lm p Is a + j (a - o) r a, ith ne flux linkage equations defined by, s a = Ls Is a + Lm Ir a r a = Lm Is a + Lr Ir a As before, by substitut

ing Eqs. into Eqs,

e have Vsa = (Rs + Ls (p + ja)) Is a + Lm (p + ja ) Ir a 0 = (Rr + Lr (p + ja - jo)) Ir a + Lm (p + ja - jo) Is a here eliminated flux linkage variables are eliminated. (21) (19) (20)

(18)

(22)

The generalized equivalent circuit on a arbitrarily rotating frame based on Eq.is sho n in .. No , depending on a specific choice of a, many forms of dynamic equivalent circuit can be established. Among them, the synchronous frame form canbe obtained by choosing a = e. This form is very useful in describing the concept

of vector control of induction motors as

ell as of PM synchronous motors because at this rotating frame, space vector is not rotating, but fixed and have a constant magnitude in steady-state. Since space vectors in the synchronous frame ill frequently be used, they are denoted ithout any superscript indicating the type of frame. Another possible reference frame used in vector control is the rotor reference frame by choosing c = o hich is , in fact, the reverse step of . ith n =1.

1.5 d-q axis equations of induction motor:

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FIG 1.5 In many cases, analysis of induction motors ith space vector model is complicated due to the the fact that e have to deal ith variables of complex nu

mbers. For any space vector Y, define t

o real quantities Sq and Sd as, S = Sq -j S d . In other ords, Sq = Re (S) and Sd = - Im (S) illustrates the relationship bet een d-q axis and complex plane on a rotating frame ith respect to stationary a-b-c frame. Note that d- and q-axes are defined on a rotating reference frame at the speed of a = p a ith respect to fixed a-b-c frame. Fig. 3.1 Definition of d-axis and q-axis on an arbitrary reference frame ith the above definitioncan be translated into the follo ing 4 equations of real variables expressed ina matrix form.

1.6 Characteristic equation:

The d-q axis dynamic equations for the squirrel cage induction motor are given b

y [l]

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V = AI (1)

here, In the above equations, subscript s denotes stator quantities, r denotesrotor quantities, q and d refer to the quadrature and direct axis quantities respectively and L, is the magnetizing inductance.

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SPEED FUNCTION

2.1 Speed Expression: If the stator voltages and stator currents are kno

n along ith the machine parameters. We have only three unkno ns r , ird and irq . We can thus solve for r (speed of induction motor) in terms of stator quantities only.First , e obtain the rotor currents as function of stator quantities and r ,from the first t o ro s of characteristic equation . since the rotor currents are not accessible in a squirrel cage induction motor . the expressions for ird and irq are obtained as:

ird= 1/Lm [(Vsd-Rsisd)dt- Lsisd] irq=1/Lm[(Vsq-Rsisq)dt-Lsisq]

We can substitute ird and irq in the last t o ro s of characteristic equation and obtain the equations of rotor speed r as: r = -[2disd/dt RrLsisd + RrVxddt + LrVxd

] /[2isq+Lr

Vxqdt] Where,

2=Lm2-LrLs, Vxd=Vsd-Rsisd, Vxq=Vsq-Rsisq The speed can berecover from this equation directly but due to singularities in this function it

is difficult to calculate speed for regular induction motor operation.

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FIG 2.1

FIG 2.2

It can be seen from the above figures of numerator and denominator functions that both aveforms are in phase, resulting in simultaneous zero-crossings, and hence singular points. Hence e cannot obtain the speed of induction motor directly. So for calculating the speed of induction motor e use artificial neural net ork.

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2.1 METHOD OF SINGULAR POINTS : One of the necessary conditions for an ANN to approximate a function is that the function should be square integrable, non-linea

r, singular and continuous.

2.1.1 Non singularity: A square matrix is nonsingular if Ax = 0n implies x = 0n.Other ise it is a singular matrix Properties of singular matrix: 1.A nn is nonsingular if and only if r(A) = n. 2.A is nonsingular if and only if A has a linearinverse A1.

2.1.2 Continuity:

FIG 2.3

A continuous function is a function for which, intuitively, small changes in the

input result in small changes in the output continuity of a function in the following intuitive terms: an infinitesimal change in the independent variable corresponds to an infinitesimal change of the18


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dependent variable .We call a function continuous, if, and only if, it is continuous at every point of its domain. More generally, we say that a function is con

tinuous on some subset of its domain if it is continuous at every point of thatsubset. 2.1.3 S uare integrable: A real or complex

valued function of a real or

complex variable is s uare

integrable on an interval if the integral of the s uare of its a absolute value, over that interval, is finite.

The basic idea in this method is to partition the main speed function having singularities into smaller function which do not have any singularities , and to train small ANNs to identify these smaller functions. The desired output can be obtained from the outputs of these ANNs by avoiding the singular points of the mainfunctions. In this case one of the simplest ways to partition the functions is to consider their numerators and denominators separately.

N1=

[2disd/dt

RrLsisd+RrVxddt+LrVxd]

D1= 2is +LrVx

dt

ANNs can be trained to approximate N1 and D1. The output of these ANNs can then bepassed through a filter which performs the re uired division at points where both the numerators and denominators are non

zero. Inputs given to the numerator ANN are: Isd,disd/dt,vsd,vsddt and isddt Input given to thedenominator ANN are: vs

,vs dt and is

dt

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Block diagram of ANN

FIG 2.4

CHAPTER

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NEURAL NETWORK

3.1 Neural Network An Artificial Neural Network (ANN) is an information processing paradigm that is inspired by the way biological nervous systems, such as thebrain, process information. The key element of this paradigm is the novel structure of the information processing system. It is composed of a large number of highly interconnected processing elements (neurons) working in unison to solve specific problems. ANNs, like people, learn by example. An ANN is configured for aspecific application, such as pattern recognition or data classification, through a learning process. Learning in biological systems involves adjustments to thesynaptic connections that exist between the neurons. This is true of ANNs as well.

Use Neural networks, with their remarkable ability to derive meaning from compli

cated or imprecise data, can be used to extract patterns and detect trends thatare too complex to be noticed by either humans or other computer techni ues. A trained neural network can be thought of as an "expert" in the category of information it has been given to analyse. This expert can then be used to provide projections given new situations of interest and answer "what if" uestions. Other advantages include: 1. Adaptive learning: An ability to learn how to do tasks based on the data given for training or initial experience. 2. Self

Organisation: An ANN can create its own organisation or representation of the information it receives during learning time. 3. Real Time Operation: ANN computations may be carried out in parallel, and special hardware devices are being designed and manufactured which take advantage of this capability. 4. Fault Tolerance via RedundantInformation Coding: Partial destruction of a network leads to the correspondingdegradation of performance. However, some network capabilities may be retained

even with major network damage.

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FIG 3.1

3.2 Definitions:

Feed forward network: Feed

forward networks have the following characteristics:1. Perceptrons are arranged in layers, with the first layer taking in inputs andthe last layer producing outputs. The middle layers have no connection with theexternal world, and hence are called hidden layers. 2. Each perceptron in one layer is connected to every perceptron on the next layer. Hence information is constantly "fed forward" from one layer to the next., and this explains why thesenetworks are called feed

forward networks. 3. There is no connection among perce

ptrons in the same layer.

Feedback Network: By using loops in the network, Feedback networks transfer sign

als in both directions. Feedback networks are powerful and complex. Feedback networks state is changing dynamically until they reach an e uilibrium point. Untilthe input changes, they remain at the e uilibrium point. Feedback architecturesare called as interactive or recurrent

Back propagation: It is a supervised learning method, and is an implementation of the Delta rule. It re uires a teacher that knows, or can calculate, the desired output for any given input. It is most useful for feed

forward networks (netwo

rks that have no feedback, or simply, that have no connections that

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loop). The term is an abbreviation for "backwards propagation of errors". Back propagation re uires that the activation function used by the artificial neurons

(or "nodes") is differentiable.

FIG 3.2

Supervised learning: Supervised learning incorporates an external teacher, so that each output unit is told what its desired response to input signals ought tobe. During the learning process global information may be re uired. Paradigms ofsupervised learning include error

correction learning, reinforcement learning a

nd stochastic learning. An important issue concerning supervised learning is theproblem of error convergence, i.e. the minimisation of error between the desired and computed unit values. The aim is to determine a set of weights which minimizes the error. Neuralwares Predict: NeuralWorks Predict is an integrated, state

of

the

art tool for rapidly creating and deploying prediction and classification applications. Predict combines neural network technology with23


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genetic algorithms, statistics, and fuzzy logic to automatically find optimal ornear

optimal solutions for a wide range of problems. Predict incorporates years

of modeling and analysis experience gained from working with customers faced with a wide variety of analysis and interpretationproblems. Predict re uires no prior knowledge of neural networks. With only minimal user involvement it addresses all the issues associated with building robust models from available empiricaldata. Predict analyzes input data to identify appropriate transforms, partitions the input data into training and test sets, selects relevant input variables,and then constructs, trains, and optimizes a neural network tailored to the problem. For advanced users, Predict also offers direct access to all key training and network parameters. 3.3 FUNCTION APPROXIMATION When input data originates from a function with real

valued outputs over a continuous range, the neural networ

k is said to perform a traditional function approximation. An example of an approximation problem could be one where the temperature of an object is to be deter

mined from secondary measurements, such as emission of radiation. Another more trivial example could be to estimate shoe size based on a persons height. These two examples involve models with one input and one output. A more advanced model of the second example might use gender as a second input in order to derive a more accurate estimate of the shoe size.

3.4 DATA FOR NEURAL NETWORK TRAINING: Induction motor parameters used in simulation work: Parameters Stator resistance Rotor resistance Stator inductance Rotorinductance Magnetizing inductance Symbol Rs Rr Ls Lr Lm Value 0.49 0.45 0.0388mH 0.0354mH 0.0354mH

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Numerator X1 9.54 8.9 9.3 9.1 10.1 10.5 9.5 8.4 9.4 8.3 8.7 8.5 9.6 10.4 10.9 11.1 11.5 11.8 11.3 11.4 11.7 12.3 12.5 12.8 12.6 12.4 12.9 13.2 13.4 13.6 X2 7.8

8.7 8.4 8.2 9.3 9.4 8.9 8.6 10.1 10.5 10.8 10.7 8.5 9.2 9.8 10.3 10.2 10.7 10.410.6 9.6 11.2 11.3 11.6 11.4 11.7 11.5 12.1 12.5 13.8 X3 4.9 4.79 2.51 1.52 2.341.21 2.4 1.59 4.5 4.4 4.35 3.4 2.9 2.5 2.4 2.1 2.12 1.9 1.8 1.6 2.1 2.5 2.4 2.24.35 4.45 4.5 4.9 5.2 5.35 X4 6.8 6.34 3.23 2.45 1.9 0.78 1.75 2.34 6.7 6.54 6.48 6.3 2.41 1.8 0.6 0.45 0.4 0.35 0.32 0.3 0.4 0.5 2.1 2.8 6.4 6.6 6.8 7.1 7.5 7.9 X5 5.1 5.31 7.13 7.81 8.12 9.89 8.3 7.9 4.98 4.95 5.1 5.15 7.9 8.5 10.15 13.515.1 15.9 16.8 17.5 14.5 13.2 10.5 9.9 5.2 5.1 4.9 3.9 3.5 3.2 N1

2.111

1.870.02 0.562 0.84 1.7761 0.961 0.6287

2.0787

2

1.94

1.82 0.54 0.97 1.87 2.695

3.0669 3.2732 3.4882 3.6583 2.93 2.5905 1.28 0.84011.889

2.005

2.1413

2.51

2.789

3.0403

X1=disd/dt ,X2=isd, X3=Vsd, X4=Vsddt, X5=isddt

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Y1 80.9 70.8 90.4 99.3 120 130.1 140.3 120.25 135.55 112.9 115.7 132.7 122.5 134.45 145.85 129.89 124.6 127.7 154.85 149.65 148.43 152.35 145.76 155.91 143.87 1

56.24 165.34 130.5 135.9 141.95

Y2 46.27 69.13 70 113 130 204 127 93 95 100 98 97.5 88 102 131.1 153 160 161 154168 149 156 101 84 137 136 134 130 125 120

Y3 700 610 138 120 108 98 100 91 490 460 425 390 130 125 116 110 108 116 112 133140 175 137 128 390 394 402 410 416 420

D10.0105

0.00813 0.000072 0.00193 0.00275 0.00553 0.00278 0.001722

0.00513

0.004440.00391

0.0033 0.000892 0.00144 0.00263 0.00354 0.0038 0.003719 0.0035

4 0.00365 0.00285 0.00251 0.001219 0.000785

0.00189

0.00201

0.00214

0.002510.00279

3.04403

Y1=dis /dt, Y2=Vs dt, Y3=is

dt

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3.5 TRAINING STEPS FOR NEURAL NETWORK:

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CONCLUSION:

This project outlines techni

ue for speed estimation of induction motor using artificial neural networks. The dynamic model of induction motor is considered andexpression for rotor speed is obtained . The expression obtained have singularities thus ANNs cannot be used to obtain the speed directly from speed function. Amethod is used in this project in which two ANNs are trained to approximate thenumerator and the denominator functions in the speed expression. By training such ANNs and using a filter to avoid singular points , the speed can be recovered .

REFERENCES: 1. Electrical Machinary by A.E. Fitzgerald. 2. Electric Machines byAshfa Hussain. 3. Control System Engineering by I. J. Nagrath and M. Gopal46


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4. Dynamic model of induction motors for vector control Dal Y. Ohm, Drivetech Inc., Blacksburg,Virginia. 5. Speed Estimation Of Induction Motor Using Artificial Ne

ural Networks by Prashant Mehrotra, John E. Quaicoe and R. Venkatesan. 6. Motor Speed Identification Via Neural Network by L.Ben Brahim. 7. Neural Network Documentation by Wolframesearch. 8. www.google.com 9. www.wikipedia.com 10. Neuralware predict

APPENDIX:

A. MATLAB COMMANDS:

>> y1= [80.9 70.8 90.4 99.3 120 130.1 140.3 120.25 135.55 112.9 115.7 132.7 122.5 134.45 145.85 129.89 124.6 127.7 154.85 149.65 148.43 152.35 145.76 155.91 143.87 156.24 165.34 130.5 135.9 141.95];

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>> y2= [46.27 69.13 70 113 88 102 131.1 153 137 136 134 130 >> y3= [700 130 390610 125 394 138 116 402 120 110 410

130 160 125 108 108 416

204 127 161 154 120]; 98 100 116 112 420];

93 168

95 149

100 156

98 101

97.5 84

91 133

490 140

460 175

425 137

390 128

>> d1= 0.12*(10^ 9)*y1+0.0354*(10^ 3)*y2 0.01734*(10^ 3)*y3; >> plot(d1); >> x1=[9.54 8.9 9.6 10.4 12.6 12.4 >> x2=[7.8 8.5 11.4 >> x3=[4.9 2.9 4.35 >> x4=[6.82.41 6.4 >> x5=[5.1 7.9 5.2 8.7 9.2 11.7 4.79 2.5 4.45 6.34 1.8 6.6 5.31 8.5 5.1 9.3 10.9 12.9 8.4 9.8 11.5 2.51 2.4 4.5 3.23 0.6 6.8 9.1 11.1 13.2 8.2 10.3 12.1 1.52 2.1 4.9 2.45 0.45 7.1 10.1 11.5 13.4 9.3 10.2 12.5 2.34 2.12 5.2 1.9 0.47.5 8.12 15.1 3.5 10.5 9.5 11.8 11.3 13.6]; 9.4 8.9 10.7 10.4 13.8]; 1.21 2.4 1.9 1.8 5.35]; 0.78 0.35 7.9]; 9.89 15.9 3.2 1.75 0.32 8.4 11.4 9.4 11.7 8.3 12.38.7 12.5 8.5 12.8

8.6 10.6

10.1 9.6

10.5 11.2

10.8 11.3

10.7 11.6

1.59 1.6

4.5 2.1

4.4 2.5

4.35 2.4

3.4 2.2


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2.34 0.3

6.7 0.4

6.54 0.5

6.48 2.1

6.3 2.8

7.13 7.81 10.15 13.5 4.9 3.9

8.3 16.8

7.9 17.5

4.98 14.5

4.95 13.2

5.1 10.5

5.15 9.9

>> n1=

(

0.12*10^(

9)*x1

0.03474*10^(

3)*x2+0.0354*x3+0.45*x4

0.22*x5); >> wr=n1./d1; >> plot(wr)

B. PLOTS:

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Numerator plot

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Denominator plot

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Speed plot

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of Induction Motor Using Artificial Neural Network and Implementation in MATLAB