speed estimation of induction motor using artificial neural network and implementation in MATLAB

8/9/2019 speed estimation 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 otherapplications. Induction motors are robust, simple, small in size, low in cost, almost maintenance-free and possess a wide range of speeds compared to DC motors. However, complexity of signalprocessing 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 Controldeveloped by Blaschke(1972) and Vas (1900) respectively is used in motor control. But it givesincorrect measurement of flux at low speed and lacks robustness. It has high drive cost, lowreliability and noise immunity. Also these methods employ speed sensors. However, thealgorithm of vector control theory requires manipulation of the electric parameters of the motorso that the governing equations in rectangular coordinates can be developed, prior knowledge ofthe state equations is necessary when the estimation theory is used to estimate the speedprecisely. However, the values of the electric parameters may deviate from the designated valuesdue 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 speedestimation cannot be employed. Two ANNs are used here to recover the speed from these twoequations. The two equations are then combined and singularities are removed. This method isrobust and is easily implementable using commercially available ANN tools.

Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.


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LIST OF FIGURES

FIGURE PAGE NO.

FIG 1.1 Induction Motor.09

FIG 1.2 Coventional Per Phase equivalent circuit......12FIG 1.3 Dynamic equivalent circuit on Stationary Frame 14

FIG 1.4 Dynamic Equivalent Circuit on Arbitrary Frame ....15

FIG 1.5 d-q Axis Equation of Induction Motor..17

FIG 2.1 Numerator Curve...20

FIG 2.2 Denominator Curve...20

FIG 2.3 Continuity..21

FIG 2.4 Block Diagram of ANN.23

FIG 3.1 Neuron Model25

FIG 3.2 MLP...26



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Table of Contents

CERTIFICATE02

ACKNOWLEDGEMENT..03

ABSTRACT.04

LIST OF FIGURES05

CHAPTERS

1. INDUCTION MOTOR

1.1 Introduction 08

1.1.1 Induction Motor 08

1.1.2 Principle 08

1.1.3 Construction 08

1.2 Speed of Induction Motor 09

1.3 Speed Control of Induction Motor 09

1.4 Dynamic Nature of Induction Motor 11

1.4.1 Per phase equivalent Circuit 12

1.4.2 Stationary Frame Circuit 14

1.4.3 Arbitrary Frame Circuit 15

1.5 d-q Axis Equation 17

1.6 Characteristic Equation 17

2. SPEED FUNCTION 19

2.1 Speed expression 19

2.2 Method of Singular Point 21

2.2.1 Non-Singularity 21

2.2.2 Continuity 21

2.2.3 Square integrable 22



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3. ARTIFICIAL NEURAL NETWORK 24

3.1 Neural Network 24

3.2 Definitions 25

3.3 Function Approximation 27

3.4 Data 27

3.5 Training 30

4. CONCLUSION 49

5. REFERENCES 50

6. APPENDIX 51

A. MATLAB Command 51

B. Plots 52



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CHAPTER 1

INDUCTION MOTOR

1.1 Introduction

1.1.1 Induction Motor

Induction motor is the most popular type of a.c. motor. It is very commonly used for industrialdrives since it is cheap, robust, efficient and reliable. It has good speed regulation and highstarting torque. It has a reasonable overload capacity. Along with variable frequency ACinverters, induction motors are used in many adjustable speed applications which do not requirefast 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 stator is built up of high-

grade 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 spider carried by the shaft.

There are two types of induction motor rotors:

1. Squirrel cage 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 control of induction motor are as follows:

1. Pole changing methods2. Stator voltage control3. Supply frequency control4. Rotor resistance control5. 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 methods 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 varied by 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 desired speed.

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 induction 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 therotor 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 efficiency 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 tothe a.c. source so as to utilize it outside the motor. Thus, the overall efficiency of the drive

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 understand an analyze vector control , the dynamic model of induction motor isnecessary . it has been found that the dynamic model equations developed on a rotating reference

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 .when we 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, slips is defined by,

s = e o

e



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= r/e

Where r is called the slip frequency, which is the frequency of actual rotor current.

The power consumption in stator circuit is given by,

Is2

RsThe power 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 =Ir

2Rr(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, we will develop dynamic model of induction motors ingeneral frame work and introduce several equivalent circuits as special cases.

With space vector notation, voltage equations on the stator and rotor circuits of induction motors

are,

Vss= RsIs

s+ p s

s (1)

Vr = Rr Ir + p r = 0 (2)

It is very convenient to transform actual rotor variables (Vr, Ir,r) from eqs.2 . on a rotor

reference frame into a new variables ( Vrs, Irs, rs) on a stator reference frame as in the

derivation of conventional steady-state equivalent circuit.

Vss= RsIs

s+ p s

s (3)

0 = RrIrs+ (p - jo) r

s (4)

Where o =p o, is the speed of the motor in electrical frequency unit and

ss= LsIs

s + LmIrs (5)

rs= LmIss + LrIrs (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 (V r, Ir, r) from . on a rotor reference

frame into a new variables ( Vrs, Ir

s, rs) on a stator reference frame as in the derivation of

conventional steady-state equivalent circuit. Let the stator to rotor winding turn ratio be n and theangular position of the rotor be , and define

Irs = (1/n) exp (j ) Ir,

rs = n exp (j ) r (7)

Also, by defining referred rotor impedances as Rr = n2 Rr, etc., we have

Vss = Rs Is

s + p ss (8)

0 = RrIrs

+ (p - jo) rs

(9)

Where o = p o, is the speed of the motor in electrical frequency unit and

ss = Ls Is

s + Lm Irs (10)

rs = Lm Is

s + LrIrs (11)

The above 4 equations (8-11) constitute a dynamic model of the induction motor on a stationary

(stator) reference frame in space vector form. These model equations may be simplified by

eliminating flux linkages as

Vss = (Rs + Ls p) Iss + Lm p Irs (12)

0 = (Rr+ Lr(p - jo)) Irs + Lm (p - jo) Is

s. (13)

From (12-13) , The dynamic equivalent circuit model on a stationary reference frame can be

drawn as in Fig.1.2 For steady-state operation with excitation frequency e, p in may be

replaced by je and after some algebraic manipulation, we get



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Vss = (Rs + je Ls ) Is

s + Lm p Irs (14)

0 = (Rr/ s + je Lr) Irs + je Lm Is

s. (15)

which 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:

Now, the previous procedure can be generalized so that the dynamic model is described on an

arbitrary reference frame rotating at a speed a, where is a special case with a,= 0 To do that,

define the new space vector on the arbitrary frame as

Y a= exp(- j a ) Ys (16)

and reconstruct all the model equations in terms of the new space vectors. In the arbitrary

reference frame, Eqs are modified to

Vsa= (Rs + Ls p) Is

a+ Lm p Ir

a+ jas

a (17)



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0 = (Rr+ Lrp) Ira+ Lm p Is

a+ j (a - o) r

a, (18)

with new flux linkage equations defined by,

sa

= LsIsa+ LmIr

a (19)

ra

= LmIsa

+ LrIra

(20)

As before, by substituting Eqs. into Eqs, we have

Vsa= (Rs + Ls (p + ja)) Is

a+ Lm (p + ja ) Ir

a (21)

0 = (Rr+ Lr(p + ja - jo)) Ira

+ Lm (p + ja - jo) Isa (22)

where eliminated flux linkage variables are eliminated.

The generalized equivalent circuit on a arbitrarily rotating frame based on Eq. is shown in ..

Now, depending on a specific choice of a, many forms of dynamic equivalent circuit can be

established. Among them, the synchronous frame form can be obtained by choosing a = e.

This form is very useful in describing the concept of vector control of induction motors as well

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 will frequently be used, they are denoted without any superscript indicating the type of

frame.

Another possible reference frame used in vector control is the rotor reference frame by choosing

c = o which is , in fact, the reverse step of . with 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 with space vector model is complicated due to the

the fact that we have to deal with variables of complex numbers. For any space vectorY, define

two real quantities Sqand Sdas,

S = Sq - j Sd .

In other words, Sq= Re (S

) and Sd= - Im (S

) illustrates the relationship between d-q axis andcomplex plane on a rotating frame with 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 with respect to fixed a-b-c

frame.

Fig. 3.1 Definition of d-axis and q-axis on an arbitrary reference frame with the above definition

can be translated into the following 4 equations of real variables expressed in a matrix form.

1.6 Characteristic equation:

The d-q axis dynamic equations for the squirrel cage induction

motor are given by [l]



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V = AI (1)

where,

In the above equations, subscript s denotes stator quantities,

r denotes rotor quantities, q and d refer to the quadrature and direct axis quantities respectively

and L, is the magnetizing inductance.

CHAPTER-2



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SPEED FUNCTION

2.1 Speed Expression:

If the stator voltages and stator currents are known along with the machine parameters. We haveonly three unknowns r , ird and irq . We can thus solve for r (speed of induction motor) in

terms of stator quantities only. First , we obtain the rotor currents as function of stator quantities

and r ,from the first two rows 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 two rows of characteristic equation and obtain the

equations of rotor speed r as:

r = -[2disd/dt RrLsisd + RrVxddt + LrVxd] /[2isq+LrVxqdt]Where,

2=Lm2-LrLs,Vxd=Vsd-Rsisd,

Vxq=Vsq-Rsisq

The speed can be recover 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

waveforms are in phase, resulting in simultaneous zero-crossings, and hence singular points.

Hence we cannot obtain the speed of induction motor directly.

So for calculating the speed of induction motor we use artificial neural network.



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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-linear, singular and continuous.

2.1.1 Non singularity:

A square matrix is nonsingular if Ax = 0n implies x = 0n. Otherwise 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 linear inverse 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 the



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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 continuous on some subset of its domain

if it is continuous at every point of that subset.

2.1.3 Square integrable:

A real or complex-valued function of a real or complex variable is square-integrable on aninterval if the integral of the square 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 main functions. 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= 2isq+LrVxqdt

ANNs can be trained to approximate N1 and D1. The output of these ANNs can then be passed

through a filter which performs the required division at points where both the numerators anddenominators are non-zero.

Inputs given to the numerator ANN are:

Isd,disd/dt,vsd,vsddt and isddt

Input given to thedenominator ANN are:

vsq,vsqdt and isqdt



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Block diagram of ANN

FIG 2.4

CHAPTER-3



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NEURAL NETWORK

3.1 Neural Network

An Artificial Neural Network (ANN) is an information processing paradigm that is inspired bythe way biological nervous systems, such as the brain, 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 a specific

application, such as pattern recognition or data classification, through a learning process.

Learning in biological systems involves adjustments to the synaptic connections that exist

between the neurons. This is true of ANNs as well.

Use

Neural networks, with their remarkable ability to derive meaning from complicated or imprecisedata, can be used to extract patterns and detect trends that are too complex to be noticed by eitherhumans or other computer techniques. 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" questions.Other advantages include:

1. Adaptive learning: An ability to learn how to do tasks based on the data given for trainingor initial experience.

2. Self-Organisation: An ANN can create its own organisation or representation of theinformation it receives during learning time.

3. Real Time Operation: ANN computations may be carried out in parallel, and specialhardware devices are being designed and manufactured which take advantage of thiscapability.

4. Fault Tolerance via Redundant Information Coding: Partial destruction of a networkleads to the corresponding degradation of performance. However, some networkcapabilities 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 and the last layerproducing outputs. The middle layers have no connection with the external world, and henceare called hidden layers.

2. Each perceptron in one layer is connected to every perceptron on the next layer. Henceinformation is constantly "fed forward" from one layer to the next., and this explains whythese networks are called feed-forward networks.

3. There is no connection among perceptrons in the same layer.

Feedback Network:

By using loops in the network, Feedback networks transfer signals in both directions. Feedback

networks are powerful and complex. Feedback networks state is changing dynamically until they

reach an equilibrium point. Until the input changes, they remain at the equilibrium point.

Feedback architectures are called as interactive or recurrent

Back propagation:

It is a supervised learning method, and is an implementation of the Delta rule. It requires a

teacher that knows, or can calculate, the desired output for any given input. It is most useful for

feed-forward networks (networks 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

requires 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 to be. During the learning process global information

may be required. Paradigms of supervised learning include error-correction learning,

reinforcement learning and stochastic learning.

An important issue concerning supervised learning is the problem of error convergence, i.e. theminimisation 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 with



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genetic algorithms, statistics, and fuzzy logic to automatically find optimal or near-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 requires no prior knowledge of neural networks. With only minimal user involvement itaddresses all the issues associated with building robust models from available empirical data.

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, theneural network 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 determinedfrom secondary measurements, such as emission of radiation. Another more trivial examplecould be to estimate shoe size based on a persons height. These two examples involve modelswith one input and one output. A more advanced model of the second example might use genderas 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 Symbol Value

Stator resistance Rs 0.49Rotor resistance Rr 0.45Stator inductance Ls 0.0388mHRotor inductance Lr 0.0354mH

Magnetizing inductance Lm 0.0354mH



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Numerator

X1 X2 X3 X4 X5 N1

9.54 7.8 4.9 6.8 5.1 -2.111

8.9 8.7 4.79 6.34 5.31 -1.87

9.3 8.4 2.51 3.23 7.13 0.02

9.1 8.2 1.52 2.45 7.81 0.562

10.1 9.3 2.34 1.9 8.12 0.84

10.5 9.4 1.21 0.78 9.89 1.7761

9.5 8.9 2.4 1.75 8.3 0.961

8.4 8.6 1.59 2.34 7.9 0.6287

9.4 10.1 4.5 6.7 4.98 -2.0787

8.3 10.5 4.4 6.54 4.95 -2

8.7 10.8 4.35 6.48 5.1 -1.94

8.5 10.7 3.4 6.3 5.15 -1.82

9.6 8.5 2.9 2.41 7.9 0.54

10.4 9.2 2.5 1.8 8.5 0.97

10.9 9.8 2.4 0.6 10.15 1.87

11.1 10.3 2.1 0.45 13.5 2.695

11.5 10.2 2.12 0.4 15.1 3.0669

11.8 10.7 1.9 0.35 15.9 3.2732

11.3 10.4 1.8 0.32 16.8 3.4882

11.4 10.6 1.6 0.3 17.5 3.6583

11.7 9.6 2.1 0.4 14.5 2.93

12.3 11.2 2.5 0.5 13.2 2.5905

12.5 11.3 2.4 2.1 10.5 1.2812.8 11.6 2.2 2.8 9.9 0.8401

12.6 11.4 4.35 6.4 5.2 -1.889

12.4 11.7 4.45 6.6 5.1 -2.005

12.9 11.5 4.5 6.8 4.9 -2.1413

13.2 12.1 4.9 7.1 3.9 -2.51

13.4 12.5 5.2 7.5 3.5 -2.789

13.6 13.8 5.35 7.9 3.2 -3.0403

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



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Y1 Y2 Y3 D1

80.9 46.27 700 -0.0105

70.8 69.13 610 -0.00813

90.4 70 138 0.000072

99.3 113 120 0.00193

120 130 108 0.00275130.1 204 98 0.00553

140.3 127 100 0.00278

120.25 93 91 0.001722

135.55 95 490 -0.00513

112.9 100 460 -0.00444

115.7 98 425 -0.00391

132.7 97.5 390 -0.0033

122.5 88 130 0.000892

134.45 102 125 0.00144

145.85 131.1 116 0.00263129.89 153 110 0.00354

124.6 160 108 0.0038

127.7 161 116 0.003719

154.85 154 112 0.00354

149.65 168 133 0.00365

148.43 149 140 0.00285

152.35 156 175 0.00251

145.76 101 137 0.001219

155.91 84 128 0.000785

143.87 137 390 -0.00189156.24 136 394 -0.00201

165.34 134 402 -0.00214

130.5 130 410 -0.00251

135.9 125 416 -0.00279

141.95 120 420 -3.04403

Y1=disq/dt, Y2=Vsqdt, Y3=isqdt



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3.5 TRAINING STEPS FOR NEURAL NETWORK:



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CONCLUSION:

This project outlines technique for speed estimation of induction motor using artificial neuralnetworks. The dynamic model of induction motor is considered and expression for rotor speed is

obtained . The expression obtained have singularities thus ANNs cannot be used to obtain the

speed directly from speed function. A method is used in this project in which two ANNs are

trained to approximate the numerator 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 by Ashfaq Hussain.3. Control System Engineering by I. J. Nagrath and M. Gopal



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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 Neural Networks by PrashantMehrotra, 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.com9. www.wikipedia.com10.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 70 113 130 204 127 93 95 100 98 97.5

88 102 131.1 153 160 161 154 168 149 156 101 84

137 136 134 130 125 120];

>> y3= [700 610 138 120 108 98 100 91 490 460 425 390

130 125 116 110 108 116 112 133 140 175 137 128

390 394 402 410 416 420];

>> d1= -0.12*(10^-9)*y1+0.0354*(10^-3)*y2-0.01734*(10^-3)*y3;

>> plot(d1);

>> 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 10.4 10.6 9.6 11.2 11.3 11.611.4 11.7 11.5 12.1 12.5 13.8];

>> x3=[4.9 4.79 2.51 1.52 2.34 1.21 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 2.2

4.35 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 13.5 15.1 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=-(-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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speed estimation of induction motor using artificial neural network and implementation in MATLAB

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