CHAPTER 3

SRM IMPLEMENTATION WITH ANN USING SENSORLESS

ALGORITHM

3.1 INTRODUCTION

Switched Reluctance Motor is a dynamic electrical machine, which converts the

reluctance torque into mechanical power. SRM is illustrated by singly excited and doubly

salient machine; there is no winding on the rotor or permanent magnets. The SRM structure

is very simple, reliable, high tolerance and low cost compared to that of natural machines.

The application of SRM incorporates variable speed operations. The torque developed in

reluctance motor is a nonlinear function of rotor position and stator current. The reluctance

drive provides constant power over a wide speed range and is highly dynamic. The torque

produced depends on the virtual position of the phase current with respect to the induction

profile. The torque does not depend on the direction of current while the torque is

proportional to the square of the current (The Fleming’s right hand rule signifies the same

direction for both d.c as well as a.c excitation). The generated back EMF depends on the

magnetic parameters of the machine, rotor position and the geometry of motor.

The switched reluctance motor is an electric motor in which torque is developed by

the tendency of its movable part to move to a position where the inductance of the excited

winding is maximized. The foundation of the reluctance motor can be traced back to 1842,

but the reinvention has been possible due to the advent of inexpensive, high-power

switching devices. The reluctance motor is a type of synchronous machine. It has wound

field coils of a DC motor for its stator windings and has no coils or magnets on its rotor. Fig

.3.1 shows its usual structure. It can be seen that both the stator and rotor have salient poles;

hence, the machine is an especially salient machine.

Fig. 3.1: Switched reluctance motor configurations

The aligned of rotor is the entirely opposite to the excited stator poles. In a magnetic

circuit, the rotating part chooses to come to the minimum reluctance position at the instance

of excitation. Whereas two rotor poles are aligned to the two stator poles, another set of rotor

poles is out of alignment with respect to a different set of stator poles.

3.2 SRM CONFIGURATIONS

.

Switched reluctance motor consists of the number of stator poles, Ns, number of

rotor poles, Nr, and the number of phases, m, (for typical motors with an even number of

diametrically opposed stator poles). The number of phases (m) is given by the number of

stator pole pairs (m=2

Ns ). Switched reluctance motor naming convention is to label the

motor by its Ns/Nr pole numbers. Fig.3.2 (a) & (b) shows the schematic diagram of the

switched reluctance motor, this is a 4-ph motor with 8-poles in stator and 6-poles in rotor.

This motor has Ns=8, Nr=6, and m=4.The rotor pole arcs, βr, and the stator pole arcs, βs,

define the flux paths and regions of changing inductance, determining how the motor can

produce torque in each phase.

When phase winding is energized, the rotor adjusts its position, such that the poles

r1, r’2 get aligned with stator poles c1 ,c’2 .Next phase a winding is excited and phase ’C’ is

De-energized. Again the motor moves to provide a low reluctance path to phase a flux. So,

the rotor poles r2, r1’get aligned with a phase poles a, a’. Next phase ‘b’ is energized and the

rotor poles r1, r’1 move to poles b1, b’. Thus, by successively energizing the stator phases the

movement of the rotor can be obtained.

(a)

(b)

Fig.3.2 (a) & (b): 8/6 SRM CONFIGURATIONS

Switched reluctance motors can be classified is made on the basis of the character of

the motion that is rotary machine, which is based on SRMs are further distinguish by the

nature of the magnetic field path as to its direction with respect to the axial length of the

machine. If the magnetic field path is perpendicular to the shaft, which may also be seen as

along the radius of the cylindrical stator and rotor, the motor is classified as a radial field. As

the flux path is along with the axial direction, the machine is called an axial field SRM.

Radial fields SRMs are most commonly used. It can be separated into shorter and longer

flux paths based on how a phase coil is placed. In the shorter flux path SRMs, the phase coil

is placed in the slots adjacent to each other, as shown in Fig. 3.3. Short flux path SRMs have

the advantage of lower core losses due to the fact that the flux reversals do not occur in

stator back iron in addition to having short flux paths. However, they have the disadvantage

of having a slightly higher mutual inductance and a possible higher uneven magnetic pull on

the rotor.

Fig. 3.3: Short flux path of SRM

The axial configuration of a SRM is shown in Fig. 3.4. These types of the SRMs are

model for applications where the total length may be restricted, such as in a ceiling fan or in

a propulsion application. The disadvantage of this configuration is that the stator laminations

have to be creased one on top of the other, the simple stacking of laminations in the radial

field configuration is dissimilar.

Fig. 3.4: Axial field switched reluctance motor

3.3 SWITCHED RELUCTANCE MOTOR PRINCIPLES OF OPERATION

Reluctance motor operates on the principle of change of magnetic energy function of

the rotor position. This requires a salient pole rotor with variable air gap between stator and

rotor. Therefore, as the rotor rotates the stator coil changes because of change of reluctance

of the flux paths. Fig.3.5. (a) shows the schematic of 4-ph reluctance motor. It has stator

windings similar to a synchronous machine, but there is no winding on the rotor.

The variation of stator phase coil inductance as a function rotor angle is shown in

fig. 3.5(b). Approximating in conventional synchronous machine pole axis is the D-axis and

leading this by

is the Q-axis.

(a)

(b)

Fig.3.5. (a): Schematic Diagram of SRM (b) Variation of Phase A

Fig.3.6 (a) shows the schematic diagram, Fig.3.6 (b) Shows the phasor diagram is

drawn with the field of a motor. While the internal voltage Eo proportional to ωLmax If

becomes zero when If is zero, it operates without a field coil in the rotor D-axis. Therefore

this operates reluctance motor.

(a)

(b)

Fig.3.6: (a) System Representation (b) phasor diagram of Reluctance Motor

For reluctance motor,

dda xivv cos0 3.1

qqad xivv sin 3.2

Power input

sxxxx

vivivp qd

qd

q

qqddi 2sin)(2

2

3.3

Thus it can be seen that when the rotor has no field winding, the motor takes power

(Pi) from the mains when the rotor is rotating at synchronous speed ωs.

Therefore the torque developed is given by,

sxxwxx

v

w

PT qd

xqd

x

x

i

d 2sin)(2

2

3.4

If the motor is loaded, the power angle δ adjusts itself to develop the required torque

to match with the load torque and the rotor continues to rotate at synchronous speed. The

rotor Q-axis always lags behind the supply voltage vector Va by the angle δ.

For nonzero average torque Td to be developed, the rotor has to be rotated fast at

synchronous speed by an external force. This is because the instantaneous torque Ti given by

d

dltTi

2

2

1 3.5

Where’ L’ is the inductance of the stator phase a is the angle between the D-axis

and stator phase ‘a’ and ‘i’ is the phase a current. From fig.3.5 (b), it can be seen that

has a second harmonic variation given by,

2cos)( xx IIL 3.6

If the current ‘i’ is given by,

twii xx sin 3.7

Then the instantaneous torque ‘T’ is given by

T=2

2sin)cos1(

2

10

2

2L

twdx

lx 3.8

The angle given by,

twsx 3.9

Where ωs is the rotor speed then

))(sincos)(sin(1 2222

twtwtwLIT xxxxxa

3.10

The above equation will give rise to a nonzero average torque only when ωx= ωy.

Therefore, reluctance motors are not self starting. To produce starting torque a

squirrel cage winding is used as shown in fig.3.7.

Because of this, the motor starts as an induction motor. When the stator is excited by

a phase supply, since the motor is on no-load, when steady speed is reached, the average slip

is small. So the rotor speeds will be very close to the synchronous speed. Because of

saliency of rotor, there will be instantaneous torque. The angle ‘θ’ will be changing slowly

with lines. The radial torque on the rotor will be of induction motor torque and the

instantaneous torque. Because of the increased torque, which is slowly changing, the rotor

speed will change.

Fig .3.7: TorqueVsTime

Fig.3.8: Torque Vs Speed

These motors are used when constant speed is the requirement. The torque‘d’ is not

very high since it depends on the difference between direct and quadrant reactances and

mechanical considerations cannot permit too much of saliency. These reluctance motors are

normally of low power rating. However, they are robust and are used for constant speed

applications where the torque requirements are high.

The speed of excitation depends on the frequency of enerzation of stator poles. The

configuration of the stator is simple. The control of stator excitation is less costly than the

inverter control of conventional induction motor. Fig.3.9 shows the schematic diagram for

the control of this motor. a, b ,c and d are the 4-ph excitation windings. T1, T2, T3 and T4 are

the respective solid state power gating devices.

Fig.3.9: Schematic diagram for the control of SRM

Fig.3.10: Control Sequence

They can be turned on by applying a positive signal to the base terminals B1, B2, B3

and B4 in specific sequence as shown in fig.3.10. Diodes D1 ,D2 , D3 and D4 ,resistances

R1,R2 , R3 and R4 are used in parallel with the a, b , c and d in order in make the respective

excitation current lie down as shown as the gating devices T1 ,T2 , T3 and T4 turned off.

Fig.3.11 shows the phase a current wave form and the variation of inductance of the phase a

coil as the rotor pole r2 moves fast the stator pole of phase a is also shown.

The torque developed on the rotor is given by,

d

djI 2

2

1 3.11

Where I is the phase current.

When

is positive,

The torque is positive, but becomes negative

When

is negative.

So, the current ‘I’ should be made as small as possible after turning off the associated

gate devices. This is achieved by the diode-resistor circuit connected in parallel to the coil.

To get the maximum average positive torque, the device T1 is turned on to build the current

to the maximum value immediately when

is positive and the current is reduced to zero, as

soon as

becomes negative by turning off T1. The instantaneous torque

developed and the gating signals for phase ‘a’ are also shown in the fig.3.11.

Fig .3.11: Performance of the Switched Reluctance Motor

Variable speed operation is possible by changing the frequency of triggering

signals for the gating devices. Speed reversal also is possible by reversing the triggering

sequence. This motor self starting, control is simple and controller is less costly. Since

torque developed is proportional to the rate of change of inductance, for a given current

rating of the stator windings, the torque developed is not very large. It is limited by the

mechanical constraints on the geometry of the rotor and stator. Therefore, for low power

variable speed industrial drives, this motor finds application. This machine also suffers from

the problem of torque pulsations on the rotor unlike in conventional synchronous or

induction machines. This causes vibrations on the rotor and generates acoustic noise.

3.3.1 POWER CONVERTERS FOR SRMs

The position of rotor is significant for the speed control of a SRM drive, as with the

rotor position, we can conclude which phase should be supplied to provide positive or

negative torque. In addition, another feature affects torque control and current reference for

hysteresis control. The block diagram of SRM control is given in Fig. 3.12 and the control

can be resolved in two parts.

(i) Current reference settling, and

(ii) Choice of the phase to be fed.

Fig. 3.12: Block diagram of the SRM control

The SRM drive structure is shown in Fig. 3.13. A typical SRM drive system is made

up of four basic components,

(i) Power converter,

(ii) Control logic circuit, and

(iii) Position sensor.

Fig. 3.13: Structure of SRM drive System

As the torque in SRM drives is independent of the excitation current polarity, the

SRM drives require only one switch per phase winding. Moreover, unlike the ac motor

drives, the SRM drives always have a phase winding in series with a switch. Thus, in case of

a shoot-through fault, the inductance of the winding limits the rate of rise in current and

provides time to initiate the protection. Additionally, the phases of SRM are independent

and, in case of one winding failure, uninterrupted operation is possible.

3.3.2 Closed Loop Control Strategies for SRM

The dynamic performance of the switched reluctance motor can be improved by

established feedback control. The basic functional block diagram of SRM motor drive

system is given in Fig.3.14.

Fig. 3.14: Block diagram of SRM Controller

Noise reducing filter (NRF) is used to reduce the noise in SRM and NRF design

involves tuning of filters. With the overall NRF, the design of the controller will adapt to the

non linear characteristics of the motor. Thus, if the motor characteristics changes with

operating conditions, the controller tunings will also change to maintain the desired control

performance. The tuning rules are implemented for obtaining the initial settings of the

controller and this depends on the application.

3.4 MATHEMATICAL MODEL OF SR MOTORS

The torque is produced in a reluctance motor by virtue of the change in the

reluctance with respect to the rotor position. Based on this principle, a reluctance motor is

different from other types of conventional machines such as the DC machine, synchronous

machine and induction machine. The basic torque or force production in reluctance

machines results from the variation of the stored magnetic energy as a function of the rotor

position. This association also concerned to most electromagnetic relays, holding magnets,

solenoid actuators, and other devices where force is produced between two magnetic

surfaces, including all machines with saliency.

3.4.1 Torque Equation

Speed control of conventional drives using variable frequency transistorized or

thyristorized converters are inevitably related with de rating and reduced efficiency due to

effects of time harmonics generated in these converters on the performance of the motor to

minimize these effects, current examination in design is intended primarily towards

modifications of the converter and associated filter circuitry are simplicity consider while at

the same time the hitherto undesirable time harmonics are actually used with advantages,

thus making system energy efficient .

The fundamental principle entails working out the appropriate design for the

armature of the drive motor modified to typical no sinusoidal wave forms expected from

converter module. In effect this method leads to a co-ordinate advance to the design of

motors and the converter units allowing the use of simple controller circuits with relatively

less restrictions on the harmonic content in their waveforms

The dual convergence approach method is based on the principle of adaptive

design, although the design of motor winding involves specialized techniques, the exercise

is restricted to the design level only, the final winding has essentially standard features with

conventional terminal requirements and it does not involve additional costs.

The important features of the development are an efficient utilization of the

torque produced by matching orders of space and time harmonics in the system, thus

increasing the machine torque and output without significant increase in losses. This leads to

improved system efficiency at lower basic cost thus pointing to a high efficient energy

management and improved power utility.

Harmonic torques can be broadly grouped in two categories

1. Torque develops same direction as the fundamental - positive torque

2. Torque generates opposite direction as the fundamental - positive torque

It is well identified that a common 2p –pole distributed armature winding with space

harmonics, when operating a non sinusoidal supply, has an effective synchronous speed,

corresponding to the fundamental supply frequency f, pole number of machine 2p.

The resulting magnetic field direction of rotation is determined by a phase sequence

of supply and sequence of phase layout of the winding. In addition, each space harmonics

component present in the winding also produces a rotating magnetic field corresponding to

each time harmonic frequency, which have speed depending on the order of space –and time

-harmonics in general mth

order space- harmonics, in connection with nth

time- harmonics.

The harmonics job can be further grouped into three categories depending on the

speed of the harmonic field.

Group A

Group A consist of those harmonics which are produced by rotating magnetic fields

that have the same synchronous speed due to the basic rotating field, Torque, this group

contributes maximum support component at all speeds of the motor. This group of harmonic

torques has highest effective contribution and can play a Principal role in increasing torque

production of motor, as well as in causing an improvement of overall performance of the

machine.

Group B

Torque produced by rotating field, which have synchronous speed less than that of

the basic synchronous speed. This group of torques may contribute towards augmentation of

the net starting torque, but shall cause dips in the overall torque slip characteristics and

would generally introduce reduction of torque in the operating zone. This group of harmonic

torques is not desirable.

Group C

This group consists of harmonic torques, which are produced by rotating fields

having synchronous speed greater than that of basic rotating field. The torques of this group

contributes over the entire motoring-zone, but effective contribution gets reduced with the

increase in the value of their synchronous speeds. This group of harmonic torques, although

has a partial utilization, may prove to be quite advantageous provided that their existence

does not cause a sizable increase in harmonic loss

To derive the basic torque equation of the SRM, consider an elementary reluctance

machine, which has single phase excited that is, it carries only one winding on the stator.

The excited winding is wound on the stator and the rotor is free to rotate. The flux linkage is,

iL )()( 3.12

Where i is the independent input variable, i.e. the current flows through the stator.

The general torque expression is,

consti

e

WT

3.13

Where W is the coenergy. The definite integral is shown in eqn. [3.14],

1

0

),(

i

diiW 3.14

The coenergy is the area of magnetization curve at any position is shown in Figure 3.15.

Fig. 3.15: Flux-Linkage Chart

So, the torque equation (3.15) becomes,

dii

T

i

e

1

0

),(

3.15

For these equations, the instantaneous torque can be pictured graphically. The work

is ∆Wm divided by ∆θ, where, ∆Wm is evolved at constant stator current as the rotor moves

through an insignificant displacement ∆θ is shown in Figure 3.16.

Fig. 3.16: Diagram of Energy Exchange

During such a displacement there is an exchange of energy with the power supply

and there is also a change in the stored field energy. The constant-current restraint ensures

that during such a displacement, the mechanical work done is exactly equal to the change in

coenergy. In a displacement ∆θ from A to B in Fig. 3.16 at constant current, the energy

exchanged with the supply is,

ABCDe SW

The change in stored field energy is,

OADOBCf SSW

And the mechanical work done must be

em TW

fe WW

)( OADOBCABCD SSS

OBCOADABCD SSS

OABS

= 1W

It can be seen that not all energy achieved from the supply is converted to

mechanical work. A quantity of it is stored in the magnetic field. The energy stored in the

magnetic field is not exhausted, but it does not exist for energy conversion during the

motion from A to B. If there is no magnetic saturation, the magnetization curves would be

straight lines. In this case, at any rotor position θ, the coenergy and the stored magnetic

energy are equal, and given by,

21 )(2

1iLWW f

Then the instantaneous torque reduces to,

LiTi

2

2

1 3.16

However, these types of the motors are the single phase SRM suffer from starting

problem and also to be approximating the blank zones between successive torque zones,

which need sufficient load inertia to pull the motor through. There is no possibility of

producing constant torque during one revolution; therefore, the most SRMs are multi-phase.

In the multi-phase case, the torque equation becomes a summation,

m

j

eje TT1

Where, Tej denotes the torque generated by the jth

phase, and m is the total phase

number.

3.4.2 Model Equations

In general, the dynamical model of an SRM is as follows,

Lme TwBT

dt

dwJ 3.17

m

j

eje TT1

3.18

j

i

j

ej diT

j

1

0

3.19

m

jN rj

)1(2

3.20

where J is the rotor's inertia moment, Bm is the viscous friction coefficient of the

rotor and TL is the load torque; ω denotes the rotor's angular speed; Ns = 2m and Nr denotes

the stator and rotor pole number respectively; θ denotes the rotor position with respect to

starting position; θj denotes the rotor position with respect to the jth

phase; ij denotes the jth

phase current; while Tej denotes the torque generated by the jth

phase.

3.5 METHODS FOR SENSORLESS ALGORITHM

The Switched Reluctance Motor drive systems incorporate a machine, drive power

electronics, controllers and position sensors. The power electronics deliver the necessary

torque generating current which is closed-loop controlled by either analog electronics or a

microprocessor. In modern decades, the trend has been that research is drifting away from

using analog equipment towards the microprocessors. The improved features are very

attractive for implementing control digitally. While SRM drives gain status, there is a rising

effort to reduce costs, improve performance, and increase reliability. Rotor position sensors

add hardware complexity, connectivity problems, and reliability issues that make the overall

drive system prone to failure. Also, there are some harsh environmental conditions that

require sealed motors. The position sensors required in SRM drives limit the possibility in

these applications.

The Motor position sensors removal is to improve the robustness of the system by

developing control algorithms that eliminate rotor position sensors. These systems are

usually called as sensorless drives, as they have no position sensors. Sensorless is a slight

misnomer, as these systems have other sensors associated with measurement of electrical

parameters, like voltage and current, used in the rotor position estimation. If sensorless

Switched Reluctance Motor drives are to become a replacement technology for induction

drive applications, sensorless methods for Reluctance Motor drives must have the same

robustness and reliability as induction drives. To attain this goal, robustness must be

designed into the algorithm because sensorless techniques are noise and error sensitive. But,

inherent reliability happens just by the exception of the sensors as well as the reduction of

hardware within.

3.5.1 Sensorless Algorithms and Methods

The SRM salient structure is the main characteristic oppressed by sensorless

algorithm developers. The Motor structure presents a recurring nature of the electrical states

with respect to rotor position. Whether the sensorless method employs a lookup table for

flux linkage, active current probing, or even neural-fuzzy methods, the flux linkage and

current are the usual quantities used to obtain rotor position. This is because of a well

identified relationship between current, flux linkage and rotor position in SRM's. If the flux

linkage and the current of an exacting phase are recognized, the position of rotor can be

derived. The different kinds by which sensorless SRM algorithms can be classified are,

(i) Hardware-intensive system like signal injection requires extra external

circuitry.

(ii) Lookup table methods can be memory concentrated.

(iii) Model-based techniques can be prone to errors, particularly if the model has

hidden or adverse characteristics.

(iv) Adaptive methods such as neural networks and fuzzy controllers are in

general computationally demanding.

3.5.2 Active Probing

Active probing has been used in hardware and difficult software procedure to inject

signals in unemployed phases. If this is done the virtual impedance can be measured during

motor running condition. These designs involve handling the timing issues associated with

probing inactive phases. Further difficulties that arise by using active probing methods are

the additional noise injected into the system and the measurement of the transient probe

signals. It is adverse to perform active probing because of these issues. Non-probing

methods are including: flux-current methods, mutual voltage model-based estimator

techniques, and back-EMF sensing, as well as adaptive methods.

3.5.3 Flux Reference

The majority of non-intrusive techniques employ various kinds of digital estimators

for flux linkage by the use of Faraday's law, as in flux reference techniques. The Flux

linkage, essentially, cannot be measured directly, thus it is very complicated to predict and

control. As flux linkage must be estimated in some way, many researchers are investigating

better ways to estimate flux linkage for use in sensorless drives. Algorithms that use flux

linkage as a control quantity typically employ a predetermined lookup table. Those methods

exploit either simulated data or modeled data to create the lookup information. In either

case, these commutation methods are employed using a reference flux linkage from the

lookup table and by comparing a runtime estimate to the lookup table reference. With doing

this contrast of the aligned condition, the commutation instant can be predicted. Therefore,

when the estimate exceeds the reference resulting from the lookup, the current is

commutated from the active phase to the next inactive phase.

The foremost complexity in using stored magnetization curves in a lookup table for

sensorless control is the perfect modeling of the Reluctance Motor. Most magnetization data

is derived from simulation instead of real-time experimental data. By contrast, SRM

magnetic characteristics are experimentally identified by a locked rotor test. In both cases,

the worth of the control relies on the precision of the stored data. Further problems arise

from injected noise or operating conditions not enclosed in the lookup table. Therefore, to

control the system by investigative methods, some analytical methods used spectator

dynamic models of the SRM and its drive, whereas others only modeled the SRM magnetic

characteristics.

3.5.4 Fuzzy and Neural

Artificial Intelligence Techniques are used for estimation of position in SRM drives

and fuzzy linear interpolation can be used to construct real time magnetization curves, even

for the intermediate positions. The charity of interpolation methods are the reduction of data

point attainment. If experimental magnetization data are used, only the aligned and

unaligned positions are derived from measurements. A combination of fuzzy interpolation

and quasi accurate analytical models can improve large memory necessities usually needed

in lookup table techniques. Other fuzzy-reasoning based techniques measure magnetization

data for several rotor positions and then store that data in the form of fuzzy rule-based

tables. Various fuzzy logic based algorithms are used to remove the estimation error and

give the motor drive with additional robust operation. These estimators improve

performance by adding features like fuzzy phase selection, fuzzy flux linkage estimation and

fuzzy angle predictors. Additionally, the rotor position estimation can be accomplished

using Neural Networks. The development of storing magnetization curves has motivated

from the direct table implementation through the reduction of data sets by interpolation

methods to the current methods by which data is stored essentially in the configuration of

the neural network. Neural networks perform like non-linear estimations. They efficiently

store data in their weight structure to both model the dynamic system and interpolate the in-

betweens. Some architecture can allow for the extrapolation of their performance for

operating conditions to which the controller has not been introduced. These are the

elementary characteristics that have popularized the use of neural controllers for many kinds

of control systems.

3.5.5 Sensorless Implementation Limitations

The tribulations of complex system with linear or non-linear controllers, is desirable

to realize the simplest method that reaches the performance required. Mainly SRM

sensorless methods require high speed processors that are capable of millions of instructions

per second (MIPS). Digital Signal Processors (DSP's), then, are ideal for sensorless

implementations. Sensorless algorithms are restricted at high speed by the speed of the DSP

to cope with large amounts of mathematical procedures. Limited amounts of memory in

modern DSP's cause large lookup tables and large Neural Nets to be quite a burden. The

Limited word size also pretenses problems for controller and implementation of neural in

fixed point DSP's due to the inability to preserve resolution when required large numbers.

3.6 ARTIFICIAL NEURAL NETWORKS

Neural networks may have various advantages over traditional control techniques

that be trained to perform definite tasks based on experimental or real-time data. It exhibits

capability of ANN's to organize information received during runtime to approximate

functions. It endows with parallel computation through multiple output architectures. ANNs

are used in system identification, adaptive control, modeling, optimization, and motion

control. In comparison, analytical models fall short due to the complexity required to

appropriately model those systems. ANN's are ideal for controlling discrete-time, non-linear

systems with large non-linear variations in their states due to their extreme non-linearity.

ANNs have successfully modeled highly complex, non-linear systems, due to their

unparalleled ability to recognize complex patterns in seemingly random data. ANN’s

architectures are primarily designed in two fashions.

(i) The Time-delay is more suitable for dynamic non-linear systems. But, they

are inherently more difficult to implement due to the architectural complexity required to

achieve estimation accuracy. Typically, the feed-forward type of neural net is most utilized

in control problems.

(ii) A feed-forward neural network, development information from input to

output through one or more layers of neurons. Feed-forward networks exhibit the greatest

compatibility for the position estimation problem in Switched Reluctance Motors.

A completely associated neural net has all of the inputs connected to each neuron in

the input layer. A partially connected network is a fully connected network with some of the

synaptic weights set to zero. It accomplished to date for SRM rotor position estimation

utilizes some sort of feed-forward neural net. A typical ANN for rotor position estimation

contains two input neurons, some number between 5 and 30 hidden neurons and 1 output

neuron. It depends on the interconnection, anywhere from several dozen to several hundred

individual weights can be contained by these networks. In addition to synaptic weights, an

activation function is utilized in each of the neurons. Typically, the activation function is

some variety of the sigmoid function. Some of the burden can be alleviated through the use

of additional lookup tables for activation function approximation. An unusually small feed-

forward neural network can be represented by some small plurality of inputs, a hidden layer

with a small plurality of neurons and an output layer with a single neuron. The neural

network with a reduced amount of input neurons and a single output neuron is also referred

to as a multi-layer perceptron.

ANN networks ease the control burdens, yet there are several outstanding issues that

may present obstacles for a system designer.

(i) ANN's maintain their accuracy through the force of large number of neurons.

If accuracy is critical, a successful neural net implementation may require a large amount of

memory to contain all the synaptic weights.

(ii) The number of connections between layers can be problematic (depends on

the size of the network). The calculations required to process the net cannot be implemented

with other control functions on most common microprocessors.

(iii) Most ANN designers then tradeoff performance versus neural size, thus,

accepting more estimation error for the ability to capture some of the benefits ANN's

provide.

(iv) Estimation error is dependent upon both the number of neurons in the hidden

layer and the number of samples in the training data set.

(v) Training data is highly effective in the performance of the network and

perform for small conduction angles that are strongly affected by the chosen training set.

3.6.1 ANN Design

At this time, there is no exact design to implement intelligent control. However, it

achieves neural design implementation to include some steps. They are

(i) Designer should define the number of input, hidden, output layers.

(ii) The activation functions that are suited for application should be chosen. (i.e.

match the function to data space dynamic range). Non-linear activation functions should

comprise the majority of the neurons while the output neurons can be linear.

(iii) The neural net weights should be initialized to random, small values to ensure

that the network is not saturated by large values of weights. Also if the initial weights are

identical, the neural net would not be trainable.

(iv) The designer should collect, select the data set for training. The training data

should include both the input and output spaces.

(v) A training supervisory algorithm should be chosen based on the type of

neural architecture that was chosen. Generally, a back-propagation type algorithm is

sufficient for feed-forward networks.

(vi) The neural net should then be trained by adapting the weights using the

supervisory algorithm. The algorithm should minimize the error between the neural output

calculated from the input space and the associated target value.

(vii) The designer should verify the network with data pairs not from the original

data set. The test data is an extraction from the original data set, yet the test data is never

presented to the network during training.

3.6.2 Training Data

The neural net is choosing the proper data set and performance limited use in

estimating SRM rotor position. ANN trained to estimate flux linkage performs much better

estimation than the one that is trained to estimate rotor position. This should be taken into

account when developing the data set to be used during training. To prevent poor position

accuracy, the data set should be randomly distributed over the entire operating range and

dimensional data reduction is done. Most neural training sets consist of data points of flux

linkage, current and the corresponding rotor position. However, several ambiguities exist in

the complete data set which should be considered by designers creating ANNs for sensorless

SRM’s drives. Several values of current and rotor angle exist for a single flux linkage value.

To overcome this concurrency, quantities from at least two phases must be measured or the

data set must be limited to the interested angular interval that produces positive torque.

There are two possible ways to generate training data,

(i) Model-based data generation, and

(ii) Experiment-based data generation.

The flux linkage values can be computed for randomly generated phase current and

rotor position values. The resulting flux linkage, phase current and rotor position values

judiciously cover the intended operating region.

3.7 SENSORLESS SRM CONTROL

The sensorless control of the SRM approach can be classified within the

magnetization-data based methods. The basic premise of the method is that an artificial

neural network forms a very efficient mapping structure for the nonlinear SRM. Through

measurement of the phase flux linkages and phase currents the neural network is able to

estimate the rotor position, thereby effectively eliminating the rotor position sensor. The

ANN training data set comprises of magnetization data of the SRM for which flux linkage

(λ) and current (i) are inputs and the corresponding position (θ) is the output. Given a

sufficiently large training data set, the ANN can build up a good correlation among λ, i and θ

using appropriate network architecture.

The basic idea behind the proposed method is the ANN which forms the efficient

mapping structure for the nonlinear SRM. The rotor position sensors were eliminated by

estimating the rotor positions, which is obtained from the measured phase values of flux

linkages and currents. The ANN training data set comprises of flux linkage (λ) and current

(i) which serve as inputs and the corresponding rotor position (θ) as output. The ANN builds

up a correlation among λ, i and θ for appropriate network architecture. Then this off-line

trained ANN is evaluated against a test data set which has different λ – I values. Fig. 3.17

explains the sensorless control algorithm.

Fig. 3.17: Sensorless Control Algorithm

3.7.1 Sensorless Algorithm

For proper torque generation, the current must be controlled in designated angular

intervals based on the saliency of the motor. A commutation scheme for this motor drive is

based on rotor position sensors that give discrete position indications. The current must be

driven through the windings at 0o–45

o intervals for positive torque generation and clockwise

rotation of the rotor.

The sensorless algorithm is developed such that the error at the mid- range of angle

is extremely low. Three timers were used for variation measurements during motor

operation to estimate time durations of (i) conduction (ii) non-conduction, and (iii) speed.

The timer functions include measuring,

(i) The time between the neural mid-range angle references (22.5 degrees),

(ii) The time between mid-range and the end of the conduction period, and

(iii) Duration of the non-conducting interval.

The principle is based on current control by calculating flux and estimate using

neural during the conduction interval and zero conduction during the countdown period. The

PWM duty should be commended to zero while the countdown progresses to confirm no

active conduction. The conduction and non-conduction intervals are controlled using a

simple flag to drive the control functions. For the positive torque region, the flag is set to 1.

The input is the rotor position estimate derived from the neural net and the output is the

control flag variable. When the neural estimate reaches the midpoint of the commutation

period, a projection based on speeds is made to predict the end of conduction period. The

projection is made from a speed estimation which is derived from the timer as follows:

(i) Timer counts up from each successive midpoint and resets.

(ii) Compare the calculated project timer value and ends the conduction interval

when a match occurs and resets. The end value is used as the start of the countdown timer,

when the end of the conduction period has been reached. The algorithm sets the non-

conduction flag (adjusts the third countdown timer to half of the second timer value just

prior to the reset).

(iii) It begins to countdown, when the third timer reaches zero, everything is reset

and the conduction flag is set to re-start the conduction region. The algorithm starts with the

rotor very close to the zero reference, which is controlled with a startup algorithm.

3.7.2 Analysis of SRM Operation

When the positive voltage is applied to the phase, the phase voltage equation of SRM

is given by,

mV

dt

diRV

3.21

where, λ- flux linkage, Vm – mutual voltage, R – phase resistance.

where,

dt

dmi

dt

dimVm )( 3.22

Neglecting mutual voltage,

d

dLi

dt

diLiRV 3.23

where, L – self inductance of stator winding. Hence, the current gradient when positive

voltage applied becomes

iR

d

dLiV

Ldt

di

)(

1 3.24

At zero excitation, the voltage equation is

dt

diR

0 3.25

which can be rewritten as

dt

dLi

dt

diLiR 0 3.26

and the current gradient is given by

iR

d

dLi

Ldt

di

)(

1 3.27

Using the above equations, the rotor position can be estimated from calibrated

conversion tables for various currents and speeds. The FPAA detects whether the energized

winding is operated in conduction mode or freewheeling mode. Moreover a three-

dimensional table is required for accessing the data.

The flux-linkage ψ is,

dtRiv )( 3.28

A mechanical setup is used to hold the rotor in position and voltage pulse is applied

by turning ON the switch. The current is made to reach nearly 20% to 30% more than the

rated peak current of the motor. The flux-linkage is measured for a set of rotor positions

spanning from 0° to 90° at steps of 10°. Since the inductance profile is symmetric with

respect to the aligned position of a particular phase the flux-linkage characteristics of a

phase will also be symmetric with respect to the aligned position. Based on this logic, flux-

linkage characteristics of an 8/6 pole SRM is obtained. The data recorded in Digital Storage

Oscilloscope (DSO), are transferred to the computer and the numerical integration is

performed and is shown in Table 3.1 and Fig. 3.18 shows the obtained relation between

inductance and rotor position for different phase currents.

Table.3.1: Flux-linkage for the respective current Vs rotor position

CURRENT (A)

R

O

T

O

R

P

O

S

I

T

I

O

N

(θ)

0 5 10 15 20 25

0 0 0.3062 0.4477 0.5446 0.6155 0.6694

10 0 0.2747 0.4035 0.4924 0.5583 0.6089

20 0 0.2435 0.3592 0.4402 0.5011 0.5483

30 0 0.2124 0.3152 0.3883 0.4438 0.4878

40 0 0.1812 0.2707 0.3359 0.3866 0.4272

50 0 0.1501 0.2265 0.2837 0.3294 0.3667

60 0 0.1189 0.1822 0.2315 0.2722 0.3061

70 0 0.0878 0.1382 0.1793 0.2149 0.2456

80 0 0.0567 0.0938 0.1272 0.1577 0.1854

90 0 0.0255 0.0495 0.0753 0.1005 0.1245

Fig. 3.18: Inductance profile as a function of current and rotor position in an SRM

A function which is dependent on rotor angle and phase current, to derive the

approximate analytical model for flux linkage is given by,

iii )())(exp(1)(),( 321 3.29

Where, α – described in Fourier series as

αa = ∑Aa cos(Bθ) 3.30

When noiseless data are used, difficulties may arise in implementation due to noise

contained in the input space. Hence, every possible electric cycle of flux linkage, phase

current and rotor position is sampled and recorded for training. A large training data set is

developed to build a correlation between input and output sets over the entire operating

range. The data set is optimized using principal component analysis (PCA) and after

generating the optimal data set, current and flux is scaled between 0 and 1. Due to ease of

implementation and compatibility back-propagation supervisory algorithm is used. The

Levenberg-Marquardt BP algorithm is used based on Gauss-Newton optimization. The BP

method is derived from a performance index based on the Newtonian error.

The performance index is given by,

V=∑e2

3.31

This performance index is applied to weighting matrix for neural net during the

training process.

The weight update is given by

VVWi 12 ][ 3.32

Where

V2 Hesian matr )( SJJ T 3.33

V jacobian matrix ( )eJ T 3.34

Where,

J – Partial derivative of error matrix.

∆W = [JTJ + S]-1 J

T e 3.35

Where, S = µI

The discrete flux linkage is expressed as,

oldsphph TRiV )( 3.36

Where, Ts – sampling time and

ψold – previous calculated flux linkage.

In eqn. 3.36 the accuracy is limited by sampling rate. A Linear Time Invariant (LTI)

relationship between Ψ, I, θ is maintained during drive operation for successful rotor

position estimation. Thus, for accurate prediction, rotor position is restricted between 20 and

40 electrical degrees. Fig. 3.19 and Fig.3.20 show how the ANN is trained in off-line and

then used as position estimator.

Fig. 3.19: off line training for ANN

Fig. 3.20: Position estimation using trained ANN

3.7.3 CURRENT REGULATION IN AN SRM

The asymmetric inverter for SRM (considering the SRM in the unaligned position),

when switches of one phase shown in Figure 3.21 are turned ON, the voltage applied in the

winding is +Vdc. Then, the current increases and reaches a reference level required by the

control. When switches are OFF, the voltage is −Vdc, and the energy is supplied back to the

source. During the motoring region, to maintain a constant current, at least one of the

switches is turned ON and OFF, depending on the controller output. If only one of them is

turned OFF while the other is chopped, then the SRM is operated in soft chopping. On the

other hand, if both switches are simultaneously turned ON and OFF, then the SRM is

operated in hard chopping.

Fig.3.21: Classical asymmetric inverter for SRMs

3.8 TORQUES-SPEED CHARACTERISTICS

The torque-speed operating point of an SRM is essentially programmable and

determined almost entirely by the control. This is one of the features that make the SRM an

attractive solution. The envelope of operating possibilities, of course, is limited by physical

constraints such as the supply voltage and the allowable temperature rise of the motor under

increasing load. Like other motors, torque is limited by the maximum allowed current, and

speed by the available bus voltage. With increasing shaft speed, a current limited region

persists until the rotor reaches a speed where the back-EMF of the motor is such that, given

the DC bus voltage limitation, we can get no more current in the winding—thus, no more

torque from the motor. At still higher speeds, the back-EMF increases and the shaft output

power begins to drop. This region is characterized by the product of torque and the square of

speed remaining constant.

SRM converts reluctance torque to mechanical power by using single excitation. It

has no winding (or) permanent magnet. The torque generated is a non linear function of

stator current and rotor position. The functional representation of the rotor vs torque has

three regions namely,

(i) Constant torque

(ii) Constant power, and

(iii) Falling power.

The torque-speed operating point of an SRM is essentially pre-calculatable and

determined by the control. This is the attractive feature of SRM, and it is limited by physical

constraints like the supply voltage and the operating temperature of the motor. The torque

developed is given by,

)tan(

1

)( tconsiT

3.37

Instantaneous torque,

LiT 2

2

1 3.38

Output torque

n

i

m iTT1

),( 3.39

The average torque,

n

phase

phaseTT

Where,

T = Torque

θ = Phase angle

L = Inductance

I = current

w = speed.

The torque characteristics of switched reluctance motor are dependent on the

relationship between the stator flux linkages and the rotor position as a function of the stator

current. The inductance corresponds to that of a stator-phase coil of the motor neglecting the

fringe effect and saturation. The significant inductance profile changes are determined in

terms of the stator and rotor arcs and number of rotor poles. From the various angles are

derived as

)(

2

2

11 rs

rP

3.40

s 12

)(23 sr 3.41

s 34 3.42

rP

2145 3.43

Where, βs and βr are the stator and rotor pole arcs, respectively, in most case βr > βs,

and Pr is the number of rotor poles.