chapter (1) mathematical modeling of dc machines...chapter (1) mathematical modeling of dc machines...

(1)

Chapter (1)

Mathematical Modeling of DC Machines

11 DC Motor Overview

The direct current (DC) motor is one of the first machines devised to

convert electrical power into mechanical power and its origins can be

traced to the disc-type machines conceived and tested by Michael

Faraday

Direct current motors (the subject of this study) convert electrical

energy into mechanical energy through the interaction of two magnetic

fields One field is produced by a magnet of poles assembly the other

field is produced by an electrical current flowing in the motor windings

These two fields result in a torque which tends to rotate the rotor As the

rotor turns the current in the windings is commutated to produce a

continuous torque output

A DC motor can be seen to be comprised of three main parts current-

carrying conductors called an armature a circuit for magnetic field

provided by magnets of poles and a commutator that switches the

direction of current in the armature as it passes a fixed point in space

Since electric motor design is based upon the placement of conductors

in a magnetic field a discussion of magnetic circuit principles will help

facilitate the understanding of motor action If a conductor were wound

into a coil with many turns the magnetic contribution of each individual

turn would add to the magnetic field intensity which exists in the space

enclosed by the coil In this way extremely strong magnetic fields can be

developed The force which acts to push the magnetic flux through a

space is called variously magnetomotance manetomotive force or simply

(2)

mmf The term magnetic flux is used to describe how much magnetism

there is in the space around a coil or permanent magnet or in the air gap

of a motor

Condition assessment of DC motors requires a basic understanding of

the design and operating characteristics of the various types available the

separately excited DC motor the PM DC motor the series motor the

shunt motor and the compound motor Each type has unique operating

characteristics and applications These characteristics enable the operator

to perform a wide variety of tasks

12 Types of DC Motors

121 Separately Excited DC Motor

The schematic circuit diagram of separately excited DC motor is

illustrated in following Figure 11 When the armature of a DC machine

rotates in the stator field a voltage is induced in the armature winding In

a DC motor it is called counter emf or back emf In either case the level

of this voltage can be calculated using Faradays Law which states that a

voltage is induced The field and armature circuits are totally separate

The field current is supplied from a secondary source

Figure 11 Separately Excited DC Motor

(3)

122 Permanent Magnets (PM) DC Motor

The magnetic field of (PM) motors is generated by permanent magnets so

no power is used to create the magnetic field structure The stator

magnetic flux remains essentially constant at all levels of armature

current and therefore the speed vs torque curve of the PM motor is

linear over an extended range The schematic circuit diagram of a

permanent magnets DC motor is illustrated in following Figure 12

Figure 12 PM DC Motor

123 Series DC Motor

Components of a series motor include the armature labeled A1 and A2

and the field S1 and S2 The same current is impressed upon the

armature and the series field The coils in the series field are made of a

few turns of large gauge wire to facilitate large current flow This

provides high starting torque approximately 2 frac14 times the rated load

torque Series motor armatures are usually lap wound Lap windings are

good for high current low voltage applications because they have

additional parallel paths for current flow Series motors have very poor

speed control running slowly with heavy loads and quickly with light

loads A series motor should never drive machines with a belt If the belt

breaks the load would be removed and cause the motor to over speed and

destroy itself in a matter of seconds The schematic circuit diagram of a

series DC motor is illustrated in following Figure 13

(4)

Figure 13 Series DC Motor

Common uses of the series motor include crane hoists where large heavy

loads will be raised and lowered and bridge and trolley drives on large

overhead cranes The series motor provides the starting torque required

for moving large loads Traction motors used to drive trains are series

motors that provide the required torque and horsepower to get massive

amounts of weight moving On the coldest days of winter the series

motor that starts your car overcomes the extreme cold temperatures and

thick lubricant to get your car going

124 Shunt DC Motor

The shunt motor is probably the most common dc motor used in industry

today Components of the shunt motor are the armature labeled A1 and

A2 and the field labeled F1 and F2 The coils in the shunt field are

composed of many turns of small wire resulting in low shunt field

current and moderate armature current This motor provides starting

torque that varies with the load applied and good speed regulation by

controlling the shunt field voltage If the shunt motor loses itrsquos field it

will accelerate slightly until CEMF rises to a value sufficient to shut off

the torque producing current In other words the shunt motor will not

destroy itself if it loses its field but it wonrsquot have the torque required to

do the job it was designed for The schematic circuit diagram of a shunt

DC motor is illustrated in following Figure 14

(5)

Figure 14 Shunt DC Motor

Some of the common uses of the shunt motor are machine shop lathes

and industry process lines where speed and tension control are critical

125 Compound DC Motor

When comparing the advantages of the series and shunt motors the

series motor has greater torque capabilities while the shunt motor has

more constant and controllable speed over various loads These two

desirable characteristics can be found in the same motor by placing both a

series field and shunt field winding on the same pole Thus we have the

compound motor The schematic circuit diagram of a compound DC

motor is illustrated in following Figure 15

The compound motor responds better to heavy load changes than a

shunt motor because of the increased current through the series field coils

This boosts the field strength providing added torque and speed

If a shunt coil is added to a series motor at light loads (when a series

motor tends to over speed) the added shunt field flux limits the top speed

eliminating self-destruction

Figure 15 Compound DC Motor

(6)

Common uses of the compound motor include elevators air

compressors conveyors presses and shears Compound motors can be

operated as shunt motors by disconnecting the series field Many

manufacturing process lines are designed this way The reason being that

most off the shelf motors are compound motors and the series field can

always be connected later to provide additional torque if needed

Compound motors can be connected two ways cumulatively and

differentially When connected cumulatively the series field is connected

to aid the shunt field providing faster response than a straight shunt

motor When connected differentially the series field opposes the shunt

field Differentially connected compound motors are sometimes referred

to as ldquosuicide motorsrdquo because of their penchant for self-destruction If

perhaps the shunt field circuit were to suddenly open during loading the

series field would then assume control and the polarity of all fields would

reverse This results in the motor stopping and then restarting in the

opposite direction It then operates as an unloaded series motor and will

destroy itself Differentially connected motors can also start in the

opposite direction if the load is too heavy Therefore it is seldom used in

industry

13 Separately Excited DC Motor Differential Equations

The DC machine as dynamic system including the interactions of the

electromagnetic and the mechanical effect is dealing within the following

section The equivalent circuit of the separately exited dc machine can be

represented in schematic from as shown in Fig 11 The electrical

equation of a DC motor is derived from the simple motor circuit

illustrated in Figure 11 The electrical relation between these variables is

given by equations (11-16) where Eb the internally generated voltage is

proportional to the motor velocity

(7)

The motor back emf constant Kv is a measure of the voltage per unit

speed generated when the rotor is turning The magnitude and polarity of

Kv are functions of the shaft angular velocity r and direction of rotation

respectively Also Kv is the motor torque constant that is a measure of

the torque-per-unit-current produced by the motor The dynamic

equation of a motor is given by

b

a

aaaa Edt

diLRiV (11)

rfafb iLE (12)

faf iLK (13)

dt

diLRiV

f

ffff (14)

ae iKT (15)

Lr

r

e Tdt

dJT

(16)

Va applied voltage

Ia motor current

Eb induced back emf voltage

La armature winding inductance

Ra armature resistance

Te motor output torque

r motor output speed

14 Block Diagram and Transfer Function of Separately Excited DC

Motor

It is necessary to depict the voltage and torque equations of DC

machine in block diagram form when considering the machine as a part

of an overall system Accurately the equations which we have already

(8)

derived for the separately excited DC motor which we will put into block

diagram form From the block diagrams we can derive the transfer

function of the DC motor which are used in the design of current and

speed controllers

141 Time Domain Block Diagram of Separately Excited DC Motor

Block diagram which portray the interconnection of the system

equations is used extensively in control system design we shall work

with time-domain equations using the p operator to denote

differentiation with respect to time dtd and the operator p1 denote

integration ion Therefore we will have no trouble converting the time-

domain block diagram so transfer functions by using the Laplace

operator dt Arranging the equation of the separately excited DC

machine into a block diagram representation is straight forward The

field and armature voltage equations and the relationship between torque

and rotor speed (11-16) may be Combined produces the armature

current torque field current and motor speed as follows

)1(

1)(

p

REVi

a

a

aaa

(17)

)(

1)(

JpTT Ler (18)

)1(

1

p

RVi

f

f

ff

(19)

Where aaa RL and fff RL

From equations (11-19) the time-domain block diagram is obtained as

shown in Fig 16

(9)

)1(

1

p

R

a

a

)1(

1

p

R

f

f

)(

1

Jp

afL ai

fi fV

eT LT

r aV

bE

Fig 16 Time domain block diagram of separately excited DC motor

142 State Equation of Separately Excited DC Motor

The so-called state equations of the system represent the formulation

of the state variables into a matrix form convention for computer

implementation The state variable of a system are define as a minimal

set of variables such that knowledge of these variables at any initial

condition time t plus information on the input excitation subsequently

applied is sufficient to determine the state of the system at any time tt

In the case of DC machine the field current fi armature current ai and

the rotor speed r The formulation of the state equations for the

separately excited dc machine can be achieved by straight forward

manipulation of the field and armature voltage equations given by (11-

14) and the equation relating torque and rotor speed given by (15-16)

In particular solving equations (11 14 16) for dt

dia dt

di f and

dt

d r

yields

a

a

rf

a

af

a

a

a VL

iL

Lii

dt

d 11

(110)

f

f

f

f

f VL

iidt

d 11

(111)

(10)

J

Tii

J

L

Jdt

d L

af

af

rr

(112)

These equations can be written in matrix form as follows

L

a

f

a

f

af

af

rf

a

af

r

a

f

a

f

r

a

f

T

V

V

J

L

L

iiJ

L

iL

Li

i

J

i

i

dt

d

1 0 0

0 1

0

0 0 1

0

0 0

0 1

0

0 0 1

(113)

143 Time Domain Transfer Functions of Separately Excited DC

Motor

After identified all the major components in the block diagram the transfer

functions of all parts in the diagram have been defined An open loop

represents the single direction of flow in a system with no knowledge of

the response On the other hand we have a closed loop system The

output of the system is being measured and fed back to the input to form

a close loop system All these explanation can be summarized by a

complete transfer function representation made up of all the block

diagrams defined in the previous sections The closed loop transfer

function is easily obtained from all blocks in the block diagram shown in

Fig 17 as follows

)1)(1()1(

)1(

)(

)(2

0JpJp

K

tV

t

maa

ma

Ta

r

L

(114)

Where 2

K

JRa

m

)1)(1()1(

)1)(1()(2

0JpJp

pJ

T

t

maa

a

VL

r

a

(115)

)1)(1()1(

)1()(2

0JpJp

K

T

ti

maa

ma

VL

a

a

(116)

(11)

)1)(1()1(

))(1(

)(

)(2

0JpJp

JpR

tV

ti

maa

aa

Ta

a

L

(117)

)1(

1

p

R

a

a

)(

1

Jp K

ai eT LT

r aV

bE

Fig 17 Time domain block diagram of separately excited DC motor at

constant flux

144 S-Domain Block Diagram of Separately Excited DC Motor



with S-domain equations using the s operator to denote differentiation

with respect to time dtd and the operator s1 denote integration ion

Therefore we will have no trouble converting the time-domain block

diagram so transfer functions by using the Laplace operator Arranging

the equation of the separately excited DC machine into a block diagram

representation is straight forward The field and armature voltage

equations and the relationship between torque and rotor speed (11-16)

may be Combined produces the armature current torque field current

and motor speed as follows

)1(

1)(

s

REVi

a

a

aaa

(118)

(12)

)(

1)(

JsTT Ler

(119)

)1(

1

s

RVi

f

f

ff

(120)

From equations (118-120) the S-domain block diagram is obtained as

shown in Fig 18

145 S-Domain Transfer Functions of Separately Excited DC Motor










Fig 19 as follows

)1)(1()1(

)1(

)(

)(2

0JsJs

K

sV

s

maa

ma

Ta

r

L

(121)

)1)(1()1(

)1)(1()(2

0JsJs

sJ

T

s

maa

a

VL

r

a

(122)

)1)(1()1(

)1()(2

0JsJs

K

T

si

maa

ma

VL

a

a

(123)

)1)(1()1(

))(1(

)(

)(2

0JsJs

JsR

sV

si

maa

aa

Ta

a

L

(124)

(13)

)1(

1

s

R

a

a

)1(

1

s

R

f

f

)(

1

Js

afL ai

fi fV

eT LT

r aV

bE

Fig 18 S-domain block diagram of separately excited DC motor

)1(

1

s

R

a

a

)(

1

Js K

ai eT LT

r aV

bE

Fig 19 S-domain block diagram of separately excited DC motor at

constant flux

(14)

Chapter (2)

Performance Characteristics of Separately Excited

DC Motor

21 Operation of the Separately Excited DC Motor

The operation of a DC motor is described briefly at first A symbolic

representation of a separately-excited DC motor is shown above The

resistance of the field winding is Rf and its inductance is Lf whereas the

resistance of the armature is Ra and its inductance is La In the

description of the motor the armature reaction effects are ignored It is

justifiable since the motor used has either interpoles or compensating

winding to minimize the effects of armature reaction The field current is

described by equation (21) If a steady voltage Vf is applied to the field

the field current settles down to a constant value as shown in equation

(22) When the field current is constant the flux induced by the field

winding remains constant and usually it is held at its rated value If

the voltage applied to the armature is Va then the differential equation

that is to be applied to the armature circuit is shown in equation (23) In

steady-state equation (24) applies The voltage ea is the back emf in

volts In a separately-excited DC motor the back emf is proportional to

the product of speed of motor r (rads) and the field ( webers) as

shown by equation(25)

dt

diLRiV

f

ffff (21)

fff RVi (22)

b

a

aaaa Edt

diLRiV (23)

baaa ERiV (24)

rb KE (25)

(15)

In equation (25) K is a coefficient and its value depends on the armature

winding If the armature current in steady-state be Ia then the power P

that is supplied to the armature is EbIa This electric power is converted to

mechanical power by the armature of the DC motor Let the torque

developed by the armature be Te the unit for torque being Nm (Newton-

metre) Then power and torque can be related as shown in equation (26-

28) On canceling the common term on both sides the torque Te

developed by the armature is obtained as presented in equation (29) If

the instantaneous armature current is ia then equation (28) applies

Torque has been denoted by Te in both equations

aba IEP (26)

rb KE (27)

raa IKP (28)

ae IKT (29)

Speed of the motor can be controlled by varying Va and holding Vf

constant at its rated value Then as the voltage applied to the armature is

raised the armature current increases first As the armature current

increases the torque developed by motor increases and hence speed of

the motor increases The drop across the armature resistance tends to be

small and hence the motor speed rises almost proportionately with the

voltage applied to the armature But there is a limit to the voltage that

can be applied to the armature and that limit is the rated voltage of the

armature voltage The speed of the motor corresponding to the rated

armature voltage and the rated field voltage is its rated speed Thus the

speed of a motor can be varied below its rated speed by controlling the

armature voltage It would be desirable that the motor should be able to

develop as high as a torque as possible and hence the voltage rated

applied to the field is held at its rated value Applying higher than the

(16)

rated voltage to either the field or the armature is not recommended

When the rated voltage is applied to the field the flux would be near the

saturation level in the poles If a voltage higher than its rated voltage is

applied to the field the flux would saturate and there would not be any

significant increase in the torque that the motor can deliver On the other

hand this would only result in increased losses in the winding Since the

total heat which the DC motor can dissipate is fixed due to its surface

area and cooling system increased losses from the excitation system

would mean that the other losses would have to reduce implying that the

armature current cannot be at its rated level and the maximum torque that

the motor can deliver may reduce Increasing the armature voltage above

its rated value is not recommended because the insulation of the armature

is designed for operation of the motor with the rated voltage applied to its

armature Moreover the torque that the motor can deliver depends on the

armature current and the field current If the motor is operated

continuously the maximum armature current should not be higher than

its rated value When the armature current and the field voltage are at

their rated level the motor generates the rated torque Hence the

maximum torque the motor can deliver continuously over a long period

of time is its rated torque when its speed is varied from a low value to its

rated speed

If the speed of the motor is to be increased beyond its rated value the

voltage applied to the armature can be held at its rated value and the field

can be weakened by reducing the voltage applied to it When the speed

of the motor is varied in this manner the maximum power that can be

supplied to the armature is fixed since both the voltage applied to the

armature and the armature current cannot exceed the rated level over a

long period

(17)

22 Dynamic Characteristics of Separately Excited DC Motor

The separately-excited DC motor are widely used and therefore the

dynamic performance of a typical DC motor is illustrated Two modes of

dynamic operation are of interest-starting from stall and changes in load

torque with the machine supplied from a constant voltage source

221 Dynamic Performance During Starting From a Constant DC

Source

This block implements a separately excited DC machine using

SIMULINKMATLAB as shown in Fig 21 An access is provided to

the field connections so that the machine model can be used as a shunt-

connected or a series-connected DC machine

Fig 21 Separately excited DC machine using SIMULINKMATLAB

The details of the SIMULINK diagram is shown in Fig 22 The first

block simulate the equation aidt

d the second block simulate the equation

fidt

d the third block simulate the equation ae iKT and the fourth block

simulate the equation )(

1)(

JsTT Ler

(18)

Fig 22 Details of Separately excited DC motor SIMULINK diagram

The no load starting characteristics of separately excited DC motor are

shown in Fig 23 The armature voltage the armature current and the

rotor speed are plotted Initially the motor is stall and at time zero 240 V

(19)

is applied to the armature terminals The peak transient current reaches to

500 A and rotor speed has an overshoot of 60 radsec (large)

Fig 23 No load starting characteristics of separately excited DC motor

(20)

222 Dynamic Performance During Sudden Change in Load Torque

The dynamic characteristics following a step change in load torque from

zero to 25 Nm are shown in Fig 24 The armature current and rotor

speed are plotted It is noted that the change in steady state rotor speed is

quite large

Fig 24 Dynamic performance of separately excited DC motor following

a sudden change in load torque

223 Dynamic Performance Using Starting Resistance

As the DC motor starts to turn the interaction of the magnetic fields

inside it causes it to generate a voltage internally This back voltage

opposes the applied voltage and the current that flows is governed by the

difference between the two So as the motor speeds up the internally

generated voltage rises the effective voltage falls less current is forced

(21)

through the motor and thus the torque falls The motor naturally stops

accelerating when the drag of the train matches the torque produced by

the motors To continue accelerating the train resistors are switched out

in steps each step increasing the effective voltage and thus the current

and torque for a little bit longer until the motor catches up This can be

heard and felt in older DC trains as a series of clunks under the floor

each accompanied by a jerk of acceleration as the torque suddenly

increases in response to the new surge of current When no resistor is left

in the circuit the full line voltage is applied directly to the motor The

trains speed remains constant at the point where the torque of the motor

governed by the effective voltage equals the drag - sometimes referred to

as balancing speed If the train starts to climb a grade the speed reduces

because drag is greater than torque But the reduction in speed causes the

back voltage to decline and thus the effective voltage rises - until the

current forced through the motor produces enough torque to match the

new drag

On an electric train the driver originally had to control the cutting out

of resistance manually This was achieved by an accelerating relay often

called a notching relay in the motor circuit as shown in Fig 25 which

monitored the fall of current as each step of resistance was cut out All

the driver had to do was select low medium or full speed called shunt

series and parallel from the way the motors were connected in the

resistance circuit) and the equipment would do the rest

As we have seen DC motors are controlled by a notching relay set

into the power circuit But there are other relays provided for motor

protection Sharp spikes of current will quickly damage a DC motor so

protective equipment is provided in the form of an overload relay

which detects excessive current in the circuit and when it occurs

switches off the power to avoid damage to the motors Power is switched

(22)

off by means of Line Breakers one or two heavy-duty switches similar to

circuit breakers which are remotely controlled They would normally be

opened or closed by the action of the drivers controller but they can also

be opened automatically by the action of the overload relay

On a historical note early equipment had a huge fuse instead of an

overload relay Some of these lasted into the 1970s and recall the

complications of changing one which involved inserting a wooden board

(called a paddle) between the shoes and the current rail This was to

isolate the current from the locomotive while you changed the fuse

A further protective device is also provided in the classic DC motor

control circuit This is the no-volt relay which detects power lost for

any reason and makes sure that the control sequence is returned to the

starting point (ie all the resistances are restored to the power circuit)

before power could be re-applied This is necessary to ensure that too

much current is not applied to a motor which lost speed while current was

off The following circuit illustrates the starting of a 5 HP 240 V DC

Machine with a three-step resistance starter Figure 25

Fig 25 Starting of a separately excited DC motor with a three-step

resistance starter

(23)

The block implements a separately excited DC machine An access is

provided to the field connections so that the machine model can be used

as a shunt-connected or a series-connected DC machine The armature

circuit and the field circuit of the DC machine model are built with blocks

from SIMULINK library It is represented by a DC motor block created

in series with a Controlled Voltage Source and a Current Measurement

block

Four internal signals are multiplexed on the SIMULINK measurement

output vector (third block output) returning

Rotor speed in rads

Armature current in A

Field current in A

Electromechanical torque in Nm

The following circuit illustrates the starting of a 5 HP 240 V DC Machine

with a three-step resistance starter using SIMULINK as shown Fig 26

The Motor Starter subsystem is shown in Figure 27

Figure 26 Starting DC motor SIMULINK diagram

(24)

Figure 27 Starter SIMULINK diagram

The DC motor current voltage torque and speed waveforms obtained at

the end of the starting test are shown in Figure 28

Fig 28 Starting performance of DC motor using starter

It is noted from this Figure that the starting current reaches to 50 A

instead of 500 A as mentioned before but the response time is very long

(25)

Chapter (3)

Open Loop Speed Control of DC Motor Drive Using Solid

State Power Devices

31 Rectification

Rectifiers can be classified as uncontrolled and controlled rectifiers

and the controlled rectifiers can be further divided into semi-controlled

and fully-controlled rectifiers Uncontrolled rectifier circuits are built

with diodes and fully-controlled rectifier circuits are built with SCRs

Both diodes and SCRs are used in semi-controlled rectifier circuits

There are several rectifier circuits rectifier configurations The popular

rectifier configurations are listed below

Single-phase semi-controlled bridge rectifier

Single-phase fully-controlled bridge rectifier

Three-phase three-pulse star-connected rectifier

Three-phase semi-controlled bridge rectifier

Three-phase fully-controlled bridge rectifier and

For low voltage high current applications a pair of three-phase three-

pulse rectifiers interconnected by an inter-phase transformer(IPT) is used

For a high current output rectifiers with IPT are preferred to connecting

devices directly in parallel There are many applications for rectifiers

Some of them are

Variable speed dc drives

32 AC to DC Conversion

321 Full Wave Rectification

A thyristor controlled rectifier employs four thyristors to achieve full

wave rectification If we a DC machine as a load this has both L and R

and generates a back emf as shown in Fig 31

(26)

Assuming that there is sufficient inductance to ensure the motor

current is continuous with the lag associated the waveforms are as above

We can see that Io and Vo are both positive therefore power is being

delivered from the supply to the motor This is normal rectification mode

If the firing angle is delayed to say 135O then the waveforms change

Fig 31 Schematic and waveforms diagrams of full wave converter

fed DC motor

(27)

We now see that Vo is ndashve and Io +ve This means that the power flow is

into the supply This is called INVERSION MODE In both cases we can

see that as S3 and S4 turn on the reverse voltage appears across S1 and S2

this is called LINE COMMUTATION

In both cases the average value of the output voltage is

cos22 V

V (31)


fed DC motor in inversion mode

The variation of the converter output Vo as defined by (31) is shown in

Fig 33

Fig 33 Output voltage variations of full wave converter

fed DC motor

(28)

322 The semi-converter

In the semi-converter two of the thyristors are replaced with diodes The

operation is the same as the full bridge converter except that the diodes

do not allow any negative voltage to the load as shown in Fig 34

Fig 34 Schematic and waveforms diagrams of full wave semi-converter

fed DC motor

The average output voltage is now given by

)cos1(2

V

V (32)

(29)

323 Three Phase Circuits

Higher power applications above several kW are best met using 3 phase

rectifiers Various configurations of rectifier are available

a- The Half Wave Rectifier

In the case of an uncontrolled diode circuit we have the following

diagram as shown in Fig 35


At any time the diode whose voltage is the most +ve will conduct We

can see that each diode conducts for a span of 120O also when D1

conducts the voltage across D2 is vBA and across D3 is vCA During this

time D2 and D3 are reverse biased Using D1 we can also say

VV

63 (34)

The thyristor controlled versions is shon in Fig 36

(30)


The output voltage waveform is given by

)cos1(63

V

V (35)

b- The Thyristor Full Wave Converter

This is by far the most common controller rectifier circuit It has the

following configuration Both diagrams represent the same format This

is the 3 phase equivalent of the full bridge rectifier S123 are fired during

the +ve half cycles of the phases to which they are connected and S456

are fired during the ndashve half cycles of the respective phases Again let us

assume that the load has significant inductance to maintain constant

current such as the DC machine examined earlier The output current will

be continuous and operation will be as follows

(31)

It should be noted that each device conducts for 120O per cycle but the

average output voltage can be expressed as

cos63 V

V (36)

This gives us waveforms as follows


Similarly to the single phase converters firing angles of 0 lt lt 90 give

+ve Vo but firing angles of 90 lt lt 180 cause vo to go ndashve and the

converter works in inversion mode this gives us Vo vs for continuous

current

(32)


fed DC motor

33 DC-to-DC Conversion

When the SCR came into use a dc-to-dc converter circuit was called a

chopper Nowadays an SCR is rarely used in a dc-to-dc converter Either

a power BJT or a power MOSFET is normally used in such a converter

and this converter is called a switch-mode power supply A switch-mode

power supply can be of one of the types listed below

Step-down switch-mode power supply

Step-up chopper

Fly-back converter and

Resonant converter

The typical applications for a switch-mode power supply or a chopper

are

DC drive

Battery charger and

DC power supply

332 Description of the Open Loop Drive System

In this section illustrates application of the SIMULINKMATLAB to

the operation of a DC motor drive in which the armature voltage is

(33)

controlled by a GTO thyristor chopper The objective of this section is to

demonstrate the use of electrical blocks in combination with SIMULINK

blocks in the simulation of an electromechanical system with a control

system The electrical part of the DC motor drive including the DC

source the DC motor and the chopper is built using blocks from the

SIMULINK and Power Electronics libraries The DC Machine block of

SIMULINK models both electrical and mechanical dynamics The load

torque-speed characteristic and the control system are built using

SIMULINK blocks

A simplified diagram of the drive system is shown in Figure 39 The

DC motor is fed by the DC source through a chopper that consists of the

GTO thyristor Th1 and the free-wheeling diode D1 The DC motor

drives a mechanical load that is characterized by the inertia J friction

coefficient B and load torque TL (which can be a function of the motor

speed)

Figure 39 Chopper-Fed DC Motor Drive

In this diagram the DC motor is represented by its equivalent circuit

consisting of inductor La and resistor Ra in series with the counter

electromotive force (emf) E

(34)

Thyristor Th1 is triggered by a pulse width modulated (PWM) signal to

control the average motor voltage Theoretical waveforms illustrating the

chopper operation are shown in Fig 310

The average armature voltage is a direct function of the chopper duty

cycle

dca VV (37)

Note that this relation is valid only when the armature current is

continuous In steady-state the armature average current is equal to

a

baa

R

EVI

(38)

The peak-to-peak current ripple is

)1(

)1(

)1(

e

eee

R

Vi

a

dc (39)

where is the duty cycle and r is the ratio between the chopper period

and the DC motor electrical time constant

)( aa RL

T (310)

Figure 310 Waveforms Illustrating the Chopper Operation

(35)

34 Steady-State Voltage and Current Waveforms

When the steady-state is attained you can stop the simulation and plot the

current and voltage waveforms using the variables Va and Ia sent back in

MATLAB workspace by the scope The DC motor current and voltage

waveforms obtained at the end of the starting test are shown in Fig 311

Figure 311 Steady-State Motor Current and Voltage Waveforms

(36)

Chapter (4)

Design and Simulation for Current amp Speed Controllers

of Separately Excited DC Motor Drive

41 Introduction

This chapter describes how a separately-excited DC motor can be

controlled in closed-loop with a Chopper-controlled supplying DC source

to its armature In a control system the system dynamics is often

described by differential equations By applying Laplace transformation

to the system differential equations the system output variables can be

related to the input variables in an algebraic form In our single input

single output system (SISO) where one input position expect one

corresponding output position We use a transfer function to model the

inputoutput relationship System Transfer Function = Ratio of the output

over the input to a control system Hence every component in a control

circuit will have a transfer function This is obvious because every

component in a control system will receive some input signal and

manipulate this signal to provide a required output Therefore we have a

series of transfer functions within the system We can relate these systems

together by a block diagram representation where the transfer functions of

each component is put into representative blocks

A separately-excited dc motor can be controlled either by varying the

voltage applied to the field winding or by varying the voltage applied to

the armature This Chapter describes how the motor can be controlled by

varying the armature voltage and it is assumed that the field is excited by

a constant voltage equaling the rated voltage of the field winding It

means that the discussion to follow assumes that the field current remains

steady at its rated value

(37)

42 Control System Design

Classical Feedback Control describes design and implementation of high-

performance feedback controllers for engineering systems This Chapter

emphasizes the pole placement and root locus approaches which is widely

used in practical engineering It presents the design methods for high-

order SISO linear and nonlinear analog and digital control systems

Modern technology allows implementation of high-performance

controllers at a very low cost Conversely several analysis tools which

were previously considered an inherent part of control system courses

limit the design to low-order (and therefore low-performance)

compensators Among these are the root-locus method the detection of

right-sided polynomial roots using the Routh-Hurwitz criterion and

manual calculations using the Laplace and Fourier transforms These

methods have been rendered obsolete by structural simulation of complex

systems multi-loop systems and nonlinear controllers all of which are

essential for good design practice

Nonlinear dynamic compensation is employed to provide global and

process stability and to improve transient responses The nearly-optimal

high-order compensators are then economically implemented using

analog and digital technology

43 Current Controller Design Using Pole Placement

With approximate model of the current loop the transfer function is given

by

)1(

)1(

)(

)(

0 aa

a

Ta

a

s

R

sV

si

L

(41)

If we use the desired response

22

2

2)(

)(

nn

n

ssR

sC

(42)

(38)

We can design the current controller as follows

)1(

1

s

R

a

a

s

KsK i

i

i

p

ai

ai

Fig 41 Block diagram of the current control loop

The closed loop transfer function can be deduced as

aa

i

iaa

i

pa

i

i

i

paa

Ta

a

RKRKs

KsKR

sI

sI

L

)1(

))(1(

)(

)(2

0

(43)

By comparing equations (42 43) yields the controller parameters

)12( anaa

i

p RK (44)

2

naa

i

i RK (45)

Now we can select the damping ratio and then we can calculate n as

follows

For s

sR1

)( therefore

22

2

2

1)(

nn

n

sssC

(46)

The inverse Laplace Transform for equation (46) will yield

)1(1)( tetC n

tn

(47)

From this equation we can calculate n at the rise time rt and 90)( rtC

44 Speed Controller Design Using Pole Placement


by

(39)

)(

)(

)(

0Js

JK

sV

s

LTa

r

(48)


)(

Js

JK

s

KsK ip

a

r

Fig 42 Block diagram of the speed control loop


)()(

))((

)(

)(2

0

JKKsJKKJs

KsKJK

s

s

ip

ip

Tr

r

L

(49)


)2( JK np (410)

KJK ni 2 (411)


before

45 Operation of the Current Controller of DC Motor

The current controller has two inputs the reference current signal

which is the output of the speed controller and a feedback signal

proportional to armature current The feedback corresponding to

armature current signal can be obtained in several ways A current

transformer can be introduced in the path of ac current from the ac

supply Another option would be to use a DC current transducer that

makes use of a Hall-effect sensor or an isolated opamp The transducer

used produces a voltage proportional to current in the armature The

(40)

difference between these two signals is processed by another PI controller

and its output is also limited to correspond to 0o and 180

o firing angle

Output of the current controller may vary between 0 V and 10 V with 0

V corresponding to 180o firing angle and 10 V corresponding 0

o firing

angle If the firing angle be and the output of current controller VC

then

)10(180 cV (412)

As output voltage of the current controller increases due to the

difference between the reference signal and the current feedback signal

the firing angle is advanced towards 0o and average output voltage of the

bridge rectifier increases This in turn leads to increased torque

generation and the motor accelerates

If the speed reference is brought down suddenly the current in the

motor cannot be reversed and hence the motor slows down due to friction

and the load This process can be slow

The question that can be raised is whether we need the current loop

The answer is that it improves the performance If there is a change in

the supply voltage even by a small amount output of the bridge circuit

tends to a fall a bit for the same firing angle The reduction in output

voltage causes a large change in armature current with speed remaining

more or less constant Then the current loop comes into action

correcting firing angle to the required value The time constant of the

armature due to its inductance and resistance tends to be of the order of

a few tens of ms and the mechanical time constant due to the moment of

inertia of motor and load and the friction is of the order of a few tenths of

a second If a current controller is not used speed would have to change

before the speed controller can come into action Since the mechanical

time constant is about at least 10 times greater there would be a

significant change in speed if there be no current controller

(41)

Normally a filter may be necessary in the feedback circuit for speed The

tacho signal usually contains a small ripple superimposed on its dc

content The frequency of the ripple is usually dependent on the speed

and the lower the speed is the lower is the frequency of this ripple

Hence the time constant of the filter may have to be set to correspond to

the lowest speed at which the motor would be required to run Since

power output varies proportionately with speed there is usually no

justification to run the motor at an extremely low speed The next section

describes how the simulation is carried out

46 Operation of Speed Controller of DC Motor

The block diagram of a dc drive is shown above It does not show all

details The DC motor has not been represented in the form of a block

diagram and the details of the load the motor drives have also not been

shown The block diagram functions as follows

For the system described here output of the system is speed of the motor

Hence when this system is to be controlled in closed-loop the parameter

that is to be set is what that speed should be It is denoted to be

r In

order to control speed in closed-loop we need a feedback signal that

corresponds to speed It can be obtained in several ways A digital tacho

or an analogue tachogenerator can be used It is assumed that an

analogue tachogenerator is used here It is coupled to the motor shaft and

its output voltage varies linearly with its speed Let the speed feedback

signal be

r This signal can be compared with the speed reference

signal and the error can be processed by the speed controller The

controller can be of one of several types It can be an integral (I)

controller or a proportional (P) controller controller or a derivative (D)

controller or PI or PD or PID controller Here both the controllers used

(42)

are PI (proportional plus integral) controllers A PI controller can lead to

fast response and zero-error for a step input

The PI controller for speed has as its input the error between the two

signals

r and r If the speed feedback signal r is lower than the

reference signal

r it means that the DC motor speed is below the set

speed and the motor needs to be accelerated In order to accelerate the

motor it should develop greater torque To develop greater torque its

armature current has to increase Hence the output of speed controller is

set to function as the reference signal for armature current It will be a

voltage corresponding to armature current with an appropriate coefficient

linking the two quantities When r lt

r the difference causes output

of the speed controller to increase Since output of speed-controller is set

to function as the armature current reference signal an increase in the

value of speed-controller output would in turn lead to an increase in

armature current

47 Operation of DC Chopper Fed of DC Motor

The rectifier circuit is made up of SCRs and the SCRs have a current

rating Hence it is necessary to ensure that current through the SCRs

remains within a safe level Hence output of the speed controller is

limited at both ends Its maximum value corresponds to the safe level for

SCRs It is not normally the rated current of the motor and it is usually

set at a value ranging from 15 times to 2 times the rated armature current

The reason is that the motor may have to develop more than the rated

torque under transient conditions to achieve fast response In order to

ensure that the motor armature current remains within its rated value

another supervisory loop may be used Another option is to use a circuit-

breaker The instantaneous trip action in the circuit breaker can be due to

(43)

magnetic effect and the overload trip can be due to thermal action A bi-

metallic strip within the circuit-breaker expands due to temperature and

would trip the circuit-breaker The lower limit on the output of speed-

controller would correspond to zero current in the armature since the

motor current in this scheme cannot be in the reverse direction

48 Simulation of the Separately Excited DC Motor Drive Using

SIMULINKMATLAB

In this section we consider a variable-speed DC motor drive using a

cascade control configuration A block diagram of this drive is shown in

Figure 43 The motor torque is controlled by the armature current Ia

which is regulated by a current control loop The motor speed is

controlled by an external loop which provides the current reference Ia

for the current control loop

Figure 43 Variable-Speed DC Motor Drive

The drive system diagram is built using electrical blocks contained in the

SIMULINK library Voltage Measurement and Current Measurement

blocks are used as the interface between the two block types The system

diagram of the DC motor using SIMULINK is shown in Fig 44

(44)

Figure 44 DC Motor Drive Using SIMULINKMATLAB

The DC machine parameters are set to the desired values by using the

dialog mask of the DC Machine block

The load torque-speed characteristic can be implemented by a

SIMULINK Function block

The motor used in this case study is a separately excited 5 HP240 V DC

motor having the following parameters Ra = 05 La = 10 mH Kv

=123 V(rads) Kv = 123 NmA

A 10mH inductor (Ls) is connected in series with the DC motor to

smooth out the armature current The constant excitation is implemented

by connecting a DC Voltage Source block to the field winding

The required trigger signal for the GTO thyristor is generated by a

hysteresis current controller which forces the motor current to follow the

reference within +h2 and -h2 limits (h is the hysteresis band) as shown

in Fig 45

The current controller is a masked block that contains

(45)

Figure 45 The hysteresis current controller

The speed control loop uses a proportional-integral (PI) controller which

is implemented by SIMULINK blocks as shown in Figure 46

Figure 46 The PI speed controller

49 Simulation Results of the DC Drive

Run the simulation by selecting Start from the Simulation menu in

Simulink Set the simulation parameters in the Simulation Parameters

menu as follows

Simulation time Start Time0 Stop time 12

Solver Type Variable-step ode23tb (stiffTR-BDF2)

Max Step Size auto

Initial Step Size auto

Relative Tolerance 1e-3

Absolute Tolerance 1e-3

The motor voltage current waveforms and motor speed are displayed on

three axes of the scope connected to the variables Vd Ia and

(46)

Once the simulation is completed you can return to the MATLAB

command window to examine the results with more details by using the

plot function

491 Drive Performance at No Load

In this test we simulate the starting transient of the DC drive The

inertia of the mechanical load is small in order to bring out the details of

the chopper commutation details The speed reference is stepped from 0

to 120 rads at t=00 s and we observe the DC motor speed and current

The transient responses for the starting of the DC motor drive are shown

in Figure 47 Note that the final system state vector x Final can be saved

by selecting Workspace IOSave to workspaceFinal state in the

Simulation Parameters window It can be used as initial state in

subsequent simulation so that the simulation can start under steady-state

conditions

492 Speed Regulation Dynamic Performance

We can study the drive dynamic performance (speed regulation

performance versus reference and load torque changes) by applying two

successive changing operating conditions to the DC drive a step change

in speed reference and a step change in load torque

Replace the block named

r (rads) and the block named Load_torque

(Nm) in the diagram by two SIMULINK step blocks with different

starting times The speed reference steps from 120 rads to 160 rads at t =

04 s and the load torque steps from 5 Nm to 25 Nm at t = 12 s The

final state vector obtained with the previous simulation can be used as

initial condition so that the simulation will start from steady-state Select

Workspace IOLoad from workspaceInitial state in the Simulation

Parameters window and restart the simulation

(47)

The obtained response of the DC motor drive to successive changes in

speed reference and load torque is shown in Figure 48

Figure 47 Starting of the DC Motor Drive

(48)

Figure 48 Dynamic Transient of the DC Motor Drive

(49)

Chapter (5)

Implementation of the Open Loop Control for Separately

Excited DC Motor

51 Introduction

In this Chapter the implementation of the DC Chopper feeding DC

motor is presented Power supply circuits driving circuits of IGBT

transistor and control circuit that generate the control signal of the

Chopper are designed and implemented

52 Experimental Setup

511 The Power Supply with Voltage Regulator Circuit

Power is supplied to the control circuit through a +5 -5 -15 +15 volt

DC power supply Power form the output of the bridge rectifier is

applied to a voltage regulators circuits that steps the voltage down to -5

+5 +15 -15 volt pure DC This circuit is fairly simple to build because

the support circuitry for the LM7805 (5-Volt voltage regulator IC)

LM7905 LM7815 and LM7915 require very few components Each

circuit consists of step down transformer an input jack a power switch a

resistor one LED a voltage regulator IC and two capacitors The out of

the bridge rectifier is brought in through the input jack and then routed to

a double pole double throw switch (DPDT) This switch is used to turn

the power to the microcontroller on and off The reason for using the

DPDT switch is to allow for disconnecting both the hot and neutral lines

The LED is used to indicate whether power to the circuit is on or off

The tantalum capacitors are used to filter the input and output voltages of

the all voltage regulators Once this testing is completed power is

(50)

applied to the circuit The student then checks the voltage regulator for

overheating Figure (51) displays the voltage regulator circuit

Fig 51 The voltage regulator circuit

522 Linear Control of Phase Angle

In this scheme illustrated in Fig 52 a control voltage Ec changes linearly

the phase angle The voltage V1 is converted to a square voltage e1 and

then to a ramp voltage e2 which is then compared with a control voltage

Ec If e2 is higher than Ec a signal ea is obtained at the output of the

comparator The time at which the rising edge of ea occurs is proportional

to Ec and defines the firing angle α This signal ea is next fed to a pulse

amplifier circuit and is used to fire IGBT The firing angle is given by

ckE (51)

This circuit was used to generate a ramp that is synchronized with the

line voltage Each comparator compares the line voltage with zero and

the RC circuit integrates the resulting square wave The reverse diode

resets the ramp to zero at each zero crossing and the series diode circuit

ORs the ramp outputs to achieve an increasing ramp which resets at each

zero crossing of the source voltage The final comparator stage is used to

dial the firing angle and the transistor drive circuit bias the IGBT

(51)

The ramp waveform and the pulse waveform for degrees were plotted

The circuit was constructed powered by a DC power supply (15V) and

its operation was confirmed The circuit diagram is shown in Fig 53

Fig 52 Linear control of phase angle

(52)

Fig 53 Circuit diagram phase angle control

523 Pulse Amplifier Circuit (Driving Circuit)

The pulses ei or ej in Fig 54 may not be strong enough to bias an IGBT

Besides the gate and emitter terminals of the IGBT are at higher

potentials of the power circuit and the control circuit should not be

directly connected to the power circuit An optical isolation or pulse-

transformer isolation is commonly used in practice to provide physical

isolation between the control circuit and the power circuit Figure 54

shows a pulse amplifier circuit using a pulse transformer isolation A

Darlington transistor is used to amplify the pulse-current If the pulses are

long (ex has a long width ) they may saturate the pulse-transformer and

the whole width of the pulse may not be transmitted The whole pulse-

width may not be necessary In such a case the pulse is modulated at a

high frequency (10-1 MHz) as shown in Fig 54 using a 555 timer or any

oscillator The duly cycle of the timer should be less than 50 so that the

flux in the transformer can reset A modulated pulse also reduces gate

dissipation in the IGBT Processing of the pulse signal (obtained from

the firing or driving circuit) at various stages is illustrated by the timing

diagram in Fig 54

(53)

Fig 54 A typical pulse amplifier circuit

524 Chopper Control

Chopper converters in general require firing pulses to turn on a main SCR

and a commutating IGBT The time interval between the firing of the

two IGBTs determines the duty cycle and hence the output voltage A

control voltage is used to control the duty cycle of the chopper Figure

55 shows a chopper firing circuit that consists mainly of four parts a

triangular wave generator a voltage comparator edge detection and pulse

(54)

amplifiers The waveforms at various parts of the circuit are also shown

in Fig 55

The three operational amplifiers Q1 and Q2 together form a triangular

wave generator that generates the triangular wave ea shown in Fig 55b

As the voltage ea decreases below 06 V (which is the forward bias

voltage of the diode D2) the output of Q2 changes from 135 V to -135

V and it in turn triggers Q3 to change state The output of Q3 which is

now negative (-135 V) makes D1 forward biased and the 22 k path

takes control of the integrator input summing junction The output of Q1

quickly rises to 135 V which in turn triggers Q2 and Q3 and changes

their outputs to positive voltages Now the diode D1 is reverse biased the

feedback loop through D1 is reverse biased and the feedback loop

through D1 is open With the diode D1 reverse biased control of the

integrator Q1 reverts to the 200 k path and the output voltage e has a

constant slope that depends on the values of the capacitor C the input

resistor R and the input voltage Vi In fact this oscillator can be used as

a voltage-controlled oscillator (VCO) The purpose of using Q2 is to

introduce a time delay so that there is enough lime to charge up the

capacitor so that ea rises to 135 V The diode D2 is used for the offset

adjustment so that ea is always above zero voltage

The operational amplifier Q4 is used as a voltage comparator If the

control voltage Ec exceeds the voltage ea the output of Q4 changes as

shown by waveform ea in Fig 55

The two monostable multivibrators are connected in such a way that

one of them is triggered by the rising edge and the other by the falling

edge of the signal On receiving the rising or falling edge the

monostable multivibrators produce two output signals whose width can

be adjusted A pulse-width in the range of 20 to 200 sec is sufficient

for firing IGBT

(55)

Fig 55 Chopper driving circuit

525 OPEN-LOOP AND CLOSED-LOOP CONTROL

The control voltage Ec in Figs 51 52 53 and 55 changes the output

voltage of the converter In an open-loop control as shown in Fig 56 the

control voltage Ec is varied by using a potentiometer In a closed-loop

control the control voltage is obtained from the difference between a

reference and the quantity to be controlled For example if the dc motor

armature current is to be controlled in a closed-loop feedback control

system as shown Fig 56 the control voltage is derived from the

difference between the reference current and the actual motor current

(56)

The Opamp comparator is used to compare values of 2 input voltages In

this control system the Opamp received voltage signal from the

potentiometer Then the Opamp amplifies the systems error voltages so

that the output voltage is enough to drive the motor For example the

input signal may be the order of a few miliamperes This is hardly

enough to actuate the motors This illustrates the need for an increase

gain It is worth mentioning that this amplifier compares the values of the

input and feedback voltage and then amplify this voltage to a magnitude

suitable to be transmitted

Fig 56 Open loop and closed loop control circuit

(57)

53 Experimental Results

We test the practical system using a resistive load and a small DC motor

Fig 57 shows the steady state voltage and current waveforms

Fig 57 Steady state voltage and current waveforms

(2)

mmf The term magnetic flux is used to describe how much magnetism

there is in the space around a coil or permanent magnet or in the air gap

of a motor

Condition assessment of DC motors requires a basic understanding of

the design and operating characteristics of the various types available the

separately excited DC motor the PM DC motor the series motor the

shunt motor and the compound motor Each type has unique operating

characteristics and applications These characteristics enable the operator

to perform a wide variety of tasks

12 Types of DC Motors

121 Separately Excited DC Motor

The schematic circuit diagram of separately excited DC motor is

illustrated in following Figure 11 When the armature of a DC machine

rotates in the stator field a voltage is induced in the armature winding In

a DC motor it is called counter emf or back emf In either case the level

of this voltage can be calculated using Faradays Law which states that a

voltage is induced The field and armature circuits are totally separate

The field current is supplied from a secondary source

Figure 11 Separately Excited DC Motor

(3)









123 Series DC Motor














(4)










124 Shunt DC Motor













(5)



















(6)



















industry










(7)







b

a

aaaa Edt

diLRiV (11)

rfafb iLE (12)

faf iLK (13)

dt

diLRiV

f

ffff (14)

ae iKT (15)

Lr

r

e Tdt

dJT

(16)

Va applied voltage

Ia motor current







Motor




(8)




speed controllers













)1(

1)(

p

REVi

a

a

aaa

(17)

)(

1)(

JpTT Ler (18)

)1(

1

p

RVi

f

f

ff

(19)



shown in Fig 16

(9)

)1(

1

p

R

a

a

)1(

1

p

R

f

f

)(

1

Jp

afL ai

fi fV

eT LT

r aV

bE















dia dt

di f and

dt

d r

yields

a

a

rf

a

af

a

a

a VL

iL

Lii

dt

d 11

(110)

f

f

f

f

f VL

iidt

d 11

(111)

(10)

J

Tii

J

L

Jdt

d L

af

af

rr

(112)


L

a

f

a

f

af

af

rf

a

af

r

a

f

a

f

r

a

f

T

V

V

J

L

L

iiJ

L

iL

Li

i

J

i

i

dt

d

1 0 0

0 1

0

0 0 1

0

0 0

0 1

0

0 0 1

(113)


Motor










Fig 17 as follows

)1)(1()1(

)1(

)(

)(2

0JpJp

K

tV

t

maa

ma

Ta

r

L

(114)

Where 2

K

JRa

m

)1)(1()1(

)1)(1()(2

0JpJp

pJ

T

t

maa

a

VL

r

a

(115)

)1)(1()1(

)1()(2

0JpJp

K

T

ti

maa

ma

VL

a

a

(116)

(11)

)1)(1()1(

))(1(

)(

)(2

0JpJp

JpR

tV

ti

maa

aa

Ta

a

L

(117)

)1(

1

p

R

a

a

)(

1

Jp K

ai eT LT

r aV

bE


constant flux













)1(

1)(

s

REVi

a

a

aaa

(118)

(12)

)(

1)(

JsTT Ler

(119)

)1(

1

s

RVi

f

f

ff

(120)


shown in Fig 18











Fig 19 as follows

)1)(1()1(

)1(

)(

)(2

0JsJs

K

sV

s

maa

ma

Ta

r

L

(121)

)1)(1()1(

)1)(1()(2

0JsJs

sJ

T

s

maa

a

VL

r

a

(122)

)1)(1()1(

)1()(2

0JsJs

K

T

si

maa

ma

VL

a

a

(123)

)1)(1()1(

))(1(

)(

)(2

0JsJs

JsR

sV

si

maa

aa

Ta

a

L

(124)

(13)

)1(

1

s

R

a

a

)1(

1

s

R

f

f

)(

1

Js

afL ai

fi fV

eT LT

r aV

bE


)1(

1

s

R

a

a

)(

1

Js K

ai eT LT

r aV

bE


constant flux

(14)

Chapter (2)


DC Motor



















dt

diLRiV

f

ffff (21)

fff RVi (22)

b

a

aaaa Edt

diLRiV (23)

baaa ERiV (24)

rb KE (25)

(15)











aba IEP (26)

rb KE (27)

raa IKP (28)

ae IKT (29)















(16)





















rated speed







long period

(17)







Source









fidt



1)(

JsTT Ler

(18)





(19)




(20)





quite large









(21)
















new drag














(22)



















resistance starter

(23)







block



Rotor speed in rads


Field current in A






(24)







(25)

Chapter (3)


State Power Devices

31 Rectification

















Some of them are







(26)







fed DC motor

(27)






cos22 V

V (31)




Fig 33


fed DC motor

(28)






fed DC motor


)cos1(2

V

V (32)

(29)












VV

63 (34)


(30)



)cos1(63

V

V (35)










(31)



cos63 V

V (36)






current

(32)


fed DC motor








Step-up chopper


Resonant converter


are

DC drive

Battery charger and

DC power supply




(33)









SIMULINK blocks






speed)





(34)





cycle

dca VV (37)



a

baa

R

EVI

(38)


)1(

)1(

)1(

e

eee

R

Vi

a

dc (39)



)( aa RL

T (310)


(35)







(36)

Chapter (4)



41 Introduction
























(37)























by

)1(

)1(

)(

)(

0 aa

a

Ta

a

s

R

sV

si

L

(41)


22

2

2)(

)(

nn

n

ssR

sC

(42)

(38)


)1(

1

s

R

a

a

s

KsK i

i

i

p

ai

ai



aa

i

iaa

i

pa

i

i

i

paa

Ta

a

RKRKs

KsKR

sI

sI

L

)1(

))(1(

)(

)(2

0

(43)


)12( anaa

i

p RK (44)

2

naa

i

i RK (45)


follows

For s

sR1

)( therefore

22

2

2

1)(

nn

n

sssC

(46)


)1(1)( tetC n

tn

(47)




by

(39)

)(

)(

)(

0Js

JK

sV

s

LTa

r

(48)


)(

Js

JK

s

KsK ip

a

r



)()(

))((

)(

)(2

0

JKKsJKKJs

KsKJK

s

s

ip

ip

Tr

r

L

(49)


)2( JK np (410)

KJK ni 2 (411)


before










(40)



o firing angle



o firing


then

)10(180 cV (412)























(41)


















r In






signal be






(42)




signals


reference signal












armature current













(43)







SIMULINKMATLAB












(44)















in Fig 45


(45)








menu as follows



Max Step Size auto






(46)



plot function











conditions















(47)




(48)


(49)

Chapter (5)


Excited DC Motor

51 Introduction






















(50)












ckE (51)








(51)





(52)



















diagram in Fig 54

(53)


524 Chopper Control







(54)


in Fig 55



























for firing IGBT

(55)











(56)











(57)





(3)









123 Series DC Motor














(4)










124 Shunt DC Motor













(5)



















(6)



















industry










(7)







b

a

aaaa Edt

diLRiV (11)

rfafb iLE (12)

faf iLK (13)

dt

diLRiV

f

ffff (14)

ae iKT (15)

Lr

r

e Tdt

dJT

(16)

Va applied voltage

Ia motor current







Motor




(8)




speed controllers













)1(

1)(

p

REVi

a

a

aaa

(17)

)(

1)(

JpTT Ler (18)

)1(

1

p

RVi

f

f

ff

(19)



shown in Fig 16

(9)

)1(

1

p

R

a

a

)1(

1

p

R

f

f

)(

1

Jp

afL ai

fi fV

eT LT

r aV

bE















dia dt

di f and

dt

d r

yields

a

a

rf

a

af

a

a

a VL

iL

Lii

dt

d 11

(110)

f

f

f

f

f VL

iidt

d 11

(111)

(10)

J

Tii

J

L

Jdt

d L

af

af

rr

(112)


L

a

f

a

f

af

af

rf

a

af

r

a

f

a

f

r

a

f

T

V

V

J

L

L

iiJ

L

iL

Li

i

J

i

i

dt

d

1 0 0

0 1

0

0 0 1

0

0 0

0 1

0

0 0 1

(113)


Motor










Fig 17 as follows

)1)(1()1(

)1(

)(

)(2

0JpJp

K

tV

t

maa

ma

Ta

r

L

(114)

Where 2

K

JRa

m

)1)(1()1(

)1)(1()(2

0JpJp

pJ

T

t

maa

a

VL

r

a

(115)

)1)(1()1(

)1()(2

0JpJp

K

T

ti

maa

ma

VL

a

a

(116)

(11)

)1)(1()1(

))(1(

)(

)(2

0JpJp

JpR

tV

ti

maa

aa

Ta

a

L

(117)

)1(

1

p

R

a

a

)(

1

Jp K

ai eT LT

r aV

bE


constant flux













)1(

1)(

s

REVi

a

a

aaa

(118)

(12)

)(

1)(

JsTT Ler

(119)

)1(

1

s

RVi

f

f

ff

(120)


shown in Fig 18











Fig 19 as follows

)1)(1()1(

)1(

)(

)(2

0JsJs

K

sV

s

maa

ma

Ta

r

L

(121)

)1)(1()1(

)1)(1()(2

0JsJs

sJ

T

s

maa

a

VL

r

a

(122)

)1)(1()1(

)1()(2

0JsJs

K

T

si

maa

ma

VL

a

a

(123)

)1)(1()1(

))(1(

)(

)(2

0JsJs

JsR

sV

si

maa

aa

Ta

a

L

(124)

(13)

)1(

1

s

R

a

a

)1(

1

s

R

f

f

)(

1

Js

afL ai

fi fV

eT LT

r aV

bE


)1(

1

s

R

a

a

)(

1

Js K

ai eT LT

r aV

bE


constant flux

(14)

Chapter (2)


DC Motor



















dt

diLRiV

f

ffff (21)

fff RVi (22)

b

a

aaaa Edt

diLRiV (23)

baaa ERiV (24)

rb KE (25)

(15)











aba IEP (26)

rb KE (27)

raa IKP (28)

ae IKT (29)















(16)





















rated speed







long period

(17)







Source









fidt



1)(

JsTT Ler

(18)





(19)




(20)





quite large









(21)
















new drag














(22)



















resistance starter

(23)







block



Rotor speed in rads


Field current in A






(24)







(25)

Chapter (3)


State Power Devices

31 Rectification

















Some of them are







(26)







fed DC motor

(27)






cos22 V

V (31)




Fig 33


fed DC motor

(28)






fed DC motor


)cos1(2

V

V (32)

(29)












VV

63 (34)


(30)



)cos1(63

V

V (35)










(31)



cos63 V

V (36)






current

(32)


fed DC motor








Step-up chopper


Resonant converter


are

DC drive

Battery charger and

DC power supply




(33)









SIMULINK blocks






speed)





(34)





cycle

dca VV (37)



a

baa

R

EVI

(38)


)1(

)1(

)1(

e

eee

R

Vi

a

dc (39)



)( aa RL

T (310)


(35)







(36)

Chapter (4)



41 Introduction
























(37)























by

)1(

)1(

)(

)(

0 aa

a

Ta

a

s

R

sV

si

L

(41)


22

2

2)(

)(

nn

n

ssR

sC

(42)

(38)


)1(

1

s

R

a

a

s

KsK i

i

i

p

ai

ai



aa

i

iaa

i

pa

i

i

i

paa

Ta

a

RKRKs

KsKR

sI

sI

L

)1(

))(1(

)(

)(2

0

(43)


)12( anaa

i

p RK (44)

2

naa

i

i RK (45)


follows

For s

sR1

)( therefore

22

2

2

1)(

nn

n

sssC

(46)


)1(1)( tetC n

tn

(47)




by

(39)

)(

)(

)(

0Js

JK

sV

s

LTa

r

(48)


)(

Js

JK

s

KsK ip

a

r



)()(

))((

)(

)(2

0

JKKsJKKJs

KsKJK

s

s

ip

ip

Tr

r

L

(49)


)2( JK np (410)

KJK ni 2 (411)


before










(40)



o firing angle



o firing


then

)10(180 cV (412)























(41)


















r In






signal be






(42)




signals


reference signal












armature current













(43)







SIMULINKMATLAB












(44)















in Fig 45


(45)








menu as follows



Max Step Size auto






(46)



plot function











conditions















(47)




(48)


(49)

Chapter (5)


Excited DC Motor

51 Introduction






















(50)












ckE (51)








(51)





(52)



















diagram in Fig 54

(53)


524 Chopper Control







(54)


in Fig 55



























for firing IGBT

(55)











(56)











(57)





(4)










124 Shunt DC Motor













(5)



















(6)



















industry










(7)







b

a

aaaa Edt

diLRiV (11)

rfafb iLE (12)

faf iLK (13)

dt

diLRiV

f

ffff (14)

ae iKT (15)

Lr

r

e Tdt

dJT

(16)

Va applied voltage

Ia motor current







Motor




(8)




speed controllers













)1(

1)(

p

REVi

a

a

aaa

(17)

)(

1)(

JpTT Ler (18)

)1(

1

p

RVi

f

f

ff

(19)



shown in Fig 16

(9)

)1(

1

p

R

a

a

)1(

1

p

R

f

f

)(

1

Jp

afL ai

fi fV

eT LT

r aV

bE















dia dt

di f and

dt

d r

yields

a

a

rf

a

af

a

a

a VL

iL

Lii

dt

d 11

(110)

f

f

f

f

f VL

iidt

d 11

(111)

(10)

J

Tii

J

L

Jdt

d L

af

af

rr

(112)


L

a

f

a

f

af

af

rf

a

af

r

a

f

a

f

r

a

f

T

V

V

J

L

L

iiJ

L

iL

Li

i

J

i

i

dt

d

1 0 0

0 1

0

0 0 1

0

0 0

0 1

0

0 0 1

(113)


Motor










Fig 17 as follows

)1)(1()1(

)1(

)(

)(2

0JpJp

K

tV

t

maa

ma

Ta

r

L

(114)

Where 2

K

JRa

m

)1)(1()1(

)1)(1()(2

0JpJp

pJ

T

t

maa

a

VL

r

a

(115)

)1)(1()1(

)1()(2

0JpJp

K

T

ti

maa

ma

VL

a

a

(116)

(11)

)1)(1()1(

))(1(

)(

)(2

0JpJp

JpR

tV

ti

maa

aa

Ta

a

L

(117)

)1(

1

p

R

a

a

)(

1

Jp K

ai eT LT

r aV

bE


constant flux













)1(

1)(

s

REVi

a

a

aaa

(118)

(12)

)(

1)(

JsTT Ler

(119)

)1(

1

s

RVi

f

f

ff

(120)


shown in Fig 18











Fig 19 as follows

)1)(1()1(

)1(

)(

)(2

0JsJs

K

sV

s

maa

ma

Ta

r

L

(121)

)1)(1()1(

)1)(1()(2

0JsJs

sJ

T

s

maa

a

VL

r

a

(122)

)1)(1()1(

)1()(2

0JsJs

K

T

si

maa

ma

VL

a

a

(123)

)1)(1()1(

))(1(

)(

)(2

0JsJs

JsR

sV

si

maa

aa

Ta

a

L

(124)

(13)

)1(

1

s

R

a

a

)1(

1

s

R

f

f

)(

1

Js

afL ai

fi fV

eT LT

r aV

bE


)1(

1

s

R

a

a

)(

1

Js K

ai eT LT

r aV

bE


constant flux

(14)

Chapter (2)


DC Motor



















dt

diLRiV

f

ffff (21)

fff RVi (22)

b

a

aaaa Edt

diLRiV (23)

baaa ERiV (24)

rb KE (25)

(15)











aba IEP (26)

rb KE (27)

raa IKP (28)

ae IKT (29)















(16)





















rated speed







long period

(17)







Source









fidt



1)(

JsTT Ler

(18)





(19)




(20)





quite large









(21)
















new drag














(22)



















resistance starter

(23)







block



Rotor speed in rads


Field current in A






(24)







(25)

Chapter (3)


State Power Devices

31 Rectification

















Some of them are







(26)







fed DC motor

(27)






cos22 V

V (31)




Fig 33


fed DC motor

(28)






fed DC motor


)cos1(2

V

V (32)

(29)












VV

63 (34)


(30)



)cos1(63

V

V (35)










(31)



cos63 V

V (36)






current

(32)


fed DC motor








Step-up chopper


Resonant converter


are

DC drive

Battery charger and

DC power supply




(33)









SIMULINK blocks






speed)





(34)





cycle

dca VV (37)



a

baa

R

EVI

(38)


)1(

)1(

)1(

e

eee

R

Vi

a

dc (39)



)( aa RL

T (310)


(35)







(36)

Chapter (4)



41 Introduction
























(37)























by

)1(

)1(

)(

)(

0 aa

a

Ta

a

s

R

sV

si

L

(41)


22

2

2)(

)(

nn

n

ssR

sC

(42)

(38)


)1(

1

s

R

a

a

s

KsK i

i

i

p

ai

ai



aa

i

iaa

i

pa

i

i

i

paa

Ta

a

RKRKs

KsKR

sI

sI

L

)1(

))(1(

)(

)(2

0

(43)


)12( anaa

i

p RK (44)

2

naa

i

i RK (45)


follows

For s

sR1

)( therefore

22

2

2

1)(

nn

n

sssC

(46)


)1(1)( tetC n

tn

(47)




by

(39)

)(

)(

)(

0Js

JK

sV

s

LTa

r

(48)


)(

Js

JK

s

KsK ip

a

r



)()(

))((

)(

)(2

0

JKKsJKKJs

KsKJK

s

s

ip

ip

Tr

r

L

(49)


)2( JK np (410)

KJK ni 2 (411)


before










(40)



o firing angle



o firing


then

)10(180 cV (412)























(41)


















r In






signal be






(42)




signals


reference signal












armature current













(43)







SIMULINKMATLAB












(44)















in Fig 45


(45)








menu as follows



Max Step Size auto






(46)



plot function











conditions















(47)




(48)


(49)

Chapter (5)


Excited DC Motor

51 Introduction






















(50)












ckE (51)








(51)





(52)



















diagram in Fig 54

(53)


524 Chopper Control







(54)


in Fig 55



























for firing IGBT

(55)











(56)











(57)





(5)



















(6)



















industry










(7)







b

a

aaaa Edt

diLRiV (11)

rfafb iLE (12)

faf iLK (13)

dt

diLRiV

f

ffff (14)

ae iKT (15)

Lr

r

e Tdt

dJT

(16)

Va applied voltage

Ia motor current







Motor




(8)




speed controllers













)1(

1)(

p

REVi

a

a

aaa

(17)

)(

1)(

JpTT Ler (18)

)1(

1

p

RVi

f

f

ff

(19)



shown in Fig 16

(9)

)1(

1

p

R

a

a

)1(

1

p

R

f

f

)(

1

Jp

afL ai

fi fV

eT LT

r aV

bE















dia dt

di f and

dt

d r

yields

a

a

rf

a

af

a

a

a VL

iL

Lii

dt

d 11

(110)

f

f

f

f

f VL

iidt

d 11

(111)

(10)

J

Tii

J

L

Jdt

d L

af

af

rr

(112)


L

a

f

a

f

af

af

rf

a

af

r

a

f

a

f

r

a

f

T

V

V

J

L

L

iiJ

L

iL

Li

i

J

i

i

dt

d

1 0 0

0 1

0

0 0 1

0

0 0

0 1

0

0 0 1

(113)


Motor










Fig 17 as follows

)1)(1()1(

)1(

)(

)(2

0JpJp

K

tV

t

maa

ma

Ta

r

L

(114)

Where 2

K

JRa

m

)1)(1()1(

)1)(1()(2

0JpJp

pJ

T

t

maa

a

VL

r

a

(115)

)1)(1()1(

)1()(2

0JpJp

K

T

ti

maa

ma

VL

a

a

(116)

(11)

)1)(1()1(

))(1(

)(

)(2

0JpJp

JpR

tV

ti

maa

aa

Ta

a

L

(117)

)1(

1

p

R

a

a

)(

1

Jp K

ai eT LT

r aV

bE


constant flux













)1(

1)(

s

REVi

a

a

aaa

(118)

(12)

)(

1)(

JsTT Ler

(119)

)1(

1

s

RVi

f

f

ff

(120)


shown in Fig 18











Fig 19 as follows

)1)(1()1(

)1(

)(

)(2

0JsJs

K

sV

s

maa

ma

Ta

r

L

(121)

)1)(1()1(

)1)(1()(2

0JsJs

sJ

T

s

maa

a

VL

r

a

(122)

)1)(1()1(

)1()(2

0JsJs

K

T

si

maa

ma

VL

a

a

(123)

)1)(1()1(

))(1(

)(

)(2

0JsJs

JsR

sV

si

maa

aa

Ta

a

L

(124)

(13)

)1(

1

s

R

a

a

)1(

1

s

R

f

f

)(

1

Js

afL ai

fi fV

eT LT

r aV

bE


)1(

1

s

R

a

a

)(

1

Js K

ai eT LT

r aV

bE


constant flux

(14)

Chapter (2)


DC Motor



















dt

diLRiV

f

ffff (21)

fff RVi (22)

b

a

aaaa Edt

diLRiV (23)

baaa ERiV (24)

rb KE (25)

(15)











aba IEP (26)

rb KE (27)

raa IKP (28)

ae IKT (29)















(16)





















rated speed







long period

(17)







Source









fidt



1)(

JsTT Ler

(18)





(19)




(20)





quite large









(21)
















new drag














(22)



















resistance starter

(23)







block



Rotor speed in rads


Field current in A






(24)







(25)

Chapter (3)


State Power Devices

31 Rectification

















Some of them are







(26)







fed DC motor

(27)






cos22 V

V (31)




Fig 33


fed DC motor

(28)






fed DC motor


)cos1(2

V

V (32)

(29)












VV

63 (34)


(30)



)cos1(63

V

V (35)










(31)



cos63 V

V (36)






current

(32)


fed DC motor








Step-up chopper


Resonant converter


are

DC drive

Battery charger and

DC power supply




(33)









SIMULINK blocks






speed)





(34)





cycle

dca VV (37)



a

baa

R

EVI

(38)


)1(

)1(

)1(

e

eee

R

Vi

a

dc (39)



)( aa RL

T (310)


(35)







(36)

Chapter (4)



41 Introduction
























(37)























by

)1(

)1(

)(

)(

0 aa

a

Ta

a

s

R

sV

si

L

(41)


22

2

2)(

)(

nn

n

ssR

sC

(42)

(38)


)1(

1

s

R

a

a

s

KsK i

i

i

p

ai

ai



aa

i

iaa

i

pa

i

i

i

paa

Ta

a

RKRKs

KsKR

sI

sI

L

)1(

))(1(

)(

)(2

0

(43)


)12( anaa

i

p RK (44)

2

naa

i

i RK (45)


follows

For s

sR1

)( therefore

22

2

2

1)(

nn

n

sssC

(46)


)1(1)( tetC n

tn

(47)




by

(39)

)(

)(

)(

0Js

JK

sV

s

LTa

r

(48)


)(

Js

JK

s

KsK ip

a

r



)()(

))((

)(

)(2

0

JKKsJKKJs

KsKJK

s

s

ip

ip

Tr

r

L

(49)


)2( JK np (410)

KJK ni 2 (411)


before










(40)



o firing angle



o firing


then

)10(180 cV (412)























(41)


















r In






signal be






(42)




signals


reference signal












armature current













(43)







SIMULINKMATLAB












(44)















in Fig 45


(45)








menu as follows



Max Step Size auto






(46)



plot function











conditions















(47)




(48)


(49)

Chapter (5)


Excited DC Motor

51 Introduction






















(50)












ckE (51)








(51)





(52)



















diagram in Fig 54

(53)


524 Chopper Control







(54)


in Fig 55



























for firing IGBT

(55)











(56)











(57)





(6)



















industry










(7)







b

a

aaaa Edt

diLRiV (11)

rfafb iLE (12)

faf iLK (13)

dt

diLRiV

f

ffff (14)

ae iKT (15)

Lr

r

e Tdt

dJT

(16)

Va applied voltage

Ia motor current







Motor




(8)




speed controllers













)1(

1)(

p

REVi

a

a

aaa

(17)

)(

1)(

JpTT Ler (18)

)1(

1

p

RVi

f

f

ff

(19)



shown in Fig 16

(9)

)1(

1

p

R

a

a

)1(

1

p

R

f

f

)(

1

Jp

afL ai

fi fV

eT LT

r aV

bE















dia dt

di f and

dt

d r

yields

a

a

rf

a

af

a

a

a VL

iL

Lii

dt

d 11

(110)

f

f

f

f

f VL

iidt

d 11

(111)

(10)

J

Tii

J

L

Jdt

d L

af

af

rr

(112)


L

a

f

a

f

af

af

rf

a

af

r

a

f

a

f

r

a

f

T

V

V

J

L

L

iiJ

L

iL

Li

i

J

i

i

dt

d

1 0 0

0 1

0

0 0 1

0

0 0

0 1

0

0 0 1

(113)


Motor










Fig 17 as follows

)1)(1()1(

)1(

)(

)(2

0JpJp

K

tV

t

maa

ma

Ta

r

L

(114)

Where 2

K

JRa

m

)1)(1()1(

)1)(1()(2

0JpJp

pJ

T

t

maa

a

VL

r

a

(115)

)1)(1()1(

)1()(2

0JpJp

K

T

ti

maa

ma

VL

a

a

(116)

(11)

)1)(1()1(

))(1(

)(

)(2

0JpJp

JpR

tV

ti

maa

aa

Ta

a

L

(117)

)1(

1

p

R

a

a

)(

1

Jp K

ai eT LT

r aV

bE


constant flux













)1(

1)(

s

REVi

a

a

aaa

(118)

(12)

)(

1)(

JsTT Ler

(119)

)1(

1

s

RVi

f

f

ff

(120)


shown in Fig 18











Fig 19 as follows

)1)(1()1(

)1(

)(

)(2

0JsJs

K

sV

s

maa

ma

Ta

r

L

(121)

)1)(1()1(

)1)(1()(2

0JsJs

sJ

T

s

maa

a

VL

r

a

(122)

)1)(1()1(

)1()(2

0JsJs

K

T

si

maa

ma

VL

a

a

(123)

)1)(1()1(

))(1(

)(

)(2

0JsJs

JsR

sV

si

maa

aa

Ta

a

L

(124)

(13)

)1(

1

s

R

a

a

)1(

1

s

R

f

f

)(

1

Js

afL ai

fi fV

eT LT

r aV

bE


)1(

1

s

R

a

a

)(

1

Js K

ai eT LT

r aV

bE


constant flux

(14)

Chapter (2)


DC Motor



















dt

diLRiV

f

ffff (21)

fff RVi (22)

b

a

aaaa Edt

diLRiV (23)

baaa ERiV (24)

rb KE (25)

(15)











aba IEP (26)

rb KE (27)

raa IKP (28)

ae IKT (29)















(16)





















rated speed







long period

(17)







Source









fidt



1)(

JsTT Ler

(18)





(19)




(20)





quite large









(21)
















new drag














(22)



















resistance starter

(23)







block



Rotor speed in rads


Field current in A






(24)







(25)

Chapter (3)


State Power Devices

31 Rectification

















Some of them are







(26)







fed DC motor

(27)






cos22 V

V (31)




Fig 33


fed DC motor

(28)






fed DC motor


)cos1(2

V

V (32)

(29)












VV

63 (34)


(30)



)cos1(63

V

V (35)










(31)



cos63 V

V (36)






current

(32)


fed DC motor








Step-up chopper


Resonant converter


are

DC drive

Battery charger and

DC power supply




(33)









SIMULINK blocks






speed)





(34)





cycle

dca VV (37)



a

baa

R

EVI

(38)


)1(

)1(

)1(

e

eee

R

Vi

a

dc (39)



)( aa RL

T (310)


(35)







(36)

Chapter (4)



41 Introduction
























(37)























by

)1(

)1(

)(

)(

0 aa

a

Ta

a

s

R

sV

si

L

(41)


22

2

2)(

)(

nn

n

ssR

sC

(42)

(38)


)1(

1

s

R

a

a

s

KsK i

i

i

p

ai

ai



aa

i

iaa

i

pa

i

i

i

paa

Ta

a

RKRKs

KsKR

sI

sI

L

)1(

))(1(

)(

)(2

0

(43)


)12( anaa

i

p RK (44)

2

naa

i

i RK (45)


follows

For s

sR1

)( therefore

22

2

2

1)(

nn

n

sssC

(46)


)1(1)( tetC n

tn

(47)




by

(39)

)(

)(

)(

0Js

JK

sV

s

LTa

r

(48)


)(

Js

JK

s

KsK ip

a

r



)()(

))((

)(

)(2

0

JKKsJKKJs

KsKJK

s

s

ip

ip

Tr

r

L

(49)


)2( JK np (410)

KJK ni 2 (411)


before










(40)



o firing angle



o firing


then

)10(180 cV (412)























(41)


















r In






signal be






(42)




signals


reference signal












armature current













(43)







SIMULINKMATLAB












(44)















in Fig 45


(45)








menu as follows



Max Step Size auto






(46)



plot function











conditions















(47)




(48)


(49)

Chapter (5)


Excited DC Motor

51 Introduction






















(50)












ckE (51)








(51)





(52)



















diagram in Fig 54

(53)


524 Chopper Control







(54)


in Fig 55



























for firing IGBT

(55)











(56)











(57)





(7)







b

a

aaaa Edt

diLRiV (11)

rfafb iLE (12)

faf iLK (13)

dt

diLRiV

f

ffff (14)

ae iKT (15)

Lr

r

e Tdt

dJT

(16)

Va applied voltage

Ia motor current







Motor




(8)




speed controllers













)1(

1)(

p

REVi

a

a

aaa

(17)

)(

1)(

JpTT Ler (18)

)1(

1

p

RVi

f

f

ff

(19)



shown in Fig 16

(9)

)1(

1

p

R

a

a

)1(

1

p

R

f

f

)(

1

Jp

afL ai

fi fV

eT LT

r aV

bE















dia dt

di f and

dt

d r

yields

a

a

rf

a

af

a

a

a VL

iL

Lii

dt

d 11

(110)

f

f

f

f

f VL

iidt

d 11

(111)

(10)

J

Tii

J

L

Jdt

d L

af

af

rr

(112)


L

a

f

a

f

af

af

rf

a

af

r

a

f

a

f

r

a

f

T

V

V

J

L

L

iiJ

L

iL

Li

i

J

i

i

dt

d

1 0 0

0 1

0

0 0 1

0

0 0

0 1

0

0 0 1

(113)


Motor










Fig 17 as follows

)1)(1()1(

)1(

)(

)(2

0JpJp

K

tV

t

maa

ma

Ta

r

L

(114)

Where 2

K

JRa

m

)1)(1()1(

)1)(1()(2

0JpJp

pJ

T

t

maa

a

VL

r

a

(115)

)1)(1()1(

)1()(2

0JpJp

K

T

ti

maa

ma

VL

a

a

(116)

(11)

)1)(1()1(

))(1(

)(

)(2

0JpJp

JpR

tV

ti

maa

aa

Ta

a

L

(117)

)1(

1

p

R

a

a

)(

1

Jp K

ai eT LT

r aV

bE


constant flux













)1(

1)(

s

REVi

a

a

aaa

(118)

(12)

)(

1)(

JsTT Ler

(119)

)1(

1

s

RVi

f

f

ff

(120)


shown in Fig 18











Fig 19 as follows

)1)(1()1(

)1(

)(

)(2

0JsJs

K

sV

s

maa

ma

Ta

r

L

(121)

)1)(1()1(

)1)(1()(2

0JsJs

sJ

T

s

maa

a

VL

r

a

(122)

)1)(1()1(

)1()(2

0JsJs

K

T

si

maa

ma

VL

a

a

(123)

)1)(1()1(

))(1(

)(

)(2

0JsJs

JsR

sV

si

maa

aa

Ta

a

L

(124)

(13)

)1(

1

s

R

a

a

)1(

1

s

R

f

f

)(

1

Js

afL ai

fi fV

eT LT

r aV

bE


)1(

1

s

R

a

a

)(

1

Js K

ai eT LT

r aV

bE


constant flux

(14)

Chapter (2)


DC Motor



















dt

diLRiV

f

ffff (21)

fff RVi (22)

b

a

aaaa Edt

diLRiV (23)

baaa ERiV (24)

rb KE (25)

(15)











aba IEP (26)

rb KE (27)

raa IKP (28)

ae IKT (29)















(16)





















rated speed







long period

(17)







Source









fidt



1)(

JsTT Ler

(18)





(19)




(20)





quite large









(21)
















new drag














(22)



















resistance starter

(23)







block



Rotor speed in rads


Field current in A






(24)







(25)

Chapter (3)


State Power Devices

31 Rectification

















Some of them are







(26)







fed DC motor

(27)






cos22 V

V (31)




Fig 33


fed DC motor

(28)






fed DC motor


)cos1(2

V

V (32)

(29)












VV

63 (34)


(30)



)cos1(63

V

V (35)










(31)



cos63 V

V (36)






current

(32)


fed DC motor








Step-up chopper


Resonant converter


are

DC drive

Battery charger and

DC power supply




(33)









SIMULINK blocks






speed)





(34)





cycle

dca VV (37)



a

baa

R

EVI

(38)


)1(

)1(

)1(

e

eee

R

Vi

a

dc (39)



)( aa RL

T (310)


(35)







(36)

Chapter (4)



41 Introduction
























(37)























by

)1(

)1(

)(

)(

0 aa

a

Ta

a

s

R

sV

si

L

(41)


22

2

2)(

)(

nn

n

ssR

sC

(42)

(38)


)1(

1

s

R

a

a

s

KsK i

i

i

p

ai

ai



aa

i

iaa

i

pa

i

i

i

paa

Ta

a

RKRKs

KsKR

sI

sI

L

)1(

))(1(

)(

)(2

0

(43)


)12( anaa

i

p RK (44)

2

naa

i

i RK (45)


follows

For s

sR1

)( therefore

22

2

2

1)(

nn

n

sssC

(46)


)1(1)( tetC n

tn

(47)




by

(39)

)(

)(

)(

0Js

JK

sV

s

LTa

r

(48)


)(

Js

JK

s

KsK ip

a

r



)()(

))((

)(

)(2

0

JKKsJKKJs

KsKJK

s

s

ip

ip

Tr

r

L

(49)


)2( JK np (410)

KJK ni 2 (411)


before










(40)



o firing angle



o firing


then

)10(180 cV (412)























(41)


















r In






signal be






(42)




signals


reference signal












armature current













(43)







SIMULINKMATLAB












(44)















in Fig 45


(45)








menu as follows



Max Step Size auto






(46)



plot function











conditions















(47)




(48)


(49)

Chapter (5)


Excited DC Motor

51 Introduction






















(50)












ckE (51)








(51)





(52)



















diagram in Fig 54

(53)


524 Chopper Control







(54)


in Fig 55



























for firing IGBT

(55)











(56)











(57)





(8)




speed controllers













)1(

1)(

p

REVi

a

a

aaa

(17)

)(

1)(

JpTT Ler (18)

)1(

1

p

RVi

f

f

ff

(19)



shown in Fig 16

(9)

)1(

1

p

R

a

a

)1(

1

p

R

f

f

)(

1

Jp

afL ai

fi fV

eT LT

r aV

bE















dia dt

di f and

dt

d r

yields

a

a

rf

a

af

a

a

a VL

iL

Lii

dt

d 11

(110)

f

f

f

f

f VL

iidt

d 11

(111)

(10)

J

Tii

J

L

Jdt

d L

af

af

rr

(112)


L

a

f

a

f

af

af

rf

a

af

r

a

f

a

f

r

a

f

T

V

V

J

L

L

iiJ

L

iL

Li

i

J

i

i

dt

d

1 0 0

0 1

0

0 0 1

0

0 0

0 1

0

0 0 1

(113)


Motor










Fig 17 as follows

)1)(1()1(

)1(

)(

)(2

0JpJp

K

tV

t

maa

ma

Ta

r

L

(114)

Where 2

K

JRa

m

)1)(1()1(

)1)(1()(2

0JpJp

pJ

T

t

maa

a

VL

r

a

(115)

)1)(1()1(

)1()(2

0JpJp

K

T

ti

maa

ma

VL

a

a

(116)

(11)

)1)(1()1(

))(1(

)(

)(2

0JpJp

JpR

tV

ti

maa

aa

Ta

a

L

(117)

)1(

1

p

R

a

a

)(

1

Jp K

ai eT LT

r aV

bE


constant flux













)1(

1)(

s

REVi

a

a

aaa

(118)

(12)

)(

1)(

JsTT Ler

(119)

)1(

1

s

RVi

f

f

ff

(120)


shown in Fig 18











Fig 19 as follows

)1)(1()1(

)1(

)(

)(2

0JsJs

K

sV

s

maa

ma

Ta

r

L

(121)

)1)(1()1(

)1)(1()(2

0JsJs

sJ

T

s

maa

a

VL

r

a

(122)

)1)(1()1(

)1()(2

0JsJs

K

T

si

maa

ma

VL

a

a

(123)

)1)(1()1(

))(1(

)(

)(2

0JsJs

JsR

sV

si

maa

aa

Ta

a

L

(124)

(13)

)1(

1

s

R

a

a

)1(

1

s

R

f

f

)(

1

Js

afL ai

fi fV

eT LT

r aV

bE


)1(

1

s

R

a

a

)(

1

Js K

ai eT LT

r aV

bE


constant flux

(14)

Chapter (2)


DC Motor



















dt

diLRiV

f

ffff (21)

fff RVi (22)

b

a

aaaa Edt

diLRiV (23)

baaa ERiV (24)

rb KE (25)

(15)











aba IEP (26)

rb KE (27)

raa IKP (28)

ae IKT (29)















(16)





















rated speed







long period

(17)







Source









fidt



1)(

JsTT Ler

(18)





(19)




(20)





quite large









(21)
















new drag














(22)



















resistance starter

(23)







block



Rotor speed in rads


Field current in A






(24)







(25)

Chapter (3)


State Power Devices

31 Rectification

















Some of them are







(26)







fed DC motor

(27)






cos22 V

V (31)




Fig 33


fed DC motor

(28)






fed DC motor


)cos1(2

V

V (32)

(29)












VV

63 (34)


(30)



)cos1(63

V

V (35)










(31)



cos63 V

V (36)






current

(32)


fed DC motor








Step-up chopper


Resonant converter


are

DC drive

Battery charger and

DC power supply




(33)









SIMULINK blocks






speed)





(34)





cycle

dca VV (37)



a

baa

R

EVI

(38)


)1(

)1(

)1(

e

eee

R

Vi

a

dc (39)



)( aa RL

T (310)


(35)







(36)

Chapter (4)



41 Introduction
























(37)























by

)1(

)1(

)(

)(

0 aa

a

Ta

a

s

R

sV

si

L

(41)


22

2

2)(

)(

nn

n

ssR

sC

(42)

(38)


)1(

1

s

R

a

a

s

KsK i

i

i

p

ai

ai



aa

i

iaa

i

pa

i

i

i

paa

Ta

a

RKRKs

KsKR

sI

sI

L

)1(

))(1(

)(

)(2

0

(43)


)12( anaa

i

p RK (44)

2

naa

i

i RK (45)


follows

For s

sR1

)( therefore

22

2

2

1)(

nn

n

sssC

(46)


)1(1)( tetC n

tn

(47)




by

(39)

)(

)(

)(

0Js

JK

sV

s

LTa

r

(48)


)(

Js

JK

s

KsK ip

a

r



)()(

))((

)(

)(2

0

JKKsJKKJs

KsKJK

s

s

ip

ip

Tr

r

L

(49)


)2( JK np (410)

KJK ni 2 (411)


before










(40)



o firing angle



o firing


then

)10(180 cV (412)























(41)


















r In






signal be






(42)




signals


reference signal












armature current













(43)







SIMULINKMATLAB












(44)















in Fig 45


(45)








menu as follows



Max Step Size auto






(46)



plot function











conditions















(47)




(48)


(49)

Chapter (5)


Excited DC Motor

51 Introduction






















(50)












ckE (51)








(51)





(52)



















diagram in Fig 54

(53)


524 Chopper Control







(54)


in Fig 55



























for firing IGBT

(55)











(56)











(57)





(9)

)1(

1

p

R

a

a

)1(

1

p

R

f

f

)(

1

Jp

afL ai

fi fV

eT LT

r aV

bE















dia dt

di f and

dt

d r

yields

a

a

rf

a

af

a

a

a VL

iL

Lii

dt

d 11

(110)

f

f

f

f

f VL

iidt

d 11

(111)

(10)

J

Tii

J

L

Jdt

d L

af

af

rr

(112)


L

a

f

a

f

af

af

rf

a

af

r

a

f

a

f

r

a

f

T

V

V

J

L

L

iiJ

L

iL

Li

i

J

i

i

dt

d

1 0 0

0 1

0

0 0 1

0

0 0

0 1

0

0 0 1

(113)


Motor










Fig 17 as follows

)1)(1()1(

)1(

)(

)(2

0JpJp

K

tV

t

maa

ma

Ta

r

L

(114)

Where 2

K

JRa

m

)1)(1()1(

)1)(1()(2

0JpJp

pJ

T

t

maa

a

VL

r

a

(115)

)1)(1()1(

)1()(2

0JpJp

K

T

ti

maa

ma

VL

a

a

(116)

(11)

)1)(1()1(

))(1(

)(

)(2

0JpJp

JpR

tV

ti

maa

aa

Ta

a

L

(117)

)1(

1

p

R

a

a

)(

1

Jp K

ai eT LT

r aV

bE


constant flux













)1(

1)(

s

REVi

a

a

aaa

(118)

(12)

)(

1)(

JsTT Ler

(119)

)1(

1

s

RVi

f

f

ff

(120)


shown in Fig 18











Fig 19 as follows

)1)(1()1(

)1(

)(

)(2

0JsJs

K

sV

s

maa

ma

Ta

r

L

(121)

)1)(1()1(

)1)(1()(2

0JsJs

sJ

T

s

maa

a

VL

r

a

(122)

)1)(1()1(

)1()(2

0JsJs

K

T

si

maa

ma

VL

a

a

(123)

)1)(1()1(

))(1(

)(

)(2

0JsJs

JsR

sV

si

maa

aa

Ta

a

L

(124)

(13)

)1(

1

s

R

a

a

)1(

1

s

R

f

f

)(

1

Js

afL ai

fi fV

eT LT

r aV

bE


)1(

1

s

R

a

a

)(

1

Js K

ai eT LT

r aV

bE


constant flux

(14)

Chapter (2)


DC Motor



















dt

diLRiV

f

ffff (21)

fff RVi (22)

b

a

aaaa Edt

diLRiV (23)

baaa ERiV (24)

rb KE (25)

(15)











aba IEP (26)

rb KE (27)

raa IKP (28)

ae IKT (29)















(16)





















rated speed







long period

(17)







Source









fidt



1)(

JsTT Ler

(18)





(19)




(20)





quite large









(21)
















new drag














(22)



















resistance starter

(23)







block



Rotor speed in rads


Field current in A






(24)







(25)

Chapter (3)


State Power Devices

31 Rectification

















Some of them are







(26)







fed DC motor

(27)






cos22 V

V (31)




Fig 33


fed DC motor

(28)






fed DC motor


)cos1(2

V

V (32)

(29)












VV

63 (34)


(30)



)cos1(63

V

V (35)










(31)



cos63 V

V (36)






current

(32)


fed DC motor








Step-up chopper


Resonant converter


are

DC drive

Battery charger and

DC power supply




(33)









SIMULINK blocks






speed)





(34)





cycle

dca VV (37)



a

baa

R

EVI

(38)


)1(

)1(

)1(

e

eee

R

Vi

a

dc (39)



)( aa RL

T (310)


(35)







(36)

Chapter (4)



41 Introduction
























(37)























by

)1(

)1(

)(

)(

0 aa

a

Ta

a

s

R

sV

si

L

(41)


22

2

2)(

)(

nn

n

ssR

sC

(42)

(38)


)1(

1

s

R

a

a

s

KsK i

i

i

p

ai

ai



aa

i

iaa

i

pa

i

i

i

paa

Ta

a

RKRKs

KsKR

sI

sI

L

)1(

))(1(

)(

)(2

0

(43)


)12( anaa

i

p RK (44)

2

naa

i

i RK (45)


follows

For s

sR1

)( therefore

22

2

2

1)(

nn

n

sssC

(46)


)1(1)( tetC n

tn

(47)




by

(39)

)(

)(

)(

0Js

JK

sV

s

LTa

r

(48)


)(

Js

JK

s

KsK ip

a

r



)()(

))((

)(

)(2

0

JKKsJKKJs

KsKJK

s

s

ip

ip

Tr

r

L

(49)


)2( JK np (410)

KJK ni 2 (411)


before










(40)



o firing angle



o firing


then

)10(180 cV (412)























(41)


















r In






signal be






(42)




signals


reference signal












armature current













(43)







SIMULINKMATLAB












(44)















in Fig 45


(45)








menu as follows



Max Step Size auto






(46)



plot function











conditions















(47)




(48)


(49)

Chapter (5)


Excited DC Motor

51 Introduction






















(50)












ckE (51)








(51)





(52)



















diagram in Fig 54

(53)


524 Chopper Control







(54)


in Fig 55



























for firing IGBT

(55)











(56)











(57)





(10)

J

Tii

J

L

Jdt

d L

af

af

rr

(112)


L

a

f

a

f

af

af

rf

a

af

r

a

f

a

f

r

a

f

T

V

V

J

L

L

iiJ

L

iL

Li

i

J

i

i

dt

d

1 0 0

0 1

0

0 0 1

0

0 0

0 1

0

0 0 1

(113)


Motor










Fig 17 as follows

)1)(1()1(

)1(

)(

)(2

0JpJp

K

tV

t

maa

ma

Ta

r

L

(114)

Where 2

K

JRa

m

)1)(1()1(

)1)(1()(2

0JpJp

pJ

T

t

maa

a

VL

r

a

(115)

)1)(1()1(

)1()(2

0JpJp

K

T

ti

maa

ma

VL

a

a

(116)

(11)

)1)(1()1(

))(1(

)(

)(2

0JpJp

JpR

tV

ti

maa

aa

Ta

a

L

(117)

)1(

1

p

R

a

a

)(

1

Jp K

ai eT LT

r aV

bE


constant flux













)1(

1)(

s

REVi

a

a

aaa

(118)

(12)

)(

1)(

JsTT Ler

(119)

)1(

1

s

RVi

f

f

ff

(120)


shown in Fig 18











Fig 19 as follows

)1)(1()1(

)1(

)(

)(2

0JsJs

K

sV

s

maa

ma

Ta

r

L

(121)

)1)(1()1(

)1)(1()(2

0JsJs

sJ

T

s

maa

a

VL

r

a

(122)

)1)(1()1(

)1()(2

0JsJs

K

T

si

maa

ma

VL

a

a

(123)

)1)(1()1(

))(1(

)(

)(2

0JsJs

JsR

sV

si

maa

aa

Ta

a

L

(124)

(13)

)1(

1

s

R

a

a

)1(

1

s

R

f

f

)(

1

Js

afL ai

fi fV

eT LT

r aV

bE


)1(

1

s

R

a

a

)(

1

Js K

ai eT LT

r aV

bE


constant flux

(14)

Chapter (2)


DC Motor



















dt

diLRiV

f

ffff (21)

fff RVi (22)

b

a

aaaa Edt

diLRiV (23)

baaa ERiV (24)

rb KE (25)

(15)











aba IEP (26)

rb KE (27)

raa IKP (28)

ae IKT (29)















(16)





















rated speed







long period

(17)







Source









fidt



1)(

JsTT Ler

(18)





(19)




(20)





quite large









(21)
















new drag














(22)



















resistance starter

(23)







block



Rotor speed in rads


Field current in A






(24)







(25)

Chapter (3)


State Power Devices

31 Rectification

















Some of them are







(26)







fed DC motor

(27)






cos22 V

V (31)




Fig 33


fed DC motor

(28)






fed DC motor


)cos1(2

V

V (32)

(29)












VV

63 (34)


(30)



)cos1(63

V

V (35)










(31)



cos63 V

V (36)






current

(32)


fed DC motor








Step-up chopper


Resonant converter


are

DC drive

Battery charger and

DC power supply




(33)









SIMULINK blocks






speed)





(34)





cycle

dca VV (37)



a

baa

R

EVI

(38)


)1(

)1(

)1(

e

eee

R

Vi

a

dc (39)



)( aa RL

T (310)


(35)







(36)

Chapter (4)



41 Introduction
























(37)























by

)1(

)1(

)(

)(

0 aa

a

Ta

a

s

R

sV

si

L

(41)


22

2

2)(

)(

nn

n

ssR

sC

(42)

(38)


)1(

1

s

R

a

a

s

KsK i

i

i

p

ai

ai



aa

i

iaa

i

pa

i

i

i

paa

Ta

a

RKRKs

KsKR

sI

sI

L

)1(

))(1(

)(

)(2

0

(43)


)12( anaa

i

p RK (44)

2

naa

i

i RK (45)


follows

For s

sR1

)( therefore

22

2

2

1)(

nn

n

sssC

(46)


)1(1)( tetC n

tn

(47)




by

(39)

)(

)(

)(

0Js

JK

sV

s

LTa

r

(48)


)(

Js

JK

s

KsK ip

a

r



)()(

))((

)(

)(2

0

JKKsJKKJs

KsKJK

s

s

ip

ip

Tr

r

L

(49)


)2( JK np (410)

KJK ni 2 (411)


before










(40)



o firing angle



o firing


then

)10(180 cV (412)























(41)


















r In






signal be






(42)




signals


reference signal












armature current













(43)







SIMULINKMATLAB












(44)















in Fig 45


(45)








menu as follows



Max Step Size auto






(46)



plot function











conditions















(47)




(48)


(49)

Chapter (5)


Excited DC Motor

51 Introduction






















(50)












ckE (51)








(51)





(52)



















diagram in Fig 54

(53)


524 Chopper Control







(54)


in Fig 55



























for firing IGBT

(55)











(56)











(57)





(11)

)1)(1()1(

))(1(

)(

)(2

0JpJp

JpR

tV

ti

maa

aa

Ta

a

L

(117)

)1(

1

p

R

a

a

)(

1

Jp K

ai eT LT

r aV

bE


constant flux













)1(

1)(

s

REVi

a

a

aaa

(118)

(12)

)(

1)(

JsTT Ler

(119)

)1(

1

s

RVi

f

f

ff

(120)


shown in Fig 18











Fig 19 as follows

)1)(1()1(

)1(

)(

)(2

0JsJs

K

sV

s

maa

ma

Ta

r

L

(121)

)1)(1()1(

)1)(1()(2

0JsJs

sJ

T

s

maa

a

VL

r

a

(122)

)1)(1()1(

)1()(2

0JsJs

K

T

si

maa

ma

VL

a

a

(123)

)1)(1()1(

))(1(

)(

)(2

0JsJs

JsR

sV

si

maa

aa

Ta

a

L

(124)

(13)

)1(

1

s

R

a

a

)1(

1

s

R

f

f

)(

1

Js

afL ai

fi fV

eT LT

r aV

bE


)1(

1

s

R

a

a

)(

1

Js K

ai eT LT

r aV

bE


constant flux

(14)

Chapter (2)


DC Motor



















dt

diLRiV

f

ffff (21)

fff RVi (22)

b

a

aaaa Edt

diLRiV (23)

baaa ERiV (24)

rb KE (25)

(15)











aba IEP (26)

rb KE (27)

raa IKP (28)

ae IKT (29)















(16)





















rated speed







long period

(17)







Source









fidt



1)(

JsTT Ler

(18)





(19)




(20)





quite large









(21)
















new drag














(22)



















resistance starter

(23)







block



Rotor speed in rads


Field current in A






(24)







(25)

Chapter (3)


State Power Devices

31 Rectification

















Some of them are







(26)







fed DC motor

(27)






cos22 V

V (31)




Fig 33


fed DC motor

(28)






fed DC motor


)cos1(2

V

V (32)

(29)












VV

63 (34)


(30)



)cos1(63

V

V (35)










(31)



cos63 V

V (36)






current

(32)


fed DC motor








Step-up chopper


Resonant converter


are

DC drive

Battery charger and

DC power supply




(33)









SIMULINK blocks






speed)





(34)





cycle

dca VV (37)



a

baa

R

EVI

(38)


)1(

)1(

)1(

e

eee

R

Vi

a

dc (39)



)( aa RL

T (310)


(35)







(36)

Chapter (4)



41 Introduction
























(37)























by

)1(

)1(

)(

)(

0 aa

a

Ta

a

s

R

sV

si

L

(41)


22

2

2)(

)(

nn

n

ssR

sC

(42)

(38)


)1(

1

s

R

a

a

s

KsK i

i

i

p

ai

ai



aa

i

iaa

i

pa

i

i

i

paa

Ta

a

RKRKs

KsKR

sI

sI

L

)1(

))(1(

)(

)(2

0

(43)


)12( anaa

i

p RK (44)

2

naa

i

i RK (45)


follows

For s

sR1

)( therefore

22

2

2

1)(

nn

n

sssC

(46)


)1(1)( tetC n

tn

(47)




by

(39)

)(

)(

)(

0Js

JK

sV

s

LTa

r

(48)


)(

Js

JK

s

KsK ip

a

r



)()(

))((

)(

)(2

0

JKKsJKKJs

KsKJK

s

s

ip

ip

Tr

r

L

(49)


)2( JK np (410)

KJK ni 2 (411)


before










(40)



o firing angle



o firing


then

)10(180 cV (412)























(41)


















r In






signal be






(42)




signals


reference signal












armature current













(43)







SIMULINKMATLAB












(44)















in Fig 45


(45)








menu as follows



Max Step Size auto






(46)



plot function











conditions















(47)




(48)


(49)

Chapter (5)


Excited DC Motor

51 Introduction






















(50)












ckE (51)








(51)





(52)



















diagram in Fig 54

(53)


524 Chopper Control







(54)


in Fig 55



























for firing IGBT

(55)











(56)











(57)





(12)

)(

1)(

JsTT Ler

(119)

)1(

1

s

RVi

f

f

ff

(120)


shown in Fig 18











Fig 19 as follows

)1)(1()1(

)1(

)(

)(2

0JsJs

K

sV

s

maa

ma

Ta

r

L

(121)

)1)(1()1(

)1)(1()(2

0JsJs

sJ

T

s

maa

a

VL

r

a

(122)

)1)(1()1(

)1()(2

0JsJs

K

T

si

maa

ma

VL

a

a

(123)

)1)(1()1(

))(1(

)(

)(2

0JsJs

JsR

sV

si

maa

aa

Ta

a

L

(124)

(13)

)1(

1

s

R

a

a

)1(

1

s

R

f

f

)(

1

Js

afL ai

fi fV

eT LT

r aV

bE


)1(

1

s

R

a

a

)(

1

Js K

ai eT LT

r aV

bE


constant flux

(14)

Chapter (2)


DC Motor



















dt

diLRiV

f

ffff (21)

fff RVi (22)

b

a

aaaa Edt

diLRiV (23)

baaa ERiV (24)

rb KE (25)

(15)











aba IEP (26)

rb KE (27)

raa IKP (28)

ae IKT (29)















(16)





















rated speed







long period

(17)







Source









fidt



1)(

JsTT Ler

(18)





(19)




(20)





quite large









(21)
















new drag














(22)



















resistance starter

(23)







block



Rotor speed in rads


Field current in A






(24)







(25)

Chapter (3)


State Power Devices

31 Rectification

















Some of them are







(26)







fed DC motor

(27)






cos22 V

V (31)




Fig 33


fed DC motor

(28)






fed DC motor


)cos1(2

V

V (32)

(29)












VV

63 (34)


(30)



)cos1(63

V

V (35)










(31)



cos63 V

V (36)






current

(32)


fed DC motor








Step-up chopper


Resonant converter


are

DC drive

Battery charger and

DC power supply




(33)









SIMULINK blocks






speed)





(34)





cycle

dca VV (37)



a

baa

R

EVI

(38)


)1(

)1(

)1(

e

eee

R

Vi

a

dc (39)



)( aa RL

T (310)


(35)







(36)

Chapter (4)



41 Introduction
























(37)























by

)1(

)1(

)(

)(

0 aa

a

Ta

a

s

R

sV

si

L

(41)


22

2

2)(

)(

nn

n

ssR

sC

(42)

(38)


)1(

1

s

R

a

a

s

KsK i

i

i

p

ai

ai



aa

i

iaa

i

pa

i

i

i

paa

Ta

a

RKRKs

KsKR

sI

sI

L

)1(

))(1(

)(

)(2

0

(43)


)12( anaa

i

p RK (44)

2

naa

i

i RK (45)


follows

For s

sR1

)( therefore

22

2

2

1)(

nn

n

sssC

(46)


)1(1)( tetC n

tn

(47)




by

(39)

)(

)(

)(

0Js

JK

sV

s

LTa

r

(48)


)(

Js

JK

s

KsK ip

a

r



)()(

))((

)(

)(2

0

JKKsJKKJs

KsKJK

s

s

ip

ip

Tr

r

L

(49)


)2( JK np (410)

KJK ni 2 (411)


before










(40)



o firing angle



o firing


then

)10(180 cV (412)























(41)


















r In






signal be






(42)




signals


reference signal












armature current













(43)







SIMULINKMATLAB












(44)















in Fig 45


(45)








menu as follows



Max Step Size auto






(46)



plot function











conditions















(47)




(48)


(49)

Chapter (5)


Excited DC Motor

51 Introduction






















(50)












ckE (51)








(51)





(52)



















diagram in Fig 54

(53)


524 Chopper Control







(54)


in Fig 55



























for firing IGBT

(55)











(56)











(57)





(13)

)1(

1

s

R

a

a

)1(

1

s

R

f

f

)(

1

Js

afL ai

fi fV

eT LT

r aV

bE


)1(

1

s

R

a

a

)(

1

Js K

ai eT LT

r aV

bE


constant flux

(14)

Chapter (2)


DC Motor



















dt

diLRiV

f

ffff (21)

fff RVi (22)

b

a

aaaa Edt

diLRiV (23)

baaa ERiV (24)

rb KE (25)

(15)











aba IEP (26)

rb KE (27)

raa IKP (28)

ae IKT (29)















(16)





















rated speed







long period

(17)







Source









fidt



1)(

JsTT Ler

(18)





(19)




(20)





quite large









(21)
















new drag














(22)



















resistance starter

(23)







block



Rotor speed in rads


Field current in A






(24)







(25)

Chapter (3)


State Power Devices

31 Rectification

















Some of them are







(26)







fed DC motor

(27)






cos22 V

V (31)




Fig 33


fed DC motor

(28)






fed DC motor


)cos1(2

V

V (32)

(29)












VV

63 (34)


(30)



)cos1(63

V

V (35)










(31)



cos63 V

V (36)






current

(32)


fed DC motor








Step-up chopper


Resonant converter


are

DC drive

Battery charger and

DC power supply




(33)









SIMULINK blocks






speed)





(34)





cycle

dca VV (37)



a

baa

R

EVI

(38)


)1(

)1(

)1(

e

eee

R

Vi

a

dc (39)



)( aa RL

T (310)


(35)







(36)

Chapter (4)



41 Introduction
























(37)























by

)1(

)1(

)(

)(

0 aa

a

Ta

a

s

R

sV

si

L

(41)


22

2

2)(

)(

nn

n

ssR

sC

(42)

(38)


)1(

1

s

R

a

a

s

KsK i

i

i

p

ai

ai



aa

i

iaa

i

pa

i

i

i

paa

Ta

a

RKRKs

KsKR

sI

sI

L

)1(

))(1(

)(

)(2

0

(43)


)12( anaa

i

p RK (44)

2

naa

i

i RK (45)


follows

For s

sR1

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22

2

2

1)(

nn

n

sssC

(46)


)1(1)( tetC n

tn

(47)




by

(39)

)(

)(

)(

0Js

JK

sV

s

LTa

r

(48)


)(

Js

JK

s

KsK ip

a

r



)()(

))((

)(

)(2

0

JKKsJKKJs

KsKJK

s

s

ip

ip

Tr

r

L

(49)


)2( JK np (410)

KJK ni 2 (411)


before










(40)



o firing angle



o firing


then

)10(180 cV (412)























(41)


















r In






signal be






(42)




signals


reference signal












armature current













(43)







SIMULINKMATLAB












(44)















in Fig 45


(45)








menu as follows



Max Step Size auto






(46)



plot function











conditions















(47)




(48)


(49)

Chapter (5)


Excited DC Motor

51 Introduction






















(50)












ckE (51)








(51)





(52)



















diagram in Fig 54

(53)


524 Chopper Control







(54)


in Fig 55



























for firing IGBT

(55)











(56)











(57)





(14)

Chapter (2)


DC Motor



















dt

diLRiV

f

ffff (21)

fff RVi (22)

b

a

aaaa Edt

diLRiV (23)

baaa ERiV (24)

rb KE (25)

(15)











aba IEP (26)

rb KE (27)

raa IKP (28)

ae IKT (29)















(16)





















rated speed







long period

(17)







Source









fidt



1)(

JsTT Ler

(18)





(19)




(20)





quite large









(21)
















new drag














(22)



















resistance starter

(23)







block



Rotor speed in rads


Field current in A






(24)







(25)

Chapter (3)


State Power Devices

31 Rectification

















Some of them are







(26)







fed DC motor

(27)






cos22 V

V (31)




Fig 33


fed DC motor

(28)






fed DC motor


)cos1(2

V

V (32)

(29)












VV

63 (34)


(30)



)cos1(63

V

V (35)










(31)



cos63 V

V (36)






current

(32)


fed DC motor








Step-up chopper


Resonant converter


are

DC drive

Battery charger and

DC power supply




(33)









SIMULINK blocks






speed)





(34)





cycle

dca VV (37)



a

baa

R

EVI

(38)


)1(

)1(

)1(

e

eee

R

Vi

a

dc (39)



)( aa RL

T (310)


(35)







(36)

Chapter (4)



41 Introduction
























(37)























by

)1(

)1(

)(

)(

0 aa

a

Ta

a

s

R

sV

si

L

(41)


22

2

2)(

)(

nn

n

ssR

sC

(42)

(38)


)1(

1

s

R

a

a

s

KsK i

i

i

p

ai

ai



aa

i

iaa

i

pa

i

i

i

paa

Ta

a

RKRKs

KsKR

sI

sI

L

)1(

))(1(

)(

)(2

0

(43)


)12( anaa

i

p RK (44)

2

naa

i

i RK (45)


follows

For s

sR1

)( therefore

22

2

2

1)(

nn

n

sssC

(46)


)1(1)( tetC n

tn

(47)




by

(39)

)(

)(

)(

0Js

JK

sV

s

LTa

r

(48)


)(

Js

JK

s

KsK ip

a

r



)()(

))((

)(

)(2

0

JKKsJKKJs

KsKJK

s

s

ip

ip

Tr

r

L

(49)


)2( JK np (410)

KJK ni 2 (411)


before










(40)



o firing angle



o firing


then

)10(180 cV (412)























(41)


















r In






signal be






(42)




signals


reference signal












armature current













(43)







SIMULINKMATLAB












(44)















in Fig 45


(45)








menu as follows



Max Step Size auto






(46)



plot function











conditions















(47)




(48)


(49)

Chapter (5)


Excited DC Motor

51 Introduction






















(50)












ckE (51)








(51)





(52)



















diagram in Fig 54

(53)


524 Chopper Control







(54)


in Fig 55



























for firing IGBT

(55)











(56)











(57)





(15)











aba IEP (26)

rb KE (27)

raa IKP (28)

ae IKT (29)















(16)





















rated speed







long period

(17)







Source









fidt



1)(

JsTT Ler

(18)





(19)




(20)





quite large









(21)
















new drag














(22)



















resistance starter

(23)







block



Rotor speed in rads


Field current in A






(24)







(25)

Chapter (3)


State Power Devices

31 Rectification

















Some of them are







(26)







fed DC motor

(27)






cos22 V

V (31)




Fig 33


fed DC motor

(28)






fed DC motor


)cos1(2

V

V (32)

(29)












VV

63 (34)


(30)



)cos1(63

V

V (35)










(31)



cos63 V

V (36)






current

(32)


fed DC motor








Step-up chopper


Resonant converter


are

DC drive

Battery charger and

DC power supply




(33)









SIMULINK blocks






speed)





(34)





cycle

dca VV (37)



a

baa

R

EVI

(38)


)1(

)1(

)1(

e

eee

R

Vi

a

dc (39)



)( aa RL

T (310)


(35)







(36)

Chapter (4)



41 Introduction
























(37)























by

)1(

)1(

)(

)(

0 aa

a

Ta

a

s

R

sV

si

L

(41)


22

2

2)(

)(

nn

n

ssR

sC

(42)

(38)


)1(

1

s

R

a

a

s

KsK i

i

i

p

ai

ai



aa

i

iaa

i

pa

i

i

i

paa

Ta

a

RKRKs

KsKR

sI

sI

L

)1(

))(1(

)(

)(2

0

(43)


)12( anaa

i

p RK (44)

2

naa

i

i RK (45)


follows

For s

sR1

)( therefore

22

2

2

1)(

nn

n

sssC

(46)


)1(1)( tetC n

tn

(47)




by

(39)

)(

)(

)(

0Js

JK

sV

s

LTa

r

(48)


)(

Js

JK

s

KsK ip

a

r



)()(

))((

)(

)(2

0

JKKsJKKJs

KsKJK

s

s

ip

ip

Tr

r

L

(49)


)2( JK np (410)

KJK ni 2 (411)


before










(40)



o firing angle



o firing


then

)10(180 cV (412)























(41)


















r In






signal be






(42)




signals


reference signal












armature current













(43)







SIMULINKMATLAB












(44)















in Fig 45


(45)








menu as follows



Max Step Size auto






(46)



plot function











conditions















(47)




(48)


(49)

Chapter (5)


Excited DC Motor

51 Introduction






















(50)












ckE (51)








(51)





(52)



















diagram in Fig 54

(53)


524 Chopper Control







(54)


in Fig 55



























for firing IGBT

(55)











(56)











(57)





(16)





















rated speed







long period

(17)







Source









fidt



1)(

JsTT Ler

(18)





(19)




(20)





quite large









(21)
















new drag














(22)



















resistance starter

(23)







block



Rotor speed in rads


Field current in A






(24)







(25)

Chapter (3)


State Power Devices

31 Rectification

















Some of them are







(26)







fed DC motor

(27)






cos22 V

V (31)




Fig 33


fed DC motor

(28)






fed DC motor


)cos1(2

V

V (32)

(29)












VV

63 (34)


(30)



)cos1(63

V

V (35)










(31)



cos63 V

V (36)






current

(32)


fed DC motor








Step-up chopper


Resonant converter


are

DC drive

Battery charger and

DC power supply




(33)









SIMULINK blocks






speed)





(34)





cycle

dca VV (37)



a

baa

R

EVI

(38)


)1(

)1(

)1(

e

eee

R

Vi

a

dc (39)



)( aa RL

T (310)


(35)







(36)

Chapter (4)



41 Introduction
























(37)























by

)1(

)1(

)(

)(

0 aa

a

Ta

a

s

R

sV

si

L

(41)


22

2

2)(

)(

nn

n

ssR

sC

(42)

(38)


)1(

1

s

R

a

a

s

KsK i

i

i

p

ai

ai



aa

i

iaa

i

pa

i

i

i

paa

Ta

a

RKRKs

KsKR

sI

sI

L

)1(

))(1(

)(

)(2

0

(43)


)12( anaa

i

p RK (44)

2

naa

i

i RK (45)


follows

For s

sR1

)( therefore

22

2

2

1)(

nn

n

sssC

(46)


)1(1)( tetC n

tn

(47)




by

(39)

)(

)(

)(

0Js

JK

sV

s

LTa

r

(48)


)(

Js

JK

s

KsK ip

a

r



)()(

))((

)(

)(2

0

JKKsJKKJs

KsKJK

s

s

ip

ip

Tr

r

L

(49)


)2( JK np (410)

KJK ni 2 (411)


before










(40)



o firing angle



o firing


then

)10(180 cV (412)























(41)


















r In






signal be






(42)




signals


reference signal












armature current













(43)







SIMULINKMATLAB












(44)















in Fig 45


(45)








menu as follows



Max Step Size auto






(46)



plot function











conditions















(47)




(48)


(49)

Chapter (5)


Excited DC Motor

51 Introduction






















(50)












ckE (51)








(51)





(52)



















diagram in Fig 54

(53)


524 Chopper Control







(54)


in Fig 55



























for firing IGBT

(55)











(56)











(57)





(17)







Source









fidt



1)(

JsTT Ler

(18)





(19)




(20)





quite large









(21)
















new drag














(22)



















resistance starter

(23)







block



Rotor speed in rads


Field current in A






(24)







(25)

Chapter (3)


State Power Devices

31 Rectification

















Some of them are







(26)







fed DC motor

(27)






cos22 V

V (31)




Fig 33


fed DC motor

(28)






fed DC motor


)cos1(2

V

V (32)

(29)












VV

63 (34)


(30)



)cos1(63

V

V (35)










(31)



cos63 V

V (36)






current

(32)


fed DC motor








Step-up chopper


Resonant converter


are

DC drive

Battery charger and

DC power supply




(33)









SIMULINK blocks






speed)





(34)





cycle

dca VV (37)



a

baa

R

EVI

(38)


)1(

)1(

)1(

e

eee

R

Vi

a

dc (39)



)( aa RL

T (310)


(35)







(36)

Chapter (4)



41 Introduction
























(37)























by

)1(

)1(

)(

)(

0 aa

a

Ta

a

s

R

sV

si

L

(41)


22

2

2)(

)(

nn

n

ssR

sC

(42)

(38)


)1(

1

s

R

a

a

s

KsK i

i

i

p

ai

ai



aa

i

iaa

i

pa

i

i

i

paa

Ta

a

RKRKs

KsKR

sI

sI

L

)1(

))(1(

)(

)(2

0

(43)


)12( anaa

i

p RK (44)

2

naa

i

i RK (45)


follows

For s

sR1

)( therefore

22

2

2

1)(

nn

n

sssC

(46)


)1(1)( tetC n

tn

(47)




by

(39)

)(

)(

)(

0Js

JK

sV

s

LTa

r

(48)


)(

Js

JK

s

KsK ip

a

r



)()(

))((

)(

)(2

0

JKKsJKKJs

KsKJK

s

s

ip

ip

Tr

r

L

(49)


)2( JK np (410)

KJK ni 2 (411)


before










(40)



o firing angle



o firing


then

)10(180 cV (412)























(41)


















r In






signal be






(42)




signals


reference signal












armature current













(43)







SIMULINKMATLAB












(44)















in Fig 45


(45)








menu as follows



Max Step Size auto






(46)



plot function











conditions















(47)




(48)


(49)

Chapter (5)


Excited DC Motor

51 Introduction






















(50)












ckE (51)








(51)





(52)



















diagram in Fig 54

(53)


524 Chopper Control







(54)


in Fig 55



























for firing IGBT

(55)











(56)











(57)





(18)





(19)




(20)





quite large









(21)
















new drag














(22)



















resistance starter

(23)







block



Rotor speed in rads


Field current in A






(24)







(25)

Chapter (3)


State Power Devices

31 Rectification

















Some of them are







(26)







fed DC motor

(27)






cos22 V

V (31)




Fig 33


fed DC motor

(28)






fed DC motor


)cos1(2

V

V (32)

(29)












VV

63 (34)


(30)



)cos1(63

V

V (35)










(31)



cos63 V

V (36)






current

(32)


fed DC motor








Step-up chopper


Resonant converter


are

DC drive

Battery charger and

DC power supply




(33)









SIMULINK blocks






speed)





(34)





cycle

dca VV (37)



a

baa

R

EVI

(38)


)1(

)1(

)1(

e

eee

R

Vi

a

dc (39)



)( aa RL

T (310)


(35)







(36)

Chapter (4)



41 Introduction
























(37)























by

)1(

)1(

)(

)(

0 aa

a

Ta

a

s

R

sV

si

L

(41)


22

2

2)(

)(

nn

n

ssR

sC

(42)

(38)


)1(

1

s

R

a

a

s

KsK i

i

i

p

ai

ai



aa

i

iaa

i

pa

i

i

i

paa

Ta

a

RKRKs

KsKR

sI

sI

L

)1(

))(1(

)(

)(2

0

(43)


)12( anaa

i

p RK (44)

2

naa

i

i RK (45)


follows

For s

sR1

)( therefore

22

2

2

1)(

nn

n

sssC

(46)


)1(1)( tetC n

tn

(47)




by

(39)

)(

)(

)(

0Js

JK

sV

s

LTa

r

(48)


)(

Js

JK

s

KsK ip

a

r



)()(

))((

)(

)(2

0

JKKsJKKJs

KsKJK

s

s

ip

ip

Tr

r

L

(49)


)2( JK np (410)

KJK ni 2 (411)


before










(40)



o firing angle



o firing


then

)10(180 cV (412)























(41)


















r In






signal be






(42)




signals


reference signal












armature current













(43)







SIMULINKMATLAB












(44)















in Fig 45


(45)








menu as follows



Max Step Size auto






(46)



plot function











conditions















(47)




(48)


(49)

Chapter (5)


Excited DC Motor

51 Introduction






















(50)












ckE (51)








(51)





(52)



















diagram in Fig 54

(53)


524 Chopper Control







(54)


in Fig 55



























for firing IGBT

(55)











(56)











(57)





(19)




(20)





quite large









(21)
















new drag














(22)



















resistance starter

(23)







block



Rotor speed in rads


Field current in A






(24)







(25)

Chapter (3)


State Power Devices

31 Rectification

















Some of them are







(26)







fed DC motor

(27)






cos22 V

V (31)




Fig 33


fed DC motor

(28)






fed DC motor


)cos1(2

V

V (32)

(29)












VV

63 (34)


(30)



)cos1(63

V

V (35)










(31)



cos63 V

V (36)






current

(32)


fed DC motor








Step-up chopper


Resonant converter


are

DC drive

Battery charger and

DC power supply




(33)









SIMULINK blocks






speed)





(34)





cycle

dca VV (37)



a

baa

R

EVI

(38)


)1(

)1(

)1(

e

eee

R

Vi

a

dc (39)



)( aa RL

T (310)


(35)







(36)

Chapter (4)



41 Introduction
























(37)























by

)1(

)1(

)(

)(

0 aa

a

Ta

a

s

R

sV

si

L

(41)


22

2

2)(

)(

nn

n

ssR

sC

(42)

(38)


)1(

1

s

R

a

a

s

KsK i

i

i

p

ai

ai



aa

i

iaa

i

pa

i

i

i

paa

Ta

a

RKRKs

KsKR

sI

sI

L

)1(

))(1(

)(

)(2

0

(43)


)12( anaa

i

p RK (44)

2

naa

i

i RK (45)


follows

For s

sR1

)( therefore

22

2

2

1)(

nn

n

sssC

(46)


)1(1)( tetC n

tn

(47)




by

(39)

)(

)(

)(

0Js

JK

sV

s

LTa

r

(48)


)(

Js

JK

s

KsK ip

a

r



)()(

))((

)(

)(2

0

JKKsJKKJs

KsKJK

s

s

ip

ip

Tr

r

L

(49)


)2( JK np (410)

KJK ni 2 (411)


before










(40)



o firing angle



o firing


then

)10(180 cV (412)























(41)


















r In






signal be






(42)




signals


reference signal












armature current













(43)







SIMULINKMATLAB












(44)















in Fig 45


(45)








menu as follows



Max Step Size auto






(46)



plot function











conditions















(47)




(48)


(49)

Chapter (5)


Excited DC Motor

51 Introduction






















(50)












ckE (51)








(51)





(52)



















diagram in Fig 54

(53)


524 Chopper Control







(54)


in Fig 55



























for firing IGBT

(55)











(56)











(57)





(20)





quite large









(21)
















new drag














(22)



















resistance starter

(23)







block



Rotor speed in rads


Field current in A






(24)







(25)

Chapter (3)


State Power Devices

31 Rectification

















Some of them are







(26)







fed DC motor

(27)






cos22 V

V (31)




Fig 33


fed DC motor

(28)






fed DC motor


)cos1(2

V

V (32)

(29)












VV

63 (34)


(30)



)cos1(63

V

V (35)










(31)



cos63 V

V (36)






current

(32)


fed DC motor








Step-up chopper


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are

DC drive

Battery charger and

DC power supply




(33)









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(34)





cycle

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41 Introduction
























(37)























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Ta

a

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(43)







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(44)















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(45)








menu as follows



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(46)



plot function











conditions















(47)




(48)


(49)

Chapter (5)


Excited DC Motor

51 Introduction






















(50)












ckE (51)








(51)





(52)



















diagram in Fig 54

(53)


524 Chopper Control







(54)


in Fig 55



























for firing IGBT

(55)











(56)











(57)





(21)
















new drag














(22)



















resistance starter

(23)







block



Rotor speed in rads


Field current in A






(24)







(25)

Chapter (3)


State Power Devices

31 Rectification

















Some of them are







(26)







fed DC motor

(27)






cos22 V

V (31)




Fig 33


fed DC motor

(28)






fed DC motor


)cos1(2

V

V (32)

(29)












VV

63 (34)


(30)



)cos1(63

V

V (35)










(31)



cos63 V

V (36)






current

(32)


fed DC motor








Step-up chopper


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DC drive

Battery charger and

DC power supply




(33)









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speed)





(34)





cycle

dca VV (37)



a

baa

R

EVI

(38)


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)( aa RL

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(36)

Chapter (4)



41 Introduction
























(37)























by

)1(

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)(

)(

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a

Ta

a

s

R

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L

(41)


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2

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)(

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1

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pa

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paa

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i RK (45)


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22

2

2

1)(

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(41)


















r In






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reference signal












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(43)







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(44)















in Fig 45


(45)








menu as follows



Max Step Size auto






(46)



plot function











conditions















(47)




(48)


(49)

Chapter (5)


Excited DC Motor

51 Introduction






















(50)












ckE (51)








(51)





(52)



















diagram in Fig 54

(53)


524 Chopper Control







(54)


in Fig 55



























for firing IGBT

(55)











(56)











(57)





(22)



















resistance starter

(23)







block



Rotor speed in rads


Field current in A






(24)







(25)

Chapter (3)


State Power Devices

31 Rectification

















Some of them are







(26)







fed DC motor

(27)






cos22 V

V (31)




Fig 33


fed DC motor

(28)






fed DC motor


)cos1(2

V

V (32)

(29)












VV

63 (34)


(30)



)cos1(63

V

V (35)










(31)



cos63 V

V (36)






current

(32)


fed DC motor








Step-up chopper


Resonant converter


are

DC drive

Battery charger and

DC power supply




(33)









SIMULINK blocks






speed)





(34)





cycle

dca VV (37)



a

baa

R

EVI

(38)


)1(

)1(

)1(

e

eee

R

Vi

a

dc (39)



)( aa RL

T (310)


(35)







(36)

Chapter (4)



41 Introduction
























(37)























by

)1(

)1(

)(

)(

0 aa

a

Ta

a

s

R

sV

si

L

(41)


22

2

2)(

)(

nn

n

ssR

sC

(42)

(38)


)1(

1

s

R

a

a

s

KsK i

i

i

p

ai

ai



aa

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iaa

i

pa

i

i

i

paa

Ta

a

RKRKs

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L

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))(1(

)(

)(2

0

(43)


)12( anaa

i

p RK (44)

2

naa

i

i RK (45)


follows

For s

sR1

)( therefore

22

2

2

1)(

nn

n

sssC

(46)


)1(1)( tetC n

tn

(47)




by

(39)

)(

)(

)(

0Js

JK

sV

s

LTa

r

(48)


)(

Js

JK

s

KsK ip

a

r



)()(

))((

)(

)(2

0

JKKsJKKJs

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s

s

ip

ip

Tr

r

L

(49)


)2( JK np (410)

KJK ni 2 (411)


before










(40)



o firing angle



o firing


then

)10(180 cV (412)























(41)


















r In






signal be






(42)




signals


reference signal












armature current













(43)







SIMULINKMATLAB












(44)















in Fig 45


(45)








menu as follows



Max Step Size auto






(46)



plot function











conditions















(47)




(48)


(49)

Chapter (5)


Excited DC Motor

51 Introduction






















(50)












ckE (51)








(51)





(52)



















diagram in Fig 54

(53)


524 Chopper Control







(54)


in Fig 55



























for firing IGBT

(55)











(56)











(57)





(23)







block



Rotor speed in rads


Field current in A






(24)







(25)

Chapter (3)


State Power Devices

31 Rectification

















Some of them are







(26)







fed DC motor

(27)






cos22 V

V (31)




Fig 33


fed DC motor

(28)






fed DC motor


)cos1(2

V

V (32)

(29)












VV

63 (34)


(30)



)cos1(63

V

V (35)










(31)



cos63 V

V (36)






current

(32)


fed DC motor








Step-up chopper


Resonant converter


are

DC drive

Battery charger and

DC power supply




(33)









SIMULINK blocks






speed)





(34)





cycle

dca VV (37)



a

baa

R

EVI

(38)


)1(

)1(

)1(

e

eee

R

Vi

a

dc (39)



)( aa RL

T (310)


(35)







(36)

Chapter (4)



41 Introduction
























(37)























by

)1(

)1(

)(

)(

0 aa

a

Ta

a

s

R

sV

si

L

(41)


22

2

2)(

)(

nn

n

ssR

sC

(42)

(38)


)1(

1

s

R

a

a

s

KsK i

i

i

p

ai

ai



aa

i

iaa

i

pa

i

i

i

paa

Ta

a

RKRKs

KsKR

sI

sI

L

)1(

))(1(

)(

)(2

0

(43)


)12( anaa

i

p RK (44)

2

naa

i

i RK (45)


follows

For s

sR1

)( therefore

22

2

2

1)(

nn

n

sssC

(46)


)1(1)( tetC n

tn

(47)




by

(39)

)(

)(

)(

0Js

JK

sV

s

LTa

r

(48)


)(

Js

JK

s

KsK ip

a

r



)()(

))((

)(

)(2

0

JKKsJKKJs

KsKJK

s

s

ip

ip

Tr

r

L

(49)


)2( JK np (410)

KJK ni 2 (411)


before










(40)



o firing angle



o firing


then

)10(180 cV (412)























(41)


















r In






signal be






(42)




signals


reference signal












armature current













(43)







SIMULINKMATLAB












(44)















in Fig 45


(45)








menu as follows



Max Step Size auto






(46)



plot function











conditions















(47)




(48)


(49)

Chapter (5)


Excited DC Motor

51 Introduction






















(50)












ckE (51)








(51)





(52)



















diagram in Fig 54

(53)


524 Chopper Control







(54)


in Fig 55



























for firing IGBT

(55)











(56)











(57)





(24)







(25)

Chapter (3)


State Power Devices

31 Rectification

















Some of them are







(26)







fed DC motor

(27)






cos22 V

V (31)




Fig 33


fed DC motor

(28)






fed DC motor


)cos1(2

V

V (32)

(29)












VV

63 (34)


(30)



)cos1(63

V

V (35)










(31)



cos63 V

V (36)






current

(32)


fed DC motor








Step-up chopper


Resonant converter


are

DC drive

Battery charger and

DC power supply




(33)









SIMULINK blocks






speed)





(34)





cycle

dca VV (37)



a

baa

R

EVI

(38)


)1(

)1(

)1(

e

eee

R

Vi

a

dc (39)



)( aa RL

T (310)


(35)







(36)

Chapter (4)



41 Introduction
























(37)























by

)1(

)1(

)(

)(

0 aa

a

Ta

a

s

R

sV

si

L

(41)


22

2

2)(

)(

nn

n

ssR

sC

(42)

(38)


)1(

1

s

R

a

a

s

KsK i

i

i

p

ai

ai



aa

i

iaa

i

pa

i

i

i

paa

Ta

a

RKRKs

KsKR

sI

sI

L

)1(

))(1(

)(

)(2

0

(43)


)12( anaa

i

p RK (44)

2

naa

i

i RK (45)


follows

For s

sR1

)( therefore

22

2

2

1)(

nn

n

sssC

(46)


)1(1)( tetC n

tn

(47)




by

(39)

)(

)(

)(

0Js

JK

sV

s

LTa

r

(48)


)(

Js

JK

s

KsK ip

a

r



)()(

))((

)(

)(2

0

JKKsJKKJs

KsKJK

s

s

ip

ip

Tr

r

L

(49)


)2( JK np (410)

KJK ni 2 (411)


before










(40)



o firing angle



o firing


then

)10(180 cV (412)























(41)


















r In






signal be






(42)




signals


reference signal












armature current













(43)







SIMULINKMATLAB












(44)















in Fig 45


(45)








menu as follows



Max Step Size auto






(46)



plot function











conditions















(47)




(48)


(49)

Chapter (5)


Excited DC Motor

51 Introduction






















(50)












ckE (51)








(51)





(52)



















diagram in Fig 54

(53)


524 Chopper Control







(54)


in Fig 55



























for firing IGBT

(55)











(56)











(57)





(25)

Chapter (3)


State Power Devices

31 Rectification

















Some of them are







(26)







fed DC motor

(27)






cos22 V

V (31)




Fig 33


fed DC motor

(28)






fed DC motor


)cos1(2

V

V (32)

(29)












VV

63 (34)


(30)



)cos1(63

V

V (35)










(31)



cos63 V

V (36)






current

(32)


fed DC motor








Step-up chopper


Resonant converter


are

DC drive

Battery charger and

DC power supply




(33)









SIMULINK blocks






speed)





(34)





cycle

dca VV (37)



a

baa

R

EVI

(38)


)1(

)1(

)1(

e

eee

R

Vi

a

dc (39)



)( aa RL

T (310)


(35)







(36)

Chapter (4)



41 Introduction
























(37)























by

)1(

)1(

)(

)(

0 aa

a

Ta

a

s

R

sV

si

L

(41)


22

2

2)(

)(

nn

n

ssR

sC

(42)

(38)


)1(

1

s

R

a

a

s

KsK i

i

i

p

ai

ai



aa

i

iaa

i

pa

i

i

i

paa

Ta

a

RKRKs

KsKR

sI

sI

L

)1(

))(1(

)(

)(2

0

(43)


)12( anaa

i

p RK (44)

2

naa

i

i RK (45)


follows

For s

sR1

)( therefore

22

2

2

1)(

nn

n

sssC

(46)


)1(1)( tetC n

tn

(47)




by

(39)

)(

)(

)(

0Js

JK

sV

s

LTa

r

(48)


)(

Js

JK

s

KsK ip

a

r



)()(

))((

)(

)(2

0

JKKsJKKJs

KsKJK

s

s

ip

ip

Tr

r

L

(49)


)2( JK np (410)

KJK ni 2 (411)


before










(40)



o firing angle



o firing


then

)10(180 cV (412)























(41)


















r In






signal be






(42)




signals


reference signal












armature current













(43)







SIMULINKMATLAB












(44)















in Fig 45


(45)








menu as follows



Max Step Size auto






(46)



plot function











conditions















(47)




(48)


(49)

Chapter (5)


Excited DC Motor

51 Introduction






















(50)












ckE (51)








(51)





(52)



















diagram in Fig 54

(53)


524 Chopper Control







(54)


in Fig 55



























for firing IGBT

(55)











(56)











(57)





(26)







fed DC motor

(27)






cos22 V

V (31)




Fig 33


fed DC motor

(28)






fed DC motor


)cos1(2

V

V (32)

(29)












VV

63 (34)


(30)



)cos1(63

V

V (35)










(31)



cos63 V

V (36)






current

(32)


fed DC motor








Step-up chopper


Resonant converter


are

DC drive

Battery charger and

DC power supply




(33)









SIMULINK blocks






speed)





(34)





cycle

dca VV (37)



a

baa

R

EVI

(38)


)1(

)1(

)1(

e

eee

R

Vi

a

dc (39)



)( aa RL

T (310)


(35)







(36)

Chapter (4)



41 Introduction
























(37)























by

)1(

)1(

)(

)(

0 aa

a

Ta

a

s

R

sV

si

L

(41)


22

2

2)(

)(

nn

n

ssR

sC

(42)

(38)


)1(

1

s

R

a

a

s

KsK i

i

i

p

ai

ai



aa

i

iaa

i

pa

i

i

i

paa

Ta

a

RKRKs

KsKR

sI

sI

L

)1(

))(1(

)(

)(2

0

(43)


)12( anaa

i

p RK (44)

2

naa

i

i RK (45)


follows

For s

sR1

)( therefore

22

2

2

1)(

nn

n

sssC

(46)


)1(1)( tetC n

tn

(47)




by

(39)

)(

)(

)(

0Js

JK

sV

s

LTa

r

(48)


)(

Js

JK

s

KsK ip

a

r



)()(

))((

)(

)(2

0

JKKsJKKJs

KsKJK

s

s

ip

ip

Tr

r

L

(49)


)2( JK np (410)

KJK ni 2 (411)


before










(40)



o firing angle



o firing


then

)10(180 cV (412)























(41)


















r In






signal be






(42)




signals


reference signal












armature current













(43)







SIMULINKMATLAB












(44)















in Fig 45


(45)








menu as follows



Max Step Size auto






(46)



plot function











conditions















(47)




(48)


(49)

Chapter (5)


Excited DC Motor

51 Introduction






















(50)












ckE (51)








(51)





(52)



















diagram in Fig 54

(53)


524 Chopper Control







(54)


in Fig 55



























for firing IGBT

(55)











(56)











(57)





(27)






cos22 V

V (31)




Fig 33


fed DC motor

(28)






fed DC motor


)cos1(2

V

V (32)

(29)












VV

63 (34)


(30)



)cos1(63

V

V (35)










(31)



cos63 V

V (36)






current

(32)


fed DC motor








Step-up chopper


Resonant converter


are

DC drive

Battery charger and

DC power supply




(33)









SIMULINK blocks






speed)





(34)





cycle

dca VV (37)



a

baa

R

EVI

(38)


)1(

)1(

)1(

e

eee

R

Vi

a

dc (39)



)( aa RL

T (310)


(35)







(36)

Chapter (4)



41 Introduction
























(37)























by

)1(

)1(

)(

)(

0 aa

a

Ta

a

s

R

sV

si

L

(41)


22

2

2)(

)(

nn

n

ssR

sC

(42)

(38)


)1(

1

s

R

a

a

s

KsK i

i

i

p

ai

ai



aa

i

iaa

i

pa

i

i

i

paa

Ta

a

RKRKs

KsKR

sI

sI

L

)1(

))(1(

)(

)(2

0

(43)


)12( anaa

i

p RK (44)

2

naa

i

i RK (45)


follows

For s

sR1

)( therefore

22

2

2

1)(

nn

n

sssC

(46)


)1(1)( tetC n

tn

(47)




by

(39)

)(

)(

)(

0Js

JK

sV

s

LTa

r

(48)


)(

Js

JK

s

KsK ip

a

r



)()(

))((

)(

)(2

0

JKKsJKKJs

KsKJK

s

s

ip

ip

Tr

r

L

(49)


)2( JK np (410)

KJK ni 2 (411)


before










(40)



o firing angle



o firing


then

)10(180 cV (412)























(41)


















r In






signal be






(42)




signals


reference signal












armature current













(43)







SIMULINKMATLAB












(44)















in Fig 45


(45)








menu as follows



Max Step Size auto






(46)



plot function











conditions















(47)




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Chapter (5)


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51 Introduction






















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51 Introduction






















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51 Introduction






















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(53)


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Chapter (5)


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51 Introduction






















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(51)





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diagram in Fig 54

(53)


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(33)









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(34)





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(49)

Chapter (5)


Excited DC Motor

51 Introduction






















(50)












ckE (51)








(51)





(52)



















diagram in Fig 54

(53)


524 Chopper Control







(54)


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(55)











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(49)

Chapter (5)


Excited DC Motor

51 Introduction






















(50)












ckE (51)








(51)





(52)



















diagram in Fig 54

(53)


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41 Introduction
























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(45)








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(46)



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(49)

Chapter (5)


Excited DC Motor

51 Introduction






















(50)












ckE (51)








(51)





(52)



















diagram in Fig 54

(53)


524 Chopper Control







(54)


in Fig 55



























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Chapter (4)



41 Introduction
























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(45)








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(46)



plot function











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(48)


(49)

Chapter (5)


Excited DC Motor

51 Introduction






















(50)












ckE (51)








(51)





(52)



















diagram in Fig 54

(53)


524 Chopper Control







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JKKsJKKJs

KsKJK

s

s

ip

ip

Tr

r

L

(49)


)2( JK np (410)

KJK ni 2 (411)


before










(40)



o firing angle



o firing


then

)10(180 cV (412)























(41)


















r In






signal be






(42)




signals


reference signal












armature current













(43)







SIMULINKMATLAB












(44)















in Fig 45


(45)








menu as follows



Max Step Size auto






(46)



plot function











conditions















(47)




(48)


(49)

Chapter (5)


Excited DC Motor

51 Introduction






















(50)












ckE (51)








(51)





(52)



















diagram in Fig 54

(53)


524 Chopper Control







(54)


in Fig 55



























for firing IGBT

(55)











(56)











(57)





(38)


)1(

1

s

R

a

a

s

KsK i

i

i

p

ai

ai



aa

i

iaa

i

pa

i

i

i

paa

Ta

a

RKRKs

KsKR

sI

sI

L

)1(

))(1(

)(

)(2

0

(43)


)12( anaa

i

p RK (44)

2

naa

i

i RK (45)


follows

For s

sR1

)( therefore

22

2

2

1)(

nn

n

sssC

(46)


)1(1)( tetC n

tn

(47)




by

(39)

)(

)(

)(

0Js

JK

sV

s

LTa

r

(48)


)(

Js

JK

s

KsK ip

a

r



)()(

))((

)(

)(2

0

JKKsJKKJs

KsKJK

s

s

ip

ip

Tr

r

L

(49)


)2( JK np (410)

KJK ni 2 (411)


before










(40)



o firing angle



o firing


then

)10(180 cV (412)























(41)


















r In






signal be






(42)




signals


reference signal












armature current













(43)







SIMULINKMATLAB












(44)















in Fig 45


(45)








menu as follows



Max Step Size auto






(46)



plot function











conditions















(47)




(48)


(49)

Chapter (5)


Excited DC Motor

51 Introduction






















(50)












ckE (51)








(51)





(52)



















diagram in Fig 54

(53)


524 Chopper Control







(54)


in Fig 55



























for firing IGBT

(55)











(56)











(57)





(39)

)(

)(

)(

0Js

JK

sV

s

LTa

r

(48)


)(

Js

JK

s

KsK ip

a

r



)()(

))((

)(

)(2

0

JKKsJKKJs

KsKJK

s

s

ip

ip

Tr

r

L

(49)


)2( JK np (410)

KJK ni 2 (411)


before










(40)



o firing angle



o firing


then

)10(180 cV (412)























(41)


















r In






signal be






(42)




signals


reference signal












armature current













(43)







SIMULINKMATLAB












(44)















in Fig 45


(45)








menu as follows



Max Step Size auto






(46)



plot function











conditions















(47)




(48)


(49)

Chapter (5)


Excited DC Motor

51 Introduction






















(50)












ckE (51)








(51)





(52)



















diagram in Fig 54

(53)


524 Chopper Control







(54)


in Fig 55



























for firing IGBT

(55)











(56)











(57)





(40)



o firing angle



o firing


then

)10(180 cV (412)























(41)


















r In






signal be






(42)




signals


reference signal












armature current













(43)







SIMULINKMATLAB












(44)















in Fig 45


(45)








menu as follows



Max Step Size auto






(46)



plot function











conditions















(47)




(48)


(49)

Chapter (5)


Excited DC Motor

51 Introduction






















(50)












ckE (51)








(51)





(52)



















diagram in Fig 54

(53)


524 Chopper Control







(54)


in Fig 55



























for firing IGBT

(55)











(56)











(57)





(41)


















r In






signal be






(42)




signals


reference signal












armature current













(43)







SIMULINKMATLAB












(44)















in Fig 45


(45)








menu as follows



Max Step Size auto






(46)



plot function











conditions















(47)




(48)


(49)

Chapter (5)


Excited DC Motor

51 Introduction






















(50)












ckE (51)








(51)





(52)



















diagram in Fig 54

(53)


524 Chopper Control







(54)


in Fig 55



























for firing IGBT

(55)











(56)











(57)





(42)




signals


reference signal












armature current













(43)







SIMULINKMATLAB












(44)















in Fig 45


(45)








menu as follows



Max Step Size auto






(46)



plot function











conditions















(47)




(48)


(49)

Chapter (5)


Excited DC Motor

51 Introduction






















(50)












ckE (51)








(51)





(52)



















diagram in Fig 54

(53)


524 Chopper Control







(54)


in Fig 55



























for firing IGBT

(55)











(56)











(57)





(43)







SIMULINKMATLAB












(44)















in Fig 45


(45)








menu as follows



Max Step Size auto






(46)



plot function











conditions















(47)




(48)


(49)

Chapter (5)


Excited DC Motor

51 Introduction






















(50)












ckE (51)








(51)





(52)



















diagram in Fig 54

(53)


524 Chopper Control







(54)


in Fig 55



























for firing IGBT

(55)











(56)











(57)





(44)















in Fig 45


(45)








menu as follows



Max Step Size auto






(46)



plot function











conditions















(47)




(48)


(49)

Chapter (5)


Excited DC Motor

51 Introduction






















(50)












ckE (51)








(51)





(52)



















diagram in Fig 54

(53)


524 Chopper Control







(54)


in Fig 55



























for firing IGBT

(55)











(56)











(57)





(45)








menu as follows



Max Step Size auto






(46)



plot function











conditions















(47)




(48)


(49)

Chapter (5)


Excited DC Motor

51 Introduction






















(50)












ckE (51)








(51)





(52)



















diagram in Fig 54

(53)


524 Chopper Control







(54)


in Fig 55



























for firing IGBT

(55)











(56)











(57)





(46)



plot function











conditions















(47)




(48)


(49)

Chapter (5)


Excited DC Motor

51 Introduction






















(50)












ckE (51)








(51)





(52)



















diagram in Fig 54

(53)


524 Chopper Control







(54)


in Fig 55



























for firing IGBT

(55)











(56)











(57)





(47)




(48)


(49)

Chapter (5)


Excited DC Motor

51 Introduction






















(50)












ckE (51)








(51)





(52)



















diagram in Fig 54

(53)


524 Chopper Control







(54)


in Fig 55



























for firing IGBT

(55)











(56)











(57)





(48)


(49)

Chapter (5)


Excited DC Motor

51 Introduction






















(50)












ckE (51)








(51)





(52)



















diagram in Fig 54

(53)


524 Chopper Control







(54)


in Fig 55



























for firing IGBT

(55)











(56)











(57)





(49)

Chapter (5)


Excited DC Motor

51 Introduction






















(50)












ckE (51)








(51)





(52)



















diagram in Fig 54

(53)


524 Chopper Control







(54)


in Fig 55



























for firing IGBT

(55)











(56)











(57)





(50)












ckE (51)








(51)





(52)



















diagram in Fig 54

(53)


524 Chopper Control







(54)


in Fig 55



























for firing IGBT

(55)











(56)











(57)





(51)





(52)



















diagram in Fig 54

(53)


524 Chopper Control







(54)


in Fig 55



























for firing IGBT

(55)











(56)











(57)





(52)



















diagram in Fig 54

(53)


524 Chopper Control







(54)


in Fig 55



























for firing IGBT

(55)











(56)











(57)





(53)


524 Chopper Control







(54)


in Fig 55



























for firing IGBT

(55)











(56)











(57)





(54)


in Fig 55



























for firing IGBT

(55)











(56)











(57)





(55)











(56)











(57)





(56)











(57)





(57)





chapter (1) mathematical modeling of dc machines...chapter (1) mathematical modeling of dc machines...

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