Project 1

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Chapter (1)

Mathematical Modeling of DC Machines

1.1 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

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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.

1.2 Types of DC Motors

1.2.1 Separately Excited DC Motor

The schematic circuit diagram of separately excited DC motor is

illustrated in following Figure 1.1. 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 Faraday's 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 1.1 Separately Excited DC Motor

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1.2.2 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 1.2.

Figure 1.2 PM DC Motor

1.2.3 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 ¼ 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 1.3.

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Figure 1.3 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.

1.2.4 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 it’s 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 won’t 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 1.4.

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Figure 1.4 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.

1.2.5 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 1.5.

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.

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Figure 1.5 Compound DC Motor

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 “suicide motors,” 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.

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1.3 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. 1.1. The electrical

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

illustrated in Figure 1.1. The electrical relation between these variables is

given by equations (1.1-1.6) where Eb, the internally generated voltage, is

proportional to the motor velocity.

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, ωr, 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:

ba

aaaa Edtdi

LRiV ++= (1.1)

rfafb iLE ω= (1.2)

faf iLK =υ (1.3)

dtdi

LRiV fffff += (1.4)

ae iKT υ= (1.5)

Lrr

e Tdt

dJT ++= βω

ω (1.6)

Va: applied voltage

Ia: motor current

Eb: induced back emf voltage

La: armature winding inductance

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Ra: armature resistance

Te: motor output torque

ωr: motor output speed

1.4 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

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.

1.4.1 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 p/1 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 (1.1-1.6) may be Combined produces the armature

current, torque, field current and motor speed as follows:

)1(/1

).(p

REVi

a

aaaa τ+

−= (1.7)

9

)(1).(β

ω+

−=Jp

TT Ler (1.8)

)1(/1

.p

RVi

f

fff τ+

= (1.9)

Where, aaa RL /=τ and fff RL /=τ

From equations. (1.1-1.9), the time-domain block diagram is obtained as

shown in Fig. 1.6.

Fig. 1.6 Time domain block diagram of separately excited DC motor

1.4.2 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 ot plus information on the input excitation subsequently

applied is sufficient to determine the state of the system at any time ott⟩ .

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

the rotor speed rω . 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 (1.1-

)1(/1

pR

a

a

τ+

)1(/1

pR

f

f

τ+

)(1β+Jp

afLai

fifV

eTLT

rωaV

bE

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1.4) and the equation relating torque and rotor speed given by (1.5-1.6).

In particular, solving equations (1.1, 1.4, 1.6) for dtdia ,

dtdi f and

dtd rω

yields:

aa

rfa

afa

aa V

Li

LL

iidtd 11

+−−= ωτ

(1.10)

ff

ff

f VL

iidtd 11

+−=τ

(1.11)

JT

iiJ

LJdt

d Laf

afrr −+−= ωβω (1.12)

These equations can be written in matrix form as follows:

−

−

−

+

−+

−

−

−

=

L

a

f

a

f

afaf

rfa

af

r

a

f

a

f

r

a

f

TV

V

J

L

L

iiJ

L

iLL

i

i

J

i

i

dtd

1 0 0

0 1 0

0 0 1

0

0 0

0 1 0

0 0 1

ωω

βτ

τ

ω

(1.13)

1.4.3 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. 1.7 as follows.

11

)//1).(/1()//1()/1(

)()(

20 JpJp

KtVt

maa

ma

Ta

r

Lβττβτ

ττω υ

++++=

=

(1.14)

Where, 2υ

τK

JRam =

)//1).(/1()//1()/1).(/1()(

20 JpJp

pJT

t

maa

a

VL

r

aβττβτ

τω++++

+=

−=

(1.15)

)//1).(/1()//1()/1()(

20 JpJp

KTti

maa

ma

VL

a

aβττβτ

ττυ++++

=−

=

(1.16)

)//1).(/1()//1()/).(/1(

)()(

20 JpJp

JpRtVti

maa

aa

Ta

a

Lβττβτ

βτ++++

+=

=

(1.17)

Fig. 1.7 Time domain block diagram of separately excited DC motor at

constant flux

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

with respect to time dtd / and the operator s/1 denote integration ion.

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

diagram, so transfer functions by using the Laplace operator. Arranging

)1(/1

pR

a

a

τ+

)(1β+Jp

υKai eT

LT

rωaV

bE

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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 (1.1-1.6)

may be Combined produces the armature current, torque, field current

and motor speed as follows:

)1(/1

).(s

REVi

a

aaaa τ+

−= (1.18)

)(1).(β

ω+

−=Js

TT Ler (1.19)

)1(/1

.s

RVi

f

fff τ+

= (1.20)

From equations. (1.18-1.20), the S-domain block diagram is obtained as

shown in Fig. 1.8.

1.4.5 S-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. 1.9 as follows.

)//1).(/1()//1()/1(

)()(

20 JsJs

KsVs

maa

ma

Ta

r

Lβττβτ

ττω υ

++++=

=

(1.21)

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)//1).(/1()//1()/1).(/1()(

20 JsJs

sJT

s

maa

a

VL

r

aβττβτ

τω++++

+=

−=

(1.22)

)//1).(/1()//1()/1()(

20 JsJs

KTsi

maa

ma

VL

a

aβττβτ

ττυ++++

=−

=

(1.23)

)//1).(/1()//1()/).(/1(

)()(

20 JsJs

JsRsVsi

maa

aa

Ta

a

Lβττβτ

βτ++++

+=

=

(1.24)

Fig. 1.8 S-domain block diagram of separately excited DC motor

Fig. 1.9 S-domain block diagram of separately excited DC motor at

constant flux

)1(/1

sR

a

a

τ+

)1(/1

sR

f

f

τ+

)(1β+Js

afLai

fifV

eTLT

rωaV

bE

)1(/1

sR

a

a

τ+

)(1β+Js

υKai eT

LT

rωaV

bE

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Chapter (2)

Performance Characteristics of Separately Excited DC Motor

2.1 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 (2.1). If a steady voltage Vf is applied to the field,

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

(2.2). When the field current is constant, the flux induced by the field

winding remains constant, and usually it is held at its rated value Φ. 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 (2.3). In

steady-state, equation (2.4) 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 rω (rad/s) and the field Φ ( webers), as

shown by equation(2.5).

dtdi

LRiV fffff += (2.1)

fff RVi /= (2.2)

ba

aaaa Edtdi

LRiV ++= (2.3)

baaa ERiV += (2.4)

rb KE ωΦ= (2.5)

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In equation (2.5), 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 (2.6-

2.8). On canceling the common term on both sides, the torque Te

developed by the armature is obtained as presented in equation (2.9). If

the instantaneous armature current is ia, then equation (2.8) applies.

Torque has been denoted by Te in both equations.

aba IEP = (2.6)

rb KE ωυ= (2.7)

raa IKP ωυ= (2.8)

ae IKT υ= (2.9)

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

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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.

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2.2 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.

2.2.1 Dynamic Performance During Starting From a Constant DC

Source

This block implements a separately excited DC machine using

SIMULINK/MATLAB as shown in Fig. 2.1. 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. 2.1 Separately excited DC machine using SIMULINK/MATLAB

The details of the SIMULINK diagram is shown in Fig. 2.2. The first

block simulate the equation aidtd , the second block simulate the equation

fidtd , the third block simulate the equation ae iKT υ= and the fourth block

simulate the equation )(

1).(β

ω+

−=Js

TT Ler

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Fig. 2.2 Details of Separately excited DC motor SIMULINK diagram

The no load starting characteristics of separately excited DC motor are

shown in Fig. 2.3. The armature voltage, the armature current and the

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

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

500 A and rotor speed has an overshoot of 60 rad/sec (large) .

Fig. 2.3 No load starting characteristics of separately excited DC motor

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2.2.2 Dynamic Performance During Sudden Change in Load Torque

The dynamic characteristics following a step change in load torque from

zero to 25 N.m are shown in Fig. 2.4. The armature current and rotor

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

quite large.

Fig. 2.4 Dynamic performance of separately excited DC motor following

a sudden change in load torque.

2.2.3 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

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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

train's 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. 2.5 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

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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 driver's 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 (i.e. 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 2.5.

Fig. 2.5 Starting of a separately excited DC motor with a three-step

resistance starter

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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 rad/s

• Armature current in A

• Field current in A

• Electromechanical torque in N.m.

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. 2.6.

The Motor Starter subsystem is shown in Figure 2.7:

Figure 2.6 Starting DC motor SIMULINK diagram

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Figure 2.7 Starter SIMULINK diagram

The DC motor current, voltage, torque and speed waveforms obtained at

the end of the starting test are shown in Figure 2.8.

Fig. 2.8 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 3.1 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,

3.2 AC to DC Conversion

3.2.1 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. 3.1.

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. 3.1 Schematic and waveforms diagrams of full wave converter

fed DC motor

27

We now see that Vo is –ve 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:

απ

cos22 VV =o (3.1)

Fig. 3.2 Schematic and waveforms diagrams of full wave converter

fed DC motor in inversion mode

The variation of the converter output, Vo, as defined by (3.1) is shown in

Fig. 3.3.

Fig. 3.3 Output voltage variations of full wave converter

fed DC motor

28

3.2.2 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. 3.4.

Fig. 3.4 Schematic and waveforms diagrams of full wave semi-converter

fed DC motor

The average output voltage is now given by,

)cos1(2 απ

+=VVo (3.2)

29

3.2.3 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. 3.5.

Fig. 3.5 Schematic and waveforms diagrams of full wave converter

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.

πVV 63

=o (3.4)

The thyristor controlled versions is shon in Fig. 3.6.

30

Fig. 3.6 Schematic and waveforms diagrams of full wave converter

The output voltage waveform is given by:

)cos1(63 απ

+=VVo (3.5)

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, S1,2,3 are fired during

the +ve half cycles of the phases to which they are connected and S4,5,6

are fired during the –ve 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:

απ

cos63 VV =o (3.6)

This gives us waveforms as follows.

Fig. 3.7 Schematic and waveforms diagrams of full wave converter

Similarly to the single phase converters, firing angles of 0 < α < 90 give

+ve Vo, but firing angles of 90 < α < 180 cause vo to go –ve and the

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

current,

32

Fig. 3.8 Output voltage variations of full wave converter

fed DC motor

3.3 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.

3.3.2 Description of the Open Loop Drive System

In this section illustrates application of the SIMULINK/MATLAB 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 3.9. 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 3.9: 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. 3.10.

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

cycle α .

dca VV α= (3.7)

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 −= (3.8)

The peak-to-peak current ripple is:

)1()1(.

)1(

τ

τατατ

−

−−−−

−−+−

=∆e

eeeRVi

a

dc (3.9)

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

and the DC motor electrical time constant.

)/( aa RLT

=τ (3.10)

Figure 3.10 Waveforms Illustrating the Chopper Operation

35

3.4 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. 3.11.

Figure 3.11 Steady-State Motor Current and Voltage Waveforms

36

Chapter (4)

Design and Simulation for Current & Speed Controllers

of Separately Excited DC Motor Drive

4.1 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

input/output 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

4.2 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.

4.3 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

sR

sVsi

Lτ+

==

(4.1)

If we use the desired response,

22

2

2)()(

nn

n

ssRsC

ωζωω

++= (4.2)

38

We can design the current controller as follows:

Fig. 4.1 Block diagram of the current control loop

The closed loop transfer function can be deduced as:

aaiiaa

ipa

ii

ipaa

Ta

a

RKRKsKsKR

sIsI

Lτττ

τ/)//1(

)).(/1()()(

20

* +++

+=

=

(4.3)

By comparing equations (4.2, 4.3) yields the controller parameters:

)/12( anaaip RK τξωτ −= (4.4)

2naa

ii RK ωτ= (4.5)

Now, we can select the damping ratio ξ and then, we can calculate nω as

follows:

For s

sR 1)( = , therefore,

22

2

2.1)(

nn

n

sssC

ωζωω

++= (4.6)

The inverse Laplace Transform for equation (4.6) will yield:

)1(1)( tetC ntn ωω +−= − (4.7)

From this equation we can calculate nω at the rise time rt and 9.0)( =rtC .

4.4 Speed Controller Design Using Pole Placement

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

by:

)1(/1

sR

a

a

τ+sKsK i

iip + ai *

ai

39

)/(/

)()(

0Js

JKsVs

LTa

r

βω υ

+=

=

(4.8)

We can design the current controller as follows:

Fig. 4.2 Block diagram of the speed control loop

The closed loop transfer function can be deduced as:

)/()//()).(/(

)()(

20

* JKKsJKKJsKsKJK

ss

ip

ip

Tr

r

L

ωυυ

ω

ωωυ

βωω

+++

+=

=

(4.9)

By comparing equations (4.2, 4.9) yields the controller parameters:

)/2( JK np βξωω −= (4.10)

υω ω KJK ni /2= (4.11)

Now, we can select the damping ratio ξ and then, we can calculate nω as

before.

4.5 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

)/(/

JsJK

βυ

+sKsK ip

ωω + aω *rω

40

used produces a voltage proportional to current in the armature. The

difference between these two signals is processed by another PI controller

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

angle. If the firing angle be α and the output of current controller VC,

then:

)10(*180 cV−=α (4.12)

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

41

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

significant change in speed if there be no current controller.

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.

4.6 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 *rω . 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 *rω . 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)

42

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

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, *rω and rω . If the speed feedback signal rω is lower than the

reference signal *rω , 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 rω < *rω , 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.

4.7 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 1.5 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-

43

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

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.

4.8 Simulation of the Separately Excited DC Motor Drive Using

SIMULINK/MATLAB

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 4.3. 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 4.3 Variable-Speed DC Motor Drive

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

SIMULINK library. Voltage Measurement and Current Measurement

44

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

diagram of the DC motor using SIMULINK. is shown in Fig. 4.4

Figure 4.4 DC Motor Drive Using SIMULINK/MATLAB

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 HP/240 V DC

motor having the following parameters: Ra = 0.5 , La = 10 mH, Kv

=1.23 V/(rad/s), Kv = 1.23 N.m/A.

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 +h/2 and -h/2 limits (h is the hysteresis band) as shown

in Fig. 4.5.

45

The current controller is a masked block that contains

Figure 4.5 The hysteresis current controller

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

is implemented by SIMULINK blocks as shown in Figure 4.6.

Figure 4.6 The PI speed controller

4.9 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 Time:0, Stop time: 1.2

Solver Type: Variable-step ode23tb (stiff/TR-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.

4.9.1 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 rad/s at t=0.0 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 4.7. Note that the final system state vector x Final can be saved

by selecting Workspace I/O/Save to workspace/Final 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.

4.9.2 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 *rω (rad/s) and the block named Load_torque

(N.m) in the diagram by two SIMULINK step blocks with different

starting times. The speed reference steps from 120 rad/s to 160 rad/s at t =

0.4 s and the load torque steps from 5 N.m to 25 N.m at t = 1.2 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 I/O/Load from workspace/Initial 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 4.8.

Figure 4.7: Starting of the DC Motor Drive

48

Figure 4.8 Dynamic Transient of the DC Motor Drive

49

Chapter (5)

Implementation of the Open Loop Control for Separately

Excited DC Motor

5.1 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.

5.2 Experimental Setup

5.1.1 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 (5.1) displays the voltage regulator circuit.

Fig. 5.1 The voltage regulator circuit

5.2.2 Linear Control of Phase Angle α

In this scheme illustrated in Fig. 5.2, a control voltage Ec changes linearly

the phase angle α . 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=α (5.1)

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, α , and the transistor drive circuit bias the IGBT.

51

The ramp waveform and the pulse waveform for α 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. 5.3.

Fig. 5.2 Linear control of phase angle

52

Fig. 5.3 Circuit diagram phase angle control

5.2.3 Pulse Amplifier Circuit (Driving Circuit)

The pulses ei or ej in Fig. 5.4 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 5.4

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. 5.4, 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

53

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

diagram in Fig. 5.4.

Fig. 5.4 A typical pulse amplifier circuit

5.2.4 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

5.5 shows a chopper firing circuit that consists mainly of four parts: a

54

triangular wave generator, a voltage comparator, edge detection and pulse

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

in Fig. 5.5.

The three operational amplifiers Q1, and Q2, together form a triangular

wave generator that generates the triangular wave ea, shown in Fig. 5.5b.

As the voltage ea decreases below 0.6 V (which is the forward bias

voltage of the diode D2), the output of Q2 changes from 13.5 V to -13.5

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

now negative (-13.5 V), makes D1 forward biased, and the 2.2 k path

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

quickly rises to 13.5 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 13.5 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. 5.5.

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

55

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

for firing IGBT.

Fig. 5.5 Chopper driving circuit

5.2.5 OPEN-LOOP AND CLOSED-LOOP CONTROL

The control voltage Ec in Figs. 5.1, 5.2, 5.3 and 5.5 changes the output

voltage of the converter. In an open-loop control as shown in Fig. 5.6, 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

56

system, as shown Fig. 5.6, the control voltage is derived from the

difference between the reference current and the actual motor current.

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 system's 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. 5.6 Open loop and closed loop control circuit

57

5.3 Experimental Results

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

Fig. 5.7 shows the steady state voltage and current waveforms.

Fig. 5.7 Steady state voltage and current waveforms