Double Frequency Buck Converter Original

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Department of Electrical & Electronics Engineering 1 | P a g e

VJIT-HYD

A

Main Project report on

DOUBLE-FREQUENCY BUCK CONVERTER

Submitted In partial fulfillment of the requirements for the award of the

degree of

B.TECH

in

Electrical & Electronics Engineering

BY

1. N.SAI SRINIVAS YASASWI 08911A0285

2. S.SRAVAN KUMAR 08911A0296

3. G.SANTHOSH 09915A0208

UNDER THE GUIDANCE OF

Prof. S.M. ZAFARULLAH (H.O.D, EEE)

Department Of Electrical & Electronics Engineering

VIDYA JYOTHI INSTITUTE OF TECHNOLOGY

(Affiliated to JNTU)

AZIZNAGAR, C.B.POST, MOINABAD, HYDERABAD 500075


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Vidya Jyothi Institute of Technology

Approved by AICTE, New Delhi & Affiliated to Jawaharlal Nehru

Technological University, Hyderabad

DEPARTMENT OF ELETRICAL AND ELECTRONICS ENGENEERING

CERTIFICATE

This is to certify that Main Project Work entitled

DOUBLE-FREQUENCY BUCK CONVERTER is a benefited

work of N.SAI SRINIVAS YASASWI, S.SRAVAN KUMAR, and

G.SANTHOSH Bearing Roll.nos 08911A0285, 08911A0296 and

09915A0208 submitted in partial fulfillment for the award of

BACHELOR OF TECHNOLOGY in ELECTRICAL AND ELECTRONICS

ENGINEERING to VIDYA JYOTHI INSTITUTE OF TECHNOLOGY

affiliated to JNTU university, Hyderabad.

The result embodied in this project has not been submitted to any

other university or institute for the award of any degree or diploma.

Internal Guide Head of the Department

T.K SRINIVAS Prof. S.M. ZAFARULLAH

Assistant professor, EEE Dept Professor and HOD, EEE Dept

VJIT-HYD VJIT-HYD

EXTERNAL EXAMINER


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A C K N O W L E D G E M E N T

We are very much thankful to our internal Guide SriT.K SRINIVAS Sir, Lecturer in Electrical &

Electronics Engineering Department for his excellent guidance and deep encouragement in

every step in to this project DOUBLE-FREQUENCY BUCK CONVERTERsuccessfully.

We convey our special thankful to Sri Zafarullah sir, Head of Electrical &

Electronics Engineering Department for all those valuable hours they has spent with us in

every possible aspect to make our project a success.

We are thankful to Sri D.Srinivas, Sri Jyoshna and Sri Geshma , Lecturer in Electrical

& electronics Engineering Department who inspired us by his enthusiastic advises from time

to time and also responding for successful completion of our project.

We are very happy to our sincere thanks to our Principal Sri venu gopal sir , for his

valuable co-operation in the successful completion of his project.

Finally I am grateful to all the staff members and lab demonstrators of EEE Dept. and

those who are directly and indirectly helpful in completion of this project.

By:

STUDENTS OF THIS PROJECT

DOUBLE-FREQUENCY BUCK CONVERTER

VIDYA JYOTHI INSTITUTE OF TECHNOLOGY.

During the Academic Year 2011-2012


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CONTENTS

Abstract i

List of symbols. ii

List of figures. iii

List of Tables. iii

Chapter- 1 (Introduction)

1.1 Introduction. 1

1.2 Organization of thesis. 3

1.3 Overview of thesis. 3

Chapter-2 (Basics of dc-dc converters)

2.1 Introduction. 5

2.1.1 Basics of dc-dc converters. 6

2.1.2 Buck converter. 9

2.3 Average model of Buck converter. 15

2.5 Conclusion. 16

Chapter-3 (Double Frequency Buck converter)

3.1 Introduction. 17

3.1.1 Proposed Double frequency buck converter. 19

3.2 Performance evaluation of DF buck converter. 24

3.2.1 Steady state response. 25

3.2.2 Transient response. 25


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3.3 Proposed double frequency buck converter fed with dc motor 26

3.3.1 Buck-converter Driven Dc Motor System 27

3.3.2 Modelling of Buck-converter Dc Motor System 28

chapter-4 (mat lab)

4.1 simulink: 31

4.2 connecting blocks 33

4.3 continuous and discrete systems: 35

4.4 making subsystems 39

Chapter-5 (Simulation and Simulation result)

5.1 Introduction. 40

5.2 PI controllers 40

5.2.1 Limitations of PI controllers. 46

5.3 Simulation. 47

5.3.1 Simulation diagrams. 47

5.3.2 Simulation result. 52

5.4 Efficiency analysis. 57

Chapter-6 (Conclusion and future work)

6.1 Conclusion. 60

6.2 Scope of future work. 60

References 61


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ABSTRACT

Improving the efficiency and dynamics of power converters is a concerned tradeoff in

power electronics. The increase of switching frequency can improve the dynamics of power

converters, but the efficiency may be degraded. A double-frequency (DF) buck converter is

proposed to address this concern. This converter is comprised of two buck cells: one works at

high frequency, and another works at low frequency. It operates in a way that current in the high-

frequency switch is diverted through the low-frequency switch. Thus, the converter can operate

at very high frequency without adding extra control circuits. Moreover, the switching loss of the

converter remains small. The proposed converter exhibits improved steady state and transient

responses with low switching loss. An ac small-signal model of the DF buck converter is also

given to show that the dynamics of output voltage depends only on the high-frequency buck cell

parameters, and is independent of the low-frequency buck cell parameters. Simulation results

demonstrate that the proposed converter greatly improves the efficiency and exhibits nearly the

same dynamics as the conventional high-frequency buck converter.

Furthermore, the proposed topology can be extended to other dcdc converters by the DFswitch-inductor three-terminal network structure.


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List of symbols

Uin,Uon . Input and output voltage of the converter.

iL, ila . Current through the high, low frequency inductor.

iSD. iS .... Current through the active, diode.

S, SD . High frequency active switches.

Sa, Da . low frequency switch and diode.

L, La .. . inductors of the double frequencybuck converter.

Fh, f1 high, and low frequency of the switches.

Ts1,Tsh .. low and high switching timeperiods.

M Multiple integers.

Uref . Reference voltage.

Uon . On state voltage of the active switch.

Uf . Total timeperiods of the switches and diodes.

IR . Load current of the converter.

R Load resistance of the converter.

Ton, Toff . turn on and turn off times of the switches and diode.

C .. capacitor of the converter.

Psf ..... the total losses of the single frequency buck converter.Pscon, Pss conduction , switching losses of the active switch.

Pdcon, Psd conduction and switching of the diode.

IL inductor average current in efficiency analysis.

Fs .. switching frequency.

Ilapk .. peak to peak low frequency inductor current ripple.

PconDf total conduction losses in the double frequency buck

converter.

PsDf total switching losses in the double frequency buck


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List of figures

Fig.2.1.1 Simple DCDC Converter.

Fig:2.1.2: output voltage as a function of time.

Fig 2.1.3: The two circuit configurations of a Buck converter: (a)On state, when the switch isclosed, and (c) Off-state, when the switch is open.

Fig 2.1.4: Naming conventions of the components, voltages and current of the Buck converter.

Fig: 2.3.1 Average model of buck converter with the added CCS.

Fig(3.1.1 )Schematic of the proposed DF buck converter.

Fig 3.1.2(a) Equivalent circuit of DF buck converter when s-on,sa=on.

Fig 3.1.2(b) Equivalent circuit of DF buck converter when s-off,sa=on;

Fig 3.1.2(c) Equivalent circuit of DF buck converter when s-on,sa=off;

Fig 3.1.2(d) Equivalent circuit of DF buck converter when s-off,sa=off.

Fig 3.2.1 current programmed mode control circuit.

Fig4.1 Simulink library browser

Fig 4 .2 Connectung blocks

Fig.4.2.1 Sources and sinks

Fig.4.3 Continous and descrete systems

Fig.4.3.1 simulink blocks

Fig4.3.2 Simulink math blocks

Fig4..3.3 Signals and systems

Fig:4.4.1setting simulation parameters:Fig:5.2.1 discrete PI controller.

Fig 5.3.1(a) simulation model of a double frequency buck converter.Fig5.3.1(b) simulation model of a high frequency buck converter.

Fig 5.3.3 simulation model of a low frequency buck converter.

Fig 5.3.2.(b)output voltage steady state response comparison of the double frequency, single high

and low frequency buck converter.

Fig 5.3.2.(b)output voltage transient response comparison of the double frequency, single high

and low frequency buck converter when load is step up.

Fig 5.3.2.(c)output voltage transient response comparison of the double frequency, single high

and low frequency buck converter when load is step down.

Fig 5.3.2(a) Switch current waveforms.

List of tables,

TABLE I: SWITCHING STATES.

TABLE 2.1: PI CONTROLLER TUNING METHOD.

TABLE 2.2: EFFECTS INCREASING PARAMETER IN PI CONTROLLER.


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1.INTRODUCTION

1.1 Introduction

The Demand of high-performance power converter is increased dramatically with the

broadening of power converters application fields. In order to improve thetransient and steady

state performance of power converters and to enhance power density, high switching frequency

is an effective method. However, switching frequency rise causes higher switching losses and

greater electromagnetic interference. This, in turn, limits the increase of switching frequency and

hinders the improvement of system performance. Active and passive soft-switching techniques

have been introduced to reduce switching losses. While these can create more favorable

switching trajectories for active power devices, they will generally increase the complexity of

control and sometimes are affected by the variable input and output condition.

In the trends of using power modules, space is limited for placing the added elements.

The complexity of power stage and control circuit also reduces the reliability of soft-switched

converters. Multiconverter paralleling method, which employs low-power converters in parallel

to enhance the power rating, has been proposed to enhance the power processing capability.

However, parallel operation has interaction problem that causes circulating current. To avoid the

circulating current, approaches such as isolation, high impedance, and one-converter approach

are utilized. These efforts increase the control complexity. The interleaving operation employs N

converters to operate in parallel with interleaved clocks, so the total dynamics can reach higher

performance due to the fact that the equivalent frequency is N times the single converter

frequency. Nevertheless, the circulating current phenomenon also exists.

A single boost-type zero-voltage-transition(ZVT) pulse width modulated converter

proposed in adopts an additional shunt resonant network to form an additional Boost cell

torealize soft switching of the main switches. However, the auxiliary switches operate in hard

switch and high frequency .A similar topology of single-phase rectifier is given in, where total

harmonic distortion of the input line current is reduced and the efficiency improved. Its operation

is different from the ZVT circuit.


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The boost-typetopology however, is not very effective to enhance the output voltage

performance that the capacitor ripple voltage is determined by the low frequency. Hence, this

topology is not in suitable for improvement of dc output transient and steady state performances.

Moreover, the main Boost circuit and the added cell are coupled, and the added Boost cell has

an effect on the inductor current input. Splitting the filter inductor of buck converter into two

parts with added auxiliary active switch and diode has been proposed to improve the output

voltage response at load current step-down transient situation, but not at load current step-up

transient situation. Additional transformer and switches are needed to realize the improvement at

step-up transient to make the circuits. function as designed, it is required to detect the load

transient event, then to trigger or shut down the auxiliary switch. This increases the complexity

of the control circuit.

Moreover, oscillations at the output voltage occur due to the frequent on and off

operations at each transient event. On the other hand, high-frequency switching converter or

linear power supply in parallel with low-frequency converter proposed and enhances the output

voltage response. Paralleling high-frequency converter approach also requires the load transient

information, while linear power supply method suffers from low efficiency. Moreover, the

parallel structure brings about the circulating current problem. Additional current sharing control

is needed to overcome this problem.

Morever to overcome this problems we are proposes a novel converter topology to

achieve high dynamic response and high efficiency of buck-type converters. This topology

consists of a high-frequency buck cell and a low-frequency buck cell; and we call it the double -

frequency buck converter (DF buck). The current flowing through the high-frequency cell is

diverted by the low frequency one, which also processes the majority of the converter power.

This current decreases rapidly so that the high-frequency cell can work at very high frequency to

improve the dynamic response. Furthermore, the efficiency is enhanced due to the low-current

processing requirement of the high-frequency cell in the DF buck converter. Unlike the parallel

structure, the proposed converter does not incur the circulating current problem. Moreover, it is

not required to detect the load transient event for control. The circuit configurationand control

strategy will be described in detail. The frequency-domain and time-domain analyses are given


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to show that the proposed topology has the same transient and steady state performance with the

single high-frequency buck converter.

1.2 Organization of thesis:

Chapter 2: This chapter deals with basics of DCDC Converters, Buck Converter,

Average model of Buck Converter.

Chapter 3: This chapter deals with Double Frequency Buck Converter.

Chapter 4: This chapter deals with Mat lab introduction

Chapter 5: This chapter deals with Simulation model,Results and Efficiency Analysis.

Chapter 6: This chapter deals with Conclusion and Future Scope.

1.3 Overview of Project:

The buck converter works in the continuous conduction mode, then the inductor

current iL can be regarded as a current source. In each switching cycle, both the current

flowing through the switch and the voltage across the diode are averaged.

To enhance the steady-state response and the transient response of the buck

converter, the switching frequency should be increased; but higher switching frequency

steps up the switching loss dramatically. An CCS, which is in parallel with the load

terminal, is added to tackle this loss problem. Fig.2 shows such modification.The load

current through the active switch is diverted by the CCS.

The propose to use a buck cell working at lower frequency to realize the CCS.

The proposed converter is called the DF buck converter, because these buck cells work attwo different frequencies. Schematic of this DF buck converter is shown in Fig. 3. The

cell containing L, S , and SDworks at higher frequency, and is called the high-frequency

buck cell. Another cell containing La, Sa, and Da works at lower frequency, and is called

the low-frequency buck cell. The high frequency buck cell is used to enhance the output

performance, and the low-frequency buck cell to improve the converter efficiency. An


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active switch, instead of a diode as in the conventional unidirectional buck converter, is

employed to realize SDin the high frequency buck cell. This active switch transfers the

energy stored in the low-frequency cell to the source during the transient stage of load

step-down. It works complementarily with high-frequency cell stage of load step-down. It

works complementarily with high-frequency cell switch S , and improves the transient

response.

The efficiency expression is analyzed in the double frequency buck converter. The

analysis is also applied to the single high frequency buck and low-frequency buck

converters.

A simple loss model is adopted here in that we just want to show the efficiency

relationship between the DF buck and single high-frequency buck, not to develop a new

loss model.

In the analysis, we have the following assumptions;

1. The conduction losses of active switch and diode are estimated, respectively,

according to their conduction voltages Uonand UF.

2. The switching transient processes are assumed to satisfy the linear current and

voltage waveforms. Moreover, the turn-on time ton is the same for all switches and

diodes, so is the turn-off time toff.

3. Since the switching loss usually dominates the total loss, losses of the output

capacitor and output inductor are not calculated here.

This result also can be reasoned from the fact that the total currents flowing through the

DF buck switches and diodes are the same as that through a single-frequency buck. On

the other hand, the total switching loss is nearly the same as the single low-frequency

buck, and is much smaller than that of the single high-frequency buck. Hence, the DF

buck converter im proves the efficiency by current diversion to the low-frequency cell.

Although assumptions and approximations are made in the aforementioned analysis, it

reveals the efficiency mechanism of the DF buck converter.


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Chapter--2 (Basics of DC to DC Converters):

2.1 Introduction:

A dc-to-dc converter is used to change the dc voltage from one level to another. In this

case, the dc input voltage is fixed and the level of the dc output voltage depends upon the

converters topology. The dc output voltage can be higher or lower than the input voltage since

the advent of diodes; the techniques have been developed to obtain the dc voltage from the time-

varying sinusoidal (ac) supply. The half-wave rectifier and the bridge rectifier are used to obtain

dc voltage from a single-phase time-varying source. To control the ripple of the rectified output

voltage, large capacitor filters are used. These circuits now referred to as the linear regulators,

operate at the frequency of the ac voltage, which is usually either 50 Hz or 60 Hz. Until about

two or three decades ago, the linear regulators were the only reliable methods to meet all dc

requirements. Some of the major problems associated with the linear regulator is its size and

weight of its components such as the transformer. The voltage regulator element in these circuits

has a comparatively high voltage across its terminals and dissipates large amounts of power,

which results in low efficiency. For this very reason, the use of linear regulators is now limited to

low power applications.

As the power semiconductor devices became more reliable and efficient in their

operation, the switched mode power supplies came into existence. In the design of these power

supplies, the semiconductor devices are either switched on or switched off. Due to the low

voltage drop across the semiconductor device when it is on, its power consumption is low. For

this reason, the switched mode power supplies are highly efficient. Since the switching action,

which simply means to turn a power semiconductor device either on or off, is usually done at

high frequencies, the relative size and weight of the components needed for its design is

comparatively small. In this chapter, our aim is to obtain a dc output voltage, which may be

higher or lower, from a fixed dc input voltage.

A very simple scheme that illustrates the principle is shown in Figure. In this case, the dc

voltage applied to the resistor is controlled via a switch, which is usually a power semiconductor

device such as an SCR, a BJT, a MOSFET, an IGBT, etc.


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Fig.2.1.1 Simple DCDC Converter

switch is closed for a fraction of the time period T and is kept open for the remainder period. Let

us say that the switch is turned on at t = 0 and rem

on time

the duty cycle. The output voltage obtained by opening and closing of the switch is shown in

Figure 2.1.1

Fig:2.1.2: output voltage as a function of time

The time during which the switch remains closed is customarily referred to as the off time(period). We can express the off time in terms of the duty cycle as Toff= (1-D) T.

2..1.1

The average output voltage may be computed as

2.1.2

Substituting, D = Ton/T, the output voltage in terms of the duty cycleis

V0= D Vs 2.1.3

In this case, the output voltage is directly proportional to the duty cycle. It is

therefore evident that the output voltage is less than the input voltage. For an ideal switch, the

efficiency of the dc-to-dc converter is 100%. This simple circuit can be designed to meet the dc


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output-voltage requirements. However, it has one major drawback. Its percent voltage ripple is

100%. The output voltage with such a high ripple content may be satisfactory for electric heaters,

light dimming circuits, etc., it is certainly not suitable for the operation of amplifiers and other

circuits requiring almost constant dc voltage. The high voltage ripple can be controlled by

placing a capacitor across the load.

The capacitor is large enough so that its voltage does not have any noticeable

change during the time the switch is off. Somewhat better circuit can be developed by including

an inductor, which is in series with the switch when the switch is on (closed), to limit the current

in rush. However, this creates another problem. Since the current in the inductor cannot change

suddenly, we have to provide at least one more switch, such a freewheeling diode, to provide a

path for the inductor current when the switch is off (open). In summary, a good dc-to-dc

converter may have, an inductor, a capacitor, and a freewheeling diode, and an electronic switch.

The placement of these elements in a circuit dictates the performance of the circuit. The three

configurations that utilize these circuit elements are (a) Buck Converter (lowering the output

voltage, step-down application), (b) Boost Converter (raising the output voltage, step-up

application), and (c) Buck-Boost Converter (lowering or raising the output voltage, step-down or

step up application).

But in these configurations, the energy transfer is not continuous. In the Buck converter,

the energy transfer from the input to the output side occurs when the static switch is in the ON

state. In the Boost Buck-Boost converters, this transfer takes place when the static switch is

turned OFF. We overcome this limitation by providing adequate filtering. The filter consists of

energy storage elements such as an inductor or capacitor or both, which serve as reservoirs of

energy and ensure that the flow of energy into the load is continuous and ripple-free

In contrast to the above, three more configurations were developed in which

energy transfer from input to the output occurs both during the ON time and the OFF time of the

static switch. They are: Cuk converter, Sepic converter, Zeta converter.

The converter has been realized using lossless elements. To the extent that they

are ideal, the inductor, capacitor, and switch do not dissipate power. Hence, the efficiency of the

converter approaches 100%. But in real case, none of the components are ideal, therefore to

reach the real efficiency of the DC-DC converter the losses of each component should be


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considered. Duty ratio D is the control parameter in DC-DC converter electronics. In most cases, D is

adjusted to regulate the output voltage, Vout.

2.1.1 Types of DC to DC Converters:

Buck Converter

Boost Converter

BuckBoost Converter

Cuk Converter

Buck converter:

A buck converter is astep-downDC to DC converter.Its design is similar to the

step-up boost converter, and like the boost converter it is a switched-mode power supply that

uses two switches (a transistor and a diode) and an inductor and a capacitor.

The simplest way to reduce a DC voltage is to use a voltage dividercircuit, but

voltage dividers waste energy, since they operate by bleeding off excess power as heat; also,

output voltage isn't regulated (varies with input voltage). A buck converter, on the other hand,

can be remarkably efficient (easily up to 95% for integrated circuits) and self-regulating, making

it useful for tasks such as converting the 12-24V typical battery voltage in a laptop down to the

few volts needed by the processor.

Buck Converter Operation:

(a) Buck Converter circuit

(b) On state, when the switch is closed
http://en.wikipedia.org/w/index.php?title=Step-down&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Step-down&action=edit&redlink=1http://en.wikipedia.org/wiki/DC_to_DC_converterhttp://en.wikipedia.org/wiki/DC_to_DC_converterhttp://en.wikipedia.org/wiki/DC_to_DC_converterhttp://en.wikipedia.org/wiki/Boost_converterhttp://en.wikipedia.org/wiki/Boost_converterhttp://en.wikipedia.org/wiki/Switched-mode_power_supplyhttp://en.wikipedia.org/wiki/Switched-mode_power_supplyhttp://en.wikipedia.org/wiki/Voltage_dividerhttp://en.wikipedia.org/wiki/Voltage_dividerhttp://en.wikipedia.org/wiki/Voltage_dividerhttp://en.wikipedia.org/wiki/Switched-mode_power_supplyhttp://en.wikipedia.org/wiki/Boost_converterhttp://en.wikipedia.org/wiki/DC_to_DC_converterhttp://en.wikipedia.org/w/index.php?title=Step-down&action=edit&redlink=1


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(c) Off-state, when the switch is open

Fig 2.1.3: The two circuit configurations of a Buck converter: (a)On state, when the switch is closed,

and (c) Off-state, when the switch is open.

The operation of the buck converter is fairly simple, with an inductorand two switches

(usually atransistorand adiode)that control the inductor. It alternates between connecting the

inductor to source voltage to store energy in the inductor and discharging the inductor into the

load.

Fig 2.1.4: Naming conventions of the components, voltages and current of the Buck converter.

Continuous mode:

A Buck converter operates in continuous mode if the current through the inductor (IL)

never falls to zero during the commutation cycle. In this mode, the operating principle is

described by the chronogram in figure 2.1.5
http://en.wikipedia.org/wiki/Inductorhttp://en.wikipedia.org/wiki/Inductorhttp://en.wikipedia.org/wiki/Transistorhttp://en.wikipedia.org/wiki/Transistorhttp://en.wikipedia.org/wiki/Transistorhttp://en.wikipedia.org/wiki/Diodehttp://en.wikipedia.org/wiki/Diodehttp://en.wikipedia.org/wiki/Diodehttp://en.wikipedia.org/wiki/Diodehttp://en.wikipedia.org/wiki/Transistorhttp://en.wikipedia.org/wiki/Inductor


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Fig 2.1.5: Voltages & currents waveforms with time in an ideal Buck converter

continuous mode

When the switch pictured above is closed, the voltage across the inductor is VL= Vi Vo.

The current through the inductor rises linearly. As the diode is reverse-biased by the

voltage source V, no current flows through it;

When the switch is opened, the diode is forward biased. The voltage across the inductor

is VL= Vo(neglecting diode drop). The current ILdecreases.

The energy stored in inductor L is

E =

L I 2.1.4

Therefore, it can be seen that the energy stored in L increases during On-time (as IL

increases) and then decrease during the Off-state. L is used to transfer energy from the input to

the output of the converter.

The rate of change of ILcan be calculated from:

V = L

2.1.5

With VLequal to Vi Voduring the On-state and to Voduring the Off-state. Therefore, the

increase in current during the On-state is given by:

I =

dt =

. 2.1.6

Identically, the decrease in current during the Off-state is given by:

ILoff = VLL

toff0 dt =

V0.toffL 2.1.7

If we assume that the converter operates in steady state, the energy stored in each

component at the end of a commutation cycle T is equal to that at the beginning of the cycle.

That means that the current ILis the same at t=0 and at t=T (see figure 2.2.3).


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Therefore,

I I = 0 2.1.8

So we can write from the above equations as:

.

. = 0 2.1.9

It is worth noting that the above integrations can be done graphically: In figure 4, is

proportional to the area of the yellow surface, and to the area of the orange surface, as

these surfaces are defined by the inductor voltage (red) curve. As these surfaces are simple

rectangles, their areas can be found easily: for the yellow rectangle and

for the orange one. For steady state operation, these areas must be equal.

As can be seen on figure 3, ton= DT toff= D DT. D is a scalar called the duty cycle with a

value between 0 and 1. This yields:

Vi V. D. T V. T D . T = 0 2.1.10This equation above can be rewritten as: V0= D.Vi 2.1.11

That yields a duty cycle being:

2.1.12

From this equation, it can be seen that the output voltage of the converter varies linearly

with the duty cycle for a given input voltage. As the duty cycle D is equal to the ratio between t on

and the period T, it cannot be more than 1. Therefore, . This is why this converter is

referred to as step-down converter.

So, for example, stepping 12v down to 3v (output voltage equal to a fourth of the input

voltage) would require a duty cycle of 25%, in our theoretically ideal circuit.


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Discontinuous mode:

In some cases, the amount of energy required by the load is small enough to be

transferred in a time lower than the whole commutation period. In this case, the current through

the inductor falls to zero during part of the period. The only difference in the principle described

above is that the inductor is completely discharged at the end of the commutation cycle. This has,

however, some effect on the previous equations.

Fig 2.1.6: Voltages and currents with time in an ideal Buck converter discontinuous mode .

We still consider that the converter operates in steady state. Therefore, the energy in the

inductor is the same at the beginning and at the end of the cycle (in the case of discontinuous

mode, it is zero). This means that the average value of the inductor voltage (V L) is zero, i.e., that

the area of the yellow and orange rectangles in figure 2.1.6 are the same. This yields:

Vi V. D. T V. . T = 0 2.1.13So the value of is:

= 2.1.14


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The output current delivered to the load (Io) is constant; as we consider that the output

capacitor is large enough to maintain a constant voltage across its terminals during a

commutation cycle. This implies that the current flowing through the capacitor has a zero

average value. Therefore, we have:

IL= I0 2.1.15

Where is the average value of the inductor current. As can be seen in figure 2.2.6, the inductor

current waveform has a triangular shape. Therefore, the average value of I L can be sorted out

geometrically as follow:

I = Imx . D . T Imx . . T

=

mx+ = I 2.1.16

The inductor current is zero at the beginning and rises during t Onup to ILmax. That means that

ILmaxis equal to:

Imx =

D. T 2.1.17

Substituting the value of ILmaxin the previous equation leads to:

I = . +2L 2.1.18

Substituting in the above expression yields:

I =. +

2L

2.1.19

This latter expression can be written as:


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V = Vi ...

+ 2.1.20

It can be seen that the output voltage of a Buck converter operating in discontinuous

mode is much more complicated than its counterpart of the continuous mode. Furthermore, the

output voltage is now a function not only of the input voltage (Vi) and the duty cycle D, but also

of the inductor value (L), the commutation period (T) and the output current (I o).

2.2 Average model of buck converter with the added CCS:

The topology of a conventional buck converter In the steady state, the input (u in) and the

output (uin) of the converter are governed by

Uo = D Uin (2.2.1)

Fig: 2.3.1 Average model of buck converter with the added CCS

where D is the duty ratio .If the buck converter works in the continuous conduction mode, then

the inductor current iL can be regarded as a current source. In each switching cycle, both the

current flowing through the switch and the voltage across the diode are averaged. The average

model of buck converter is, shown in Fig.(2.3.1), excluding the added controlled current source

(CCS) ILa, and its governing equations are,

IS= D IL (2.2.2)

UD= D Uin (2.2.3)

ISD= (1 D) IL (2.2.4)


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To enhance the steady-state response and the transient response of the buck converter, the

switching frequency shouldbe increased; but higher switching frequency steps up the switching

loss dramatically. An CCS, which is in parallel with the load terminal, is added to tackle this loss

problem. Fig.2 shows such modification.The load current through the active switch is diverted by

the CCS. The currents through the active switch and the diode can be expressed as,

I S= D (IL ILa) (2.2.5)

I'SD=(1D)(ILILa). (2.2.6)

It can be seen from (5) and (6) that when the load current and the CCS are the same, both

the currents through the active switch and the diode are nearly zero.

2.3 Conclusion:

To enhance the steady-state response and the transient response of the buck converter,

the switching frequency shouldbe increased; but higher switching frequency steps up the

switching loss dramatically. An CCS, which is in parallel with the load terminal, is added to

tackle this loss.

But the disadvantage of CCS(controlled current source),which is in parallel with theload terminal causes a circulating current problem. To overcome this problem instead of

ccs the method proposed to use a buck cell working at lower frequency to realize the CCS. The

proposed converter is called the Double Frequency buck converter.


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Chapter-3

3 Proposed double frequency buck converter

3.1Introduction

Improving the efficiency and dynamics of power converters is a concerned tradeoff in

power electronics. The increase of switching frequency can improve the dynamics of power

converters, but the efficiency may be degraded. A double-frequency (DF) buck converter is

proposed to address this concern. This converter is comprised of two buck cells: one works at

high frequency, and another works at low frequency. It operates in a way that current in the high-

frequency switch is diverted through the low-frequency switch. Thus, the converter can operate

at very high frequency without adding extra control circuits. Moreover, the switching loss of the

converter remains small. The proposed converter exhibits improved steady state and transient

responses with low switching loss. An ac small-signal model of the DF buck converter is also

given to show that the dynamics of output voltage depends only on the high-frequency buck cell

parameters, and is independent of the low-frequency buck cell parameters. Simulation and

experimental results demonstrate that the proposed converter greatly improves the efficiency and

exhibits nearly the same dynamics as the conventional high-frequency buck converter

To enhance the steady-state response and the transient response of the buck converter,

the switching frequency shouldbe increased; but higher switching frequency steps up the

switching loss dramatically. For these purpose a novel converter topology used to achieve high

dynamic response and high efficiency of buck-type converters. This topology consists of a high-

frequency buck cell and a low-frequency buck cell; and we call it the double- frequency buck

converter (DF buck)


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3.1.1 Proposed double frequency buck converter:

Fig(3.1.1 )Schematic of the proposed DF buck converter.

The proposed converter is called the Double Frequency(DF) buck converter, because

these buck cells work at two different frequencies. Schematic of this DF buck converter is shown

in Fig. 3.1.1.

The cell containing L, S , and SD works at higher frequency, and is called the high-

frequency buck cell. Another cell containing La, Sa, and Da works at lower frequency, and is

called the low-frequency buck cell. The high frequency buck cell is used to enhance the output

performance, and the low-frequency buck cell to improve the converter efficiency. An active

switch, instead of a diode as in the conventional unidirectional buck converter, is employed to

realize SDin the high frequency buck cell. This active switch transfers the energy stored in the

low-frequency cell to the source during the transient stage of load step-down. It works

complementarily with high-frequency cell stage of load step-down. It works complementarily

with high-frequency cell switch S , and improves the transient response.

The switch S is controlled to operate at the high frequency fh, and the corresponding

switching period is Tsh. On the other hand, the switch Sa is controlled to work at a low

frequency fl,and the corresponding switching period is Tsl. Assume that the high frequency is an

integer multiples of the low frequency, i.e.,

fh= M f1. (3.1.1)

At each low-frequency cycle, four switching states exist Table I lists the switching

states according to the status of switches S and Sa The state a denotes that both switches S and Sa


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are on. The equivalent circuit is shown in Fig.3.1.2(a). In a similar manner, the equivalent

circuits of states b, c, and d are shown in Fig.3.1.2(b)(d), respectively.

TABLE I

SWITCHING STATES

State

Active Switches

S Sa

a ON ON

b OFF ON

c ON OFF

d OFF OFF

State a:

Fig 3.1.2(a) Equivalent circuit of DF buck converter when s-on,sa=on.

In this state, the voltage uLacross the inductor L is positive, and the voltage uLaacross

Lais zero. Hence, the current iLflowing throughL rises, and the current iLaflowing throughLa

does not change.

The governing equations of statea are expressed as

uL = Uin U0 (3.1.2)

i =

u =

(3.1.3)

uLa = 0 (3.1.4)


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i =

= 0 (3.1.5)

State b :

Fig 3.1.2(b) Equivalent circuit of DF buck converter when s-off,sa=on;

At this state, the voltage uL across L is negative, so the current iL decreases. The

voltage uLaacross Lais positive, and the current iLa flowing through Larises.

The governing equations of state b can be described by

uL = -U0 (3.1.6)

i =

u =

(3.1.7)

uLa = Uin (3.1.8)

i =

u

= (3.1.9)

State c:

Fig 3.1.2(c) Equivalent circuit of DF buck converter when s=on, sa=off;


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The voltage uLacross L is positive, so the current iLrises. Since the voltage uLaacross La

is negative, the current iLathrough Ladecreases.

In state c, the equivalent circuit equations are derived as,

uL = Uin U0 (3.1.10)

i =

u =

(3.1.11)

uLa = - Uin (3.1.12)

i =

=

(3.1.13)

State d:

Fig 3.1.2(d) Equivalent circuit of DF buck converter when s-off, sa=off;

In state d, the equivalent circuit equations are derived as

uL= - U0 (3.1.14)

i =

u =

(3.1.15)

ULa= 0 (3.1.16)

i =

= 0 (3.1.17)

The voltage uLacross L is negative, so the current iLflowing throughL decreases. The

voltage uLaacross Lais zero, and the current iLaflowing throughLaremains the same.

The current iLaflowing throughLaremains the same cell does not affect the output

inductor voltage, which has the same waveform and value as that of the conventional buck

converter. That is, the voltage across the output inductor is U in Uowhen the switch is on, and is

Uowhen the switch is off. The voltage and current waveforms of DF buck in one low frequency


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cycle Tslare shown in Fig. 5, where M = 4. In the conduction mode of low-frequency switch, the

voltage across the low-frequency inductor La alternates between zero and Uin.

Thus, the equivalent slope of the current iLais positive. At the switch-off interval, uLa

varies from zero to Uin, the equivalent slope of iLabecomes negative. As a result, if we employ

proper control method, the low-frequency inductor can be controlled to follow the output

inductor current.

Fig3.1.3: Voltage and current waveforms in one switching period Tsl.


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3.2 Performance evaluation of double frequency buck converter:

The current programmed mode (CPM) control circuit used to control the proposed DF

buck converter is shown in Fig.3.2.1. In the control diagram, the output voltage is fed back and

compared with Uref. The quantity Rf ic is used as the current reference for the buck cells. The

currents flowing through inductorsL and La are expected to be equal to this reference value in

the steady state. The low-frequency buck cell diverts the current flowing through high-frequency

switches S and SD. This control circuit, like standard current mode control, does not need

additional load transient information, which is not the case in other methods.

Since no specific control circuit is required, complexity of the control circuitryof the DF

buck converter is similar to that of the conventional buck converter. The implementation is

simple and can be done by commercial CPM chips.

Fig 3.2.1 current programmed mode control circuit


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3.2.1 Steady state performance:

Performance of the DF buck converter is evaluated by looking at the steady-state and

transient responses of three circuits a DF buck, a single high-frequency buck converter whose

switching frequency is the same as the higher frequency of DF buck, and a single low-frequency

buck converter whose switching frequency is equal to the lower frequency of DF buck.

Parameters used in the simulation are

uin= 48 V, Uo= 10 V, C= 470 F

DF buck : L = 100 H, La= 1 mH, fl= 10 kHz

fh= 100 kHz

High-frequency buck : L = 100 H, f= 100 kHz

Low-frequency buck : La= 1 mH, f= 10 kHz.

In the steady state we can observe that output voltage waveforms of various buck

converters. It can be seen that the steady state performance of DF buck and that of single high-

frequency buck converter are almost the same

3.2.2 Transient Performance Analysis

This section investigates the transient response of the DF buck converter. If the load

resistance is reduced from 2R to R, the load current will increase from 0.5 IR to IR. Since the

currents through inductor L and Lacannot change abruptly, at this transient instant, the output

voltage decreases due to the increased load current that is partially supplied by the output

capacitor. The feedback control loop regulates the duty ratio of each buck cell to control the

current of inductor L, iL, and the current of La, iLa. It increases the duty ratio of the high

frequency switch so that iL rises Then, iLa rises too. Note that the low-frequency inductance is

selected to be larger than the high-frequency one to reduce the current ripple of iLa.


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If the inductor has larger inductance, the current flowing through it will have

lower dynamic response speed with the same voltage excitation. As shown in Fig. 5, when low-

frequency switch is on, the average voltage applied to low-frequency inductor is(1d) times the

input voltage Uin. This is the same as the voltage across the high-frequency inductor, U inUo ,

when high-frequency switch is on. On the other hand, when the low-frequency switch is off, the

average voltage across low frequency inductor is dtimes Uin. This average voltage is also the

same as that across the high-frequency inductor when high-frequency switch is off. Hence, i La

rises slower than iL. Moreover, the current through the high-frequency switch increases

momentarily, but soon back to the steady state level due to the current feedback loop.

If the load resistance is increased from R to 2R, then the load current will

decrease from IRto 0.5 IR, so is the low-frequency inductor current iLa. At this moment, iLacan

freewheel through SDwhen the switch S is off. When S is on, the energy stored in La can be fed

back to the source via the switch S .

As a result, the impact to output response by the low-frequency inductor is

largely alleviated. it is observed that the DF buck and the single high-frequency buck converters

exhibit almost the same transient responses during load changing, and much better than the

single low-frequency buck converter does. The effect of switch current diversion of the high-

frequency cell and the low frequency cell is also investigated

3.3 Proposed double frequency buck converter fed with dc motor

Dc motor has good speed control respondence, wide speed control

range. It is widely used in speed control systems which need high control requirements, such as

rolling mill, double-hulled tanker, and high precision digital tools. When it needs control the

speed stepless and smoothness, the mostly used way is to adjust the armature voltage of motor.

One of the most common methods to drive a dc motor is by using PWM signals with respect to

the motor input voltage. However, the underlying hard switching strategy causes unsatisfactory

dynamic behavior. The resulting trajectories exhibit a very noisy shape. This causes large forces

acting on the motor mechanics and also large currents which detrimentally stress the electronic

components of the motor as well as of the power supply. Since it is usually necessary to add a

power supply component, anyway, this contribution shall present a control for the entire system


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of buck-converter/dc motor. The combination of dc to dc power converters with dc motors has

been reported.

In particular, the composition of a buck converter with a dc motor has been proposed. The buck

type switched dc to dc converter is well known in power-electronics. Due to the fact that the

converter contains two energy storing elements, a coil and a capacitor, smooth dc output voltages

and currents with very small current ripple can be generated. The control issue of the

converter/motor is to design the controller so that the dc motor can track a prescribed trajectory

velocity precisely with minimum error. In order to achieve these objectives, various methods

using different technique have been proposed. DC machines are extensively used in many

industrial a pplications such as servo control and traction tasks due to their effectiveness,

robustness and the traditional relative ease in the devising of appropriate feedback control

schemes, especially those of the PI and PID types. The increasing availability of feedback

controller design techniques and the rapid development of circuit simulations programs, such as

PSpice, offer much wider possibilities to analyze, and redesign, currently used dc motor drive

systems.. The smooth trajectory input track ing using dynamic feedback controller for buck-

converter

3.3.1 Buck-converter Driven Dc Motor System:

The simplified model of the overall system buck-converter driven dc motor is shown in Figure 1.

The switching devices have been replaced by an ideally switched volta ge source. This isindicated by the multiplication of Ue with the switching variable An additional resistance R L

coil windings. The motor has been modeled by an inductance L M with ohmic resistance R M

and electromagnetic voltage source K E An input voltage U e has been used which value is

equal to the maximum voltage of the dc motor. In this st udy, the buck converter circuit with coil

inductance, L, coil resistance, R L and capacitance, C is considered.


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3.3.2 Modelling of Buck-converter Dc Motor System:

This section provides a brief description on the modelling of the buck-converter driven dc motor,

as a basis of a simulation environment for development and assessment of the proposed control

techniques. The dynamic system composed from converter/motor is considered in this

investigation and derived in the transfer function and state-space forms. Considering the dynamic

system of the convert er/motor, the system can be modelled as

Advantages of DC motor:

Ease of control

Deliver high starting torque

Near-linear performance

Disadvantages:

High maintenance

Large and expensive (compared to induction motor)

Not suitable for high-speed operation due tocommutator and brushes

Not suitable in explosive or very clean Environment


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CHAPTER-4

MATLAB

Matlab is a high-performance language for technical computing. It integrates

computation, visualization, and programming in an easy-to-use environment where problems and

solutions are expressed in familiar mathematical notation. Typical uses include Math and

computation Algorithm development Data acquisition Modeling, simulation, and prototyping

Data analysis, exploration, and visualization Scientific and engineering graphics Application

development, including graphical user interface building.

Matlab is an interactive system whose basic data element is an array that does not require

dimensioning. This allows you to solve many technical computing problems, especially those

with matrix and vector formulations, in a fraction of the time it would take to write aprogram in

a scalar no interactive language such as C or Fortran.

The name matlab stands for matrix laboratory. Matlab was originally written to provide

easy access to matrix software developed by the linpack and eispack projects. Today, matlab

engines incorporate the lapack and blas libraries, embedding the state of the art in software for

matrix computation.

Matlab has evolved over a period of years with input from many users. In university

environments, it is the standard instructional tool for introductory and advanced courses in

mathematics, engineering, and science. In industry, matlab is the tool of choice for high-

productivity research, development, and analysis.

Matlab features a family of add-on application-specific solutions called toolboxes. Very

important to most users of matlab, toolboxes allow you to learn and apply specialized

technology. Toolboxes are comprehensive collections of matlab functions (M-files) that extend

the matlab environment to solve particular classes of problems. Areas in which toolboxes are

available include signal processing, control systems, neural networks, fuzzy logic, wavelets,

simulation, and many others.

The matlab system consists of five main parts:


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Development Environment. This is the set of tools and facilities that help you use matlab

functions and files. Many of these tools are graphical user interfaces. It includes the matlab

desktop and Command Window, a command history, an editor and debugger, and browsers for

viewing help, the workspace, files, and the search path.

The matlab Mathematical Function Library. This is a vast collection of computational

algorithms ranging from elementary functions, like sum, sine, cosine, and complex arithmetic, to

more sophisticated functions like matrix inverse, matrix eigenvalues, Bessel functions, and fast

Fourier transforms.

The matlab Language. This is a high-level matrix/array language with control flow

statements, functions, data structures, input/output, and object-oriented programming features. It

allows both "programming in the small" to rapidly create quick and dirty throw-away programs,

and "programming in the large" to create large and complex application programs.

Matlab has extensive facilities for displaying vectors and matrices as graphs, as well as

annotating and printing these graphs. It includes high-level functions for two-dimensional and

three-dimensional data visualization, image processing, animation, and presentation graphics. It

also includes low-level functions that allow you to fully customize the appearance of graphics as

well as to build complete graphical user interfaces on your matlab applications.

The matlab Application Program Interface (API). This is a library that allows you to

write C and Fortran programs that interact with matlab. It includes facilities for calling routines

from matlab (dynamic linking), calling matlab as a computational engine, and for reading and

writing MAT-files.


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4.1 SIMULINK:

INTRODUCTION:

Simulink is a software add-on to matlab which is a mathematical tool developed by The

Math works,(http://www.mathworks.com) a company based in Natick. Matlab is powered by

extensive numerical analysis capability. Simulink is a tool used to visually program a dynamic

system (those governed by Differential equations) and look at results. Any logic circuit, or

control system for a dynamic system can be built by using standard building blocks available in

Simulink Libraries. Various toolboxes for different techniques, such as Fuzzy Logic, Neural

Networks, dsp, Statistics etc. are available with Simulink, which enhance the processing power

of the tool. The main advantage is the availability of templates / building blocks, which avoid the

necessity of typing code for small mathematical processes.

CONCEPT OF SIGNAL AND LOGIC FLOW:

In Simulink, data/information from various blocks are sent to another block by lines

connecting the relevant blocks. Signals can be generated and fed into blocks dynamic /

static).Data can be fed into functions. Data can then be dumped into sinks, which could be

scopes, displays or could be saved to a file. Data can be connected from one block to another,

can be branched, multiplexed etc. In simulation, data is processed and transferred only at

Discrete times, since all computers are discrete systems. Thus, a simulation time step (otherwise

called an integration time step) is essential, and the selection of that step is determined by the

fastest dynamics in the simulated system.


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Fig4.1 Simulink library browser


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4.2 CONNECTING BLOCKS:

Fig 4 .2 Connectung blocks

To connect blocks, left-click and drag the mouse from the output of one block to the

input of another block.

4.2.1 SOURCES AND SINKS:

The sources library contains the sources of data/signals that one would use in a dynamic

system simulation. One may want to use a constant input, a sinusoidal wave, a step, a repeating

sequence such as a pulse train, a ramp etc. One may want to test disturbance effects, and can use

the random signal generator to simulate noise. The clock may be used to create a time index for

plotting purposes. The ground could be used to connect to any unused port, to avoid warning

messages indicating unconnected ports.


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The sinks are blocks where signals are terminated or ultimately used. In most cases, we

would want to store the resulting data in a file, or a matrix of variables. The data could be

displayed or even stored to a file. the stop block could be used to stop the simulation if the input

to that block (the signal being sunk) is non-zero. Figure 3 shows the available blocks in the

sources and sinks libraries. Unused signals must be terminated, to prevent warnings about

unconnected signals.

Fig.4.2.1 Sources and sinks


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4.3 CONTINUOUS AND DISCRETE SYSTEMS:

All dynamic systems can be analyzed as continuous or discrete time systems. Simulink

allows you to represent these systems using transfer functions, integration blocks, delay blocks

etc.

Fig.4.3 Continous and descrete systems


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4.3.1 NON-LINEAR OPERATORS:

A main advantage of using tools such as Simulink is the ability to simulate non-linearsystems and arrive at results without having to solve analytically. It is very difficult to arrive at

an analytical solution for a system having non-linearities such as saturation, signup function,

limited slew rates etc. In Simulation, since systems are analyzed using iterations, non-linearities

are not a hindrance. One such could be a saturation block, to indicate a physical limitation on a

parameter, such as a voltage signal to a motor etc. Manual switches are useful when trying

simulations with different cases. Switches are the logical equivalent of if-then statements in

programming.

Fig.4.3.1 simulink blocks


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4.3.2 MATHEMATICAL OPERATIONS:

Mathematical operators such as products, sum, logical operations such as and, or, etc.

.can be programmed along with the signal flow. Matrix multiplication becomes easy with the

matrix gain block. Trigonometric functions such as sin or tan inverse (at an) are also available.

Relational operators such as equal to, greater than etc. can also be used in logic circuits

Fig4.3.2 Simulink math blocks


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4.3.3 SIGNALS & DATA TRANSFER:

In complicated block diagrams, there may arise the need to transfer data from one portion

to another portion of the block. They may be in different subsystems. That signal could be

dumped into a goto block, which is used to send signals from one subsystem to another.

Multiplexing helps us remove clutter due to excessive connectors, and makes

matrix(column/row) visualization easier.

Fig4..3.3 Signals and systems


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4.4 MAKING SUBSYSTEMS

Drag a subsystem from the Simulink Library Browser and place it in the parent blockwhere you would like to hide the code. The type of subsystem depends on the purpose of the

block. In general one will use the standard subsystem but other subsystems can be chosen. For

instance, the subsystem can be a triggered block, which is enabled only when a trigger signal is

received.

Open (double click) the subsystem and create input / output PORTS, which transfer

signals into and out of the subsystem. The input and output ports are created by dragging them

from the Sources and Sinks directories respectively. When ports are created in the subsystem,

they automatically create ports on the external (parent) block. This allows for connecting the

appropriate signals from the parent block to the subsystem.

4.4.1 SETTING SIMULATION PARAMETERS:

Running a simulation in the computer always requires a numerical technique to solve a

differential equation. The system can be simulated as a continuous system or a discrete system

based on the blocks inside. The simulation start and stop time can be specified. In case of

variable step size, the smallest and largest step size can be specified. A Fixed step size is

recommended and it allows for indexing time to a precise number of points, thus controlling the

size of the data vector. Simulation step size must be decided based on the dynamics of the

system. A thermal process may warrant a step size of a few seconds, but a DC motor in the

system may be quite fast and may require a step size of a few milliseconds.

Fig:4.4.1setting simulation parameters:


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Chapter-5

5 Simulation Results:

5.1 Introduction:

A proportional-integral controller (PI controller) is a generic control loop feedback

mechanism widely used in industrial control systems. A PI controller attempts to correct the

error between a measured process variable and a desired set point by calculating and then

outputting a corrective action that can adjust the process accordingly.

The PI controller calculation involves two parameters; the Proportional, the Integral

values. The Proportional value determines the reaction to the current error, the Integraldetermines the reaction based on the sum of recent errors and the Derivative determines the

reaction to the rate at which the error has been changing. The weighted sum of these three

actions is used to adjust the process via a control element such as the position of a control valve

or the power supply of a heating element. By "tuning" the three constants in the PI requirements.

The response of the controller can be described in terms of the controller algorithm the PI can

provide control action designed for specific process responsiveness of the controller to an error,

the degree to which the controller overshoots the set point and the degree of system oscillation.

5.2 PI controllers:

5.2.1 Proportional term:

The proportional term makes a change to the output that is proportional to the current

error value. The proportional response can be adjusted by multiplying the error by a constant Kp,

called the proportional gain.

The proportional term is given by:

Pout= Kpe(t) (4.1)

Where

Pout: Proportional output


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Kp : Proportional Gain, a tuning parameter

e : Error = SPPV

t : Time or instantaneous time (the present)

A high proportional gain results in a large change in the output for a given change in the

error. If the proportional gain is too high, the system can become unstable (See the section on

Loop Tuning) In contrast, a small gain results in a small output response to a large input error,

and a less responsive (or sensitive) controller. If the proportional gain is too low, the control

action may be too small when responding to system disturbances.

In the absence of disturbances pure proportional control will not settle at its target value,

but will retain a steady state error that is a function of the proportional gain and the process gain.

Despite the steady-state offset, both tuning theory and industrial practice indicate that it is the

proportional term that should contribute the bulk of the output change.

5.2.2 Integral term:

The contribution from the integral term is proportional to both the magnitude of the error

and the duration of the error. Summing the instantaneous error over time (integrating the error)

gives the accumulated offset that should have been corrected previously. The accumulated error

is then multiplied by the integral gain and added to the controller output. The magnitude of the

contribution of the integral term to the overall control action is determined by the integral gain,

Ki.

The integral term is given by:

I out=K

Where

Iout: Integral output

Ki : Integral Gain, a tuning parameter

e : Error = SP PV

: Time in the past contributing to the integral response


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The integral term (when added to the proportional term) accelerates the movement of the

process towards set point and eliminates the residual steady-state error that occurs with a

proportional only controller. However, since the integral term is responding to accumulated

errors from the past, it can cause the present value to overshoot the set point value (cross over the

set point and then create a deviation in the other direction). For further notes regarding integral

gain tuning and controller stability, see the section on Loop Tuning.

The output from the three terms, the proportional, and the integral terms are summed to

calculate the output of the PI controller.

Fig:5.2.1 Discrete PI controller

First estimation is the equivalent of the proportional action of a PI controller. The integralaction of a PI controller can be thought of as gradually adjusting the output when it is almost

right. Derivative action can be thought of as making smaller and smaller changes as one gets

close to the right level and stopping when it is just right, rather than going too far. Making a

change that is too large when the error is small is equivalent to a high gain controller and will

lead to overshoot. If the controller were to repeatedly make changes.


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Those were too large and repeatedly overshoot the target, this control loop would be

termed unstable and the output would oscillate around the set point in either a constant, a

growing or a decaying sinusoid. A human would not do this because we are adaptive controllers,

learning from the process history, but PI controllers do not have the ability to learn and must be

set up correctly. Selecting the correct gains for effective control is known as tuning the

controller.

If a controller starts from a stable state at zero error (PV = SP), then further changes by the

controller will be in response to changes in other measured or unmeasured inputs to the process

that impact on the process, and hence on the PV. Variables that impact on the process other than

the MV are known as disturbances and generally controllers are used to reject disturbances

and/or implement set point changes.

In theory, a controller can be used to control any process which has a measurable output

(PV), a known ideal value for that output (SP) and an input to the process (MV) that will affect

the relevant PV. Controllers are used in industry to regulate temperature, pressure, flow rate,

chemical composition, level in a tank containing fluid, speed and practically every other variable

for which a measurement exists. Automobile cruise control is an example of a process outside of

industry which utilizes automated control. Kp: Proportional Gain - Larger Kp typically means

faster response since the larger the error, the larger the feedback to compensate. An excessively

large proportional gain will lead to process instability. Ki: Integral Gain Larger Kiimplies steady

state errors are eliminated quicker. The trade-off is larger overshoot: any negative error

integrated during transient response must be integrated away by positive error before we reach

steady state. Kd: Derivative Gain - Larger Kd decreases overshoot, but slows down transient

response and may lead to instability

5.2.3 Loop tuning:

If the PI controller parameters (the gains of the proportional, integral terms) are chosen

incorrectly, the controlled process input can be unstable, i.e. its output diverges, with or without

oscillation, and is limited only by saturation or mechanical breakage. Tuning a control loop is the

adjustment of its control parameters (gain/proportional band, integral gain/reset) to the optimum

values for the desired control response.


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Some processes must not allow an overshoot of the process variable beyond the set point

if, for example, this would be unsafe. Other processes must minimize the energy expended in

reaching a new set point. Generally, stability of response (the reverse of instability) is required

and the process must not oscillate for any combination of process conditions and set points.

Some processes have a degree of non-linearity and so parameters that work well at full-load

conditions don't work when the process is starting up from no-load. This section describes some

traditional manual methods for loop tuning.

There are several methods for tuning a PI loop. The most effective methods generally

involve the development of some form of process model, and then choosing P, I, based on the

dynamic model parameters. Manual "tune by feel" methods have proven time and again to be

inefficient, inaccurate, and often dangerous. The choice of method will depend largely on

whether or not the loop can be taken "offline" for tuning, and the response time of the system. If

the system can be taken offline, the best tuning method often involves subjecting the system to a

step change in input, measuring the output as a function of time, and using this response to

determine the control parameters.


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If the system must remain online, one tuning method is to first set the I value to zero.

Increase the P until the output of the loop oscillates, and then the P should be left set to be

approximately half of that value for a "quarter amplitude decay" type response. Then increase I

until any offset is correct in sufficient time for the process. However too much I will cause

instability. Finally, increase D, if required, until the loop is acceptably quick to reach its

reference after a load disturbance. However too much D will cause excessive response and

overshoot. A fast PI loop tuning usually overshoots slightly to reach the set point more quickly;

however, some systems cannot accept overshoot, in which case a "critically damped" tune is

required, which will require a P setting significantly less than half that of the P setting causing

oscillation.


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5.2.4 Limitations of PI control

While PI controllers are applicable to many control problems, they can perform poorly

in some applications. PI controllers, when used alone, can give poor performance when the PI

loop gains must be reduced so that the control system does not overshoot, oscillate or "hunt"

about the control set point value. The control system performance can be improved by

combining the PI controller functionality with that of a Feed-Forward control output as described

in Control Theory. Any information or intelligence derived from the system state can be "fed

forward" or combined with the PI output to improve the overall system performance. The Feed-

Forward value alone can often provide a major portion of the controller output. The PI controller

can then be used to respond to whatever difference or "error" that remains between the controller

set point and the feedback value. Since the Feed-Forward output is not a function of the process

feedback, it can never cause the control system to oscillate, thus improving the system response

and stability.

Another problem faced with PI controllers is that they are linear. Thus, performance of PI

controllers in non-linear systems (such as HVAC systems) is variable. Often PI controllers are

enhanced through methods such as gain scheduling or fuzzy logic. Further practical application

issues can arise from instrumentation connected to the controller. A high enough sampling rate

and measurement precision and measurement accuracy (more relevant to FF and MPC).

A problem with the differential term is that small amounts of measurement or process

noise can cause large amounts of change in the output. Sometimes it is helpful to filter the

measurements, with a running average, also known as a low-pass filter. However, low-pass

filtering and derivative control cancel each other out, so reducing noise by instrumentation

means is a much better choice. Alternatively, the differential band can be turned off in most

systems with little loss of control. This is equivalent to using the PI controller as a PID

controller.


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5.3 Simulation:

5.3.1(a) Simulation Model of a Double Frequency Buck Converter.

Fig 5.3.1(a) simulation model of a double frequency buck converter


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5.3.1(b) simulation model of a high frequency buck converter:

Fig5.3.1 (b) simulation model of a high frequency buck converter


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5.3.1(C) simulation model of a low frequency buck converter:

Fig5.3.1(c) simulation model of a low frequency buck converter

\


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5.3.1(D) Simulation model of a double frequency buck converter fed with dc motor

Fig 5.3.1(d) simulation model of a double frequency buck converter fed with dc motor

Discrete,= 1e-006 .

powergui

v+-

te

To Workspace3

wm

To Workspace2

ia

To Workspace1t

To Workspace

Step

Scope6

Scope3

Scope2

Scope1

Scope

S

R

Q

!Q

S-R

Flip-Flop1

S

R

Q

!Q

S-R

Flip-Flop


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5.3.1(e) Simulation result for double frequency buck converter fed

with dc motor

Fig : 5.3.1(e) Double frequency buck converter fed with dc motor output

armature current ,eletromagentic torque ,speed wave forms


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5.3.2Simulation result:

5.3.2(a) steady state response:

Fig 5.3.2.(b) output voltage steady state response comparison of the double frequency, single

high and low frequency buck converter.

Ripple voltage in double frequency buck converter = 5x104vRipple voltage in single high frequency buck converter = 1x103vRipple voltage in single low frequency buck converter = 1x10v

The output voltage waveforms of various buck converters are shown in Fig. 7.in the above large

magnitudes denote that the low frequency buck converter output voltage in steady state. It can be

seen that the steady state performance of DF buck and that of single high-frequency buck

converter are almost the same.

DF

HF


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5.3.2(b) transient response when load is step up:

Fig 5.3.2.(b)output voltage transient response comparison on of the double frequency, single

high and low frequency buck converter when load is step up

Output voltage Transient response comparison of the double frequency, high frequency and low

frequency buck converter when load is increased from R to 2R as shown in above fig

4.3.2(b).transient response of the double frequency buck converter is same as the transient

response of the single high frequency buck converter.

Lf


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5.3.2(c) transient response when load is step down:

Fig 5.3.2.(c): output voltage transient response comparison of the double frequency, single high

and low frequency buck converter when load is step down

Output voltage Transient response comparison of the double frequency, high frequency andlow frequency buck converter when load is decreased from 2R to R as shown in above fig

4.3.2(c). Transient response of the double frequency buck converter is same as the transient

response of the single high frequency buck converter. In single low frequency transient response

is increased.

Df

Hf

Lf


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5.3.2(d) step change waveforms

Fig 5.3.2(c) step change waveforms of the double frequency buck converter, single high

frequency, and low frequency buck converter.

The above figure shows step change wave forms of the double frequency buck converter, single

high frequency, and low frequency buck converter. Load current is changes when load resistance

is reduced from 4 to 2 .Then the load current will increase from 0.5 IR to IR. (2.5 to 5A).as

shown in above figure.

.

Df

Hf

Lf


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5.3.2(e) switching states of the switches(S, Sd, Sa)

Fig 5.3.2(e) switching states of the high frequency buck cell switches(S, Sd),and low frequency

switch Saof the double frequency buck converter.

The above figure shows the switching states of the high frequency buck cell switches (S,

Sd), and low frequency switch Sa of the double frequency buck converter. That shows high

frequency is 10 times of the low frequency. Where S a is the low frequency switch and its

switching frequency is 10khz, and S, Sd are the high frequency switch and its switching

frequency is 100khz.


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Fig 5.3.2(a): Switch current waveforms.

The current waveforms are shown in Fig. 4.3.2(a). The waveform with large magnitude

denotes the current flowing through the low-frequency switch isa, and the small magnitude is the

current of the high-frequency switch is. The load is changed from 4 to 2 at the 12-ms time

instant. A major portion of the increased load current (shown in Fig. 4.3.2) is diverted to the low-

frequency buck cell, while the current through the high-frequency switch remains the same. The

current diversion enables the reduction of switching loss in high-frequency buck cell and

improves the efficiency.


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5.4 Efficiency Analysis:

In order to analyze the efficiency improvement of the proposed Double Frequency

buck converter, the efficiency expression is analyzed in th

Double Frequency Buck Converter Original

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