Cycloconverters - Musaliar Collegemusaliarcollege.com/ICTEEE/ICTeee.pdf · 2019-06-03 · •Advantage •Disadvantage. INTRODUCTION •A cycloconverter is a device that converts

Cycloconverters

Anjali.S

Asst.Professor,

Dept. of EEE,

MCET

CONTENTS

• Introduction

• Types

• Application

• Advantage

• Disadvantage

INTRODUCTION

• A cycloconverter is a device that converts ACpower at one frequency into AC output power power at a different frequency with a one stage conversion.

• AC to AC conversion

• Force commutation

• Cycloconverters are used in high power applications driving induction and synchronous motors.

Introduction contd….

TYPES

1.Step up cycloconverter ( Fo>Fs )

2.Step down cycloconverter( Fo<Fs )

1.1φ to 1φ Cycloconverter

a. BRIDGE CONFIGURATION

Types Contd….

b.MIDPOINT CONFIGURATION

Types Contd….

2 . 3φ to 1φ Cycloconverter

Types Contd….

Types Contd….

3 . 3φ to 3φ Cycloconverter

Types Contd….

Applications

• Cement mill drives

• Ship propulsion drives

• Rolling mill drives

• Scherbius drives

• Ore grinding mills

• Mine winders

Advantages

• No “DC LINK” required as in case of inverters

to get sine waveforms

• Bidirectional power flow possible.

• Variable firing angle control possible

provides high quality Sine wave at low

frequencies.

filters also gets eliminated

will reduce losses and will increase efficiency.

Disadvantages

• Smooth stepless control of o/p frequency is not

possible.

• More distortion at low frequencies.

• Control circuit is difficult to design and

complex.

• Input power factor is poor at large values of α.

THANK YOU

Prepared By,

Ciya Paulose

Asst.Professor

EEE Dept.,MCET

6/3/2019 1

Outline What is frequency response

Frequency Response PlotsBode and Nyquist (Polar)

Rules for Constructing Bode Plot

6/3/2019 2

What is frequency responseAn important alternative approach to system analysis and design is the frequency response method.

The frequency response of a system is defined as the steady-state response of the system to a sinusoidal input signal. We will investigate the steady-state response of the system to the sinusoidal input as the frequency varies.

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Advantages of the frequency response method

The sinusoidal input signal for various ranges of frequency and amplitude is readily available.

It is the most reliable and uncomplicated method for the experimental analysis of a system.

Control of system bandwidth.

The TF describing the sinusoidal steady-state behaviour of the system is easily obtained by replacing s with jω in the system TF.

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Frequency response plots Polar plot

The TF G(s) can be described in the frequency domain by

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The above equation is used for

the polar plot representation of

the frequency response in the

polar plane.

)(Im)(,)(Re)(where),()()()(

jGXjGRjXRsGjGjs

polar plane

Alternatively, the TF G(jω) can be represented by

)()()()( )( GejGjG jj

)(

)(tan)(,)()()(where 1222

R

XXRG

Frequency response plots (cont’d)

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Consider a simple RC circuit. The

TF of the system is

1

1

)(

)()(

1

2

RCssV

sVsG

The sinusoidal steady-state TF is

RCjRCjjG

1where,

1/

1

1)(

1)( 1

1

The polar plot is obtained from

21

1

2

1

2

1

1

/1

/

/1

1

1/

/1)()()(

j

jjXRjG

To draw the polar plot, R(ω) and

X(ω) at typical frequencies, e.g.,

ω=0, ∞, are to be determined.

polar plot

Example – polar plot

Frequency response plots (cont’d)

Limitations of polar plots:

The addition of poles and zeros requires the recalculation of the frequency response.

The effect of individual poles and zeros is not indicated.

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Bode plot

A more widely used graphical tool to plot frequency response

is the Bode diagram.

)(log20dBin gain cLogarithmi 10 G

)()()( GjG

The TF in the frequency domain can be written as

For a Bode diagram, we normally use

Magnitude versus ω and phase versus ω are plotted separately.

Bode diagramAdvantages of Bode plots:

Multiplication of magnitudes can be converted into addition by virtue of the definition of logarithmic gain.

Straight-line asymptotes are simple to be used for sketching an approximate log-magnitude curve.

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The use of a logarithmic scale for the frequency is a more judicious

choice than a linear scale of frequency as this expands the low

frequency range, which is more important in practical systems.

An interval of two frequencies with a

ratio equal to 10 is called a decade.

The slope of the asymptotic line in the

figure is -20dB/decade.

To draw Bode Plot there are four steps:

1.Rewrite the transfer function in proper form.

2.Separate the transfer function into its constituent parts.

3.Draw the Bode diagram for each part.

4.Draw the overall Bode diagram by adding up the results from part 3.

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1.Rewrite the transfer function in proper form.

Make both the lowest order term in the numerator and denominator unity.

Example 1:

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2.Separate the transfer function into its constituent parts.

The next step is to split up the function into its constituent parts. There are seven types of parts:

1. A constant

2. Poles at the origin

3. Zeros at the origin

4. Real Poles

5. Real Zeros

6. Complex conjugate poles

7. Complex conjugate zeros

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2.Separate the transfer function into its constituent parts.

This function has a constant of 2,

a zero at s=-10, and poles at s=-3 and s=-50.

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Example 2:

3.Draw the Bode diagram for each part.

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3.Draw the Bode diagram for each part.

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Cont’d

Draw Bode Plot Procedure

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n

b

1

s

b

0 dbSlope=

-20n db/dec

Magnitude Phase

-90n°

n

b

s

b

0 dbSlope=

+20n db/dec

Magnitude

Phase

+90n°

n

b

1

s1

Phase0°

-90n°

0.1b

10b

b

0 dbSlope=

-20n db/dec

Magnitude

n

b

s1

Slope=

+20n db/dec

b

0 db

Magnitude Phase

0°

+90n°

0.1b

10b

Draw Bode Plot Procedure

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n2

b b

1

s 1 s1

Q

Phase0°

-180n°

0.1b

10b

b

0 dbSlope=

-40n db/dec

Magnitude

Slope=

+40n db/dec

b

0 db

Magnitude Phase

0°

+180n°

0.1b

10b

n2

b b

s 1 s1

Q

Draw Bode Plot Procedure

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Bode Plot Procedure The following example illustrates this procedure:

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2

1000 s 20 s 200G s

2 s 2 s 50 7500

2 2

2

1) Put in break frequency format:

s200000 s 1

1000 s 20 s 200 10G s

2 s 2 s 100 s 100002 s 2 s 50 7500

s s100000 s 1 10 s 1

10 10

s s s1 s 100 s 10000 11 1 100

21 s

11 100

1.Rewrite the transfer function in proper form.

2.Separate the transfer function into its constituent parts.

2

4) Create the preliminary Magnitude plot of:

1

s1

Gs

1

1

s 1 s1

s

100 1 100

s1

100

1

1

1

3.Draw the Bode diagram for each part.

Bode Plot Procedure

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4.Draw the overall Bode diagram by adding up the results from part 3.

Bode Plot Procedure

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Check your AnsWer! Step 2: Separate the transfer function into its

constituent parts.

The transfer function has 2 components: A constant of 3.3

A pole at s= -30

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2

1

s1

11

s 1 s1

100 1 100

6)

1

0

Create the Phase plot o

s

1

s1

10

f:

G s1

Bode Plot Procedure

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Create the Phase Plot

Bode Plot Procedure

The Phase plot compared to the computer generated plot then becomes:

6/3/2019 23

Try This!

6/3/2019 24

Draw the Bode Diagram for the transfer function:

REMEMBER the four steps:

1.Rewrite the transfer function in proper form.

2.Separate the transfer function into its constituent parts.

3.Draw the Bode diagram for each part.

4.Draw the overall Bode diagram by adding up the results from part 3.

Check your Answer!

Step 1: Rewrite the transfer function in proper form.

Make both the lowest order term in the numerator and denominator unity. The numerator is an order 0 polynomial, the denominator is order 1.

6/3/2019 25

Check your AnsWer!

Step 3: Draw the Bode diagram for each part.

The constant is the cyan line (A quantity of 3.3 is equal to 10.4 dB). The phase is constant at 0 degrees.

The pole at 30 rad/sec is the blue line. It is 0 dB up to the break frequency, then drops off with a slope of -20 dB/dec. The phase is 0 degrees up to 1/10 the break frequency (3 rad/sec) then drops linearly down to -90 degrees at 10 times the break frequency (300 rad/sec).

Step 4: Draw the overall Bode diagram by adding up the results from step 3.

The overall asymptotic plot is the translucent pink line, the exact response is the black line.

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Definition of Gain Margin and Phase Margin

The loop gain Transfer function L(s)

The gain margin is defined as the multiplicative amount that the magnitude of L(s) can be increased before the closed loop system goes unstable

Phase margin is defined as the amount of additional phase lag that can be associated with L(s) before the closed-loop system goes unstable

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Summary

Root locus analysis

Frequency response plots

Nyquist (nyquist)

Bode (bode)

Gain Margin

Phase Margin

6/3/2019 28

NON LINEAR CONTROL SYSTEMS

Prepared by,Ciya PauloseAsst.Professor

EEE Dept.,MCET

Control theory

Control theory is divided into two branches.

1)Linear control theory

2)Non linear control theory

Linear control theory

• It applies to systems made of devices whichobey the superposistion principle. They aregoverned by linear differential equation. Amajor subclass is systems which in additionhave parameters which do not change withtime, called linear time invaiant(LTI) systems.These systems can be solved by powerfulfrequency domain mathematical techniques ofgreat generality, such as the Laplacetransform, Fourier transforms, Ztransforms, Bode plot, root locus, and NyquistStabilty Criterion.

Nonlinear control theory

• Nonlinear control theory is the area of control theorywhich deals with systems that are nonlinear, time-variant, or both. Control theory is an interdisciplinarybranch of engineering and mathematics, that isconcerned with the behavior of dynamicalsystems with inputs, and how to modify the output bychanges in the input using feedback,feedforward,or signal filtering. The system to be controlled is calledthe “plant". One way to make the output of a systemfollow a desired reference signal is to compare theoutput of the plant to the desired output, andprovide feedback to the plant to modify the output tobring it closer to the desired output.

Nonlinear control theory

• Nonlinear control theory covers a wider class ofsystems that do not obey the superpositionprinciple. It applies to more real-world systems,because all real control systems are nonlinear.These systems are often governed by nonlineardifferential equations. The mathematicaltechniques which have been developed to handlethem are more rigorous and much less general,often applying only to narrow categories ofsystems.These include limitcycle theory, ,Liapunov stability theory,and describing functions.

Characteristics of Nonlinear Systems

• Some characteristics of nonlinear dynamic systems are

• They do not follow the principle of superposition (linearity and homogeneity).

• They may have multiple isolated equilibrium points.

• They may exhibit properties such as limit cycle .

Various types of non linearities

• Saturation non linearities

• Dead zone non linearities

• Relay (ON/OFF controller) non linearities

• Friction non linearities

• Backlash non linearities

Saturation non linearities

Dead zone non linearities

This type of non linearity isshown by various electrical

devices like motors, DC servo

motors, actuators etc. Dead zonenon linearities refer to acondition in which outputbecomes zero when the inputcrosses certain limiting value.

Relay (ON/OFF controller) non linearities

Figure shows the idealcharacteristics of abidirectional relay. Inpractice relay will notrespond instantaneously.

THANK YOU