application of laplace transform in controls

8/13/2019 Application of Laplace Transform in Controls

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Laplace transform is an integral transform

linear ordinary differential equations.

It is a very powerful mathematical tool applied in

control systems.


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components forming a system configuration that.

In their simplest form, control systems take in

a a as npu , process e a a, an en senout signals as output


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The open loop system is the simplest type of control system,

as oes no a e accoun o e ou pu . e npu a a s

processed, then sent as output, e.g. a microwave oven

A person selects the The embedded The microwave

microwave power andthe time for cooking.This input is sent to the

computer processesthe data, and sendsa signal to the

generator cooks thefood for the requiredtime at the required

The problem with this open loop system is that the,it is already burnt there is no account of output.


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A closed loo s stem uses feedback rovided b

sensors. Feedback is where information from the output

gets used as part of the input. A feedback loop providesextra data, which is processed with the input data.


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, . .

flight control system

The pilot operates The planes control box The wing flaps

the aircraft into asteep turn.

Feedback also

processes this data andsends signals to the

wing flaps and engines.

the necessaryadjustments.

forms part of theinput.

Sensors monitor the tilt of the aircraft and send this information to the controlbox. This becomes part of the input. When the required amount

of tilt has been reached, the computer sends signals to thewing flaps and engine to stop any further adjustments.


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The first a lications of feedback control

appeared in the development of float regulator

mechanisms in Greece in the eriod 300 to 1B.C.

water level and controlsthe valve that covers

the water inlet in theboiler


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The first feedback system to be invented in modernEurope was the temperature regulator of Cornelis

Drebbel (1572-1633) of Holland. - v

pressure regulator for steam boilers in 1681. Papins

similar to a pressure-cooker valve. Regulator forsteam boilers in 1681.

The first automatic feedback controller used in an

industrial process is generally agreed to be James ,controlling the speed of a steam engine.


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This all mechanical devicemeasured the speed of theoutput shaft and utilized the

movement of the flyball with

therefore the amount ofsteam entering the engine.

,

ball weights raise and moveaway from the shaft axis, thusclosing the valve.


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steam engine.

1920s Minorsky worked on automatic controllers for steering ships.

1930s Nyquist developed a method for analyzing the stability of controlled

systems

s requency response me o s ma e poss e o es gn near c ose -

loop control systems

1950s Root-locus method due to Evans was full develo ed

1960s State space methods, optimal control, adaptive control and

1980s Learning controls are begun to investigated and developed.

Present and on-going research fields. Recent application of modern control

theory includes such non-engineering systems such as biological, biomedical,

-


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The oal of control en ineerin desi n is toobtain the configuration, specifications, and

identification of the ke arameters of aproposed system to meet an actual need.


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The first step in the design process consists ofestablishing the system goals.

The second step is to identify the variables thatwe es re o con ro or examp e, e ve oc y othe motor).

terms of the accuracy you must attain. The fourth step is to configure a system that will

result in the desired control performance. Systemconfiguration normally consist of a sensor, the

,controller


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The fifth step consists of identifying a candidateor t e actuator. s w , o course, epen on

the process, but the actuation chosen must be

of the process. The sixth step is is the selection of a controller,

which often consists of a summing amplifier thatwill compare the desired response and the actual

measurement signal to an amplifier.

The seventh ste is the ad ustment of theparameters of the system in order to achieve thedesired performance.


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using quantitative mathematical models of


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Electrical Inductance Describing Equation Energy or Power

v21 Lti

d E

2L i

v211

Fd E

1 F2

Translational Spring

2

Rotational Spring

21k t

Td

d E

2 k

P21 I Qd E

1I Q

u nert a


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Electrical Capacitance

Translational Mass

i Ctv 21

d

d E

2M v 21

2

F Mtv 2

d

d E

1

2M v 2

2

T J 2d E

1J 2

2

Fluid Capacitance

d 1 2

Thermal Capacitancetd 2

q Ct

t

T 2

d

E Ct T 2


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Electrical Resistance

Translational Damper

i 1

Rv 21 P

1

Rv 21

2

F b v 21 P b v 212

T b 21 P b 212

Fluid Resistance

Q 1

RfP21 P

1

RfP21

2

Thermal Resistance

1T P

1T

Rt Rt


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M2

y t( )d

2

b y t( )d+ k y t( )+ r t( )td


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v t( ) d 1 tR t

vd

L

0

v

r

y t( ) K1e 1 t

sin 1t 1+


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ELECTRIC SHIP CONCEPT

VisionVision

ElectricallyElectricallyElectricallyElectrically

Technology

IntegratedIntegratedPowerPowerSystemSystem

IntegratedIntegratedPowerPowerSystemSystem

Al lAl lElectricElectric

ShipShip

Al lAl lElectricElectric

ShipShip

ShipShipShipShip

Main Power

Electric Drive

Reduce # of PrimeMovers

Fuel savings

Insertion

WarfightingCapabilities

Reduced manning

AutomationEliminate auxiliary

systems (steam,hydraulics, compressed

Propulsion

Motor

Motor

Drive Generator

Prime

Mover

a r

ShipService

Power

ConversionowerModule


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on ro ys ems ng neer ng y orman .

Nise e ec ron cs ng neers an oo , on

Laplace Transform and its Application by Sarina

Control Systems Engineering a Practical, , . .


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application of laplace transform in controls

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