Application Of Laplace Transform In Controls 5j536m

CONTROL SYSTEMS ENGINEERING

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Laplace transform is an integral transform method which is particularly useful in solving linear ordinary differential equations.

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It is a very powerful mathematical tool applied in various areas of engineering especially in control systems.

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A control system is an interconnection of components forming a system configuration that will provide a desired system response response. In their simplest form, control systems take in d t as input, data i t process the th data, d t and d th then send d out signals as output…

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There are two main types of control system… system

Open L O Loop System

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Closed Loop System

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The open loop system is the simplest type of control system, as it d does nott ttake k t off th the output. t t The Th input i t data d t is i processed, then sent as output, e.g. a microwave oven…

A person selects the microwave power and the time for cooking. This input is sent to the embedded computer `

The embedded computer processes the data, and sends a signal to the microwave generator

The microwave generator cooks the food for the required time at the required power

The problem with this open loop system is that the food even if microwave oven will keep cooking the food, it is already burnt – there is no of output.

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A cclosed osed loop oop system syste uses eedbac provided p o ded by sensors. is where information from the output gets used as part of the input. A loop provides extra data, which is processed with the input data.

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Most control systems are closed loop systems systems, e e.g. g a flight control system…

The pilot operates the control to put the aircraft into a steep turn. also forms part of the input.

The plane’s control box (a large computer) processes this data and sends signals to the wing flaps and engines.

The wing flaps and engines make the necessary adjustments.

Sensors monitor the tilt of the aircraft and send this information to the control box. This becomes part of the input. When the required amount of tilt has been reached, the computer sends signals to the wing flaps and engine to stop any further adjustments.

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The first applications pp of control appeared in the development of float regulator mechanisms in Greece in the p period 300 to 1 B.C.

The float detects the water level and controls the valve that covers the water inlet in the boiler

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The first system to be invented in modern Europe was the temperature regulator of Cornelis Drebbel (1572-1633) of Holland. Dennis Papin (1647-1712) (1647 1712) in invented ented the first pressure regulator for steam boilers in 1681. Papin’s pressure regulator was a form of safety regulator similar to a pressure-cooker valve. Regulator for steam boilers in 1681. The first automatic controller used in an industrial process is generally agreed to be James Watt’ss flyball governor, governor developed in 1769 for Watt controlling the speed of a steam engine.

This all mechanical device measured the speed of the output shaft and utilized the movement of the flyball with speed to control the valve and therefore the amount of steam entering the engine. As the speed increase, increase the ball weights raise and move away from the shaft axis, thus closing g the valve.

18th Century James Watt’s Watt s centrifugal governor for the speed control of a steam engine. 1920s Minorsky worked on automatic controllers for steering ships. 1930s Nyquist developed a method for analyzing the stability of controlled systems 1940s Frequency 1940 F response methods th d made d it possible ibl tto d design i lilinear closedl d loop control systems 1950s Root-locus method due to Evans was fullyy developed p 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, economic and socio-economic socio economic systems

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The e goal goa of o control co t o e engineering g ee g des design g is s to obtain the configuration, specifications, and identification of the key yp parameters of a proposed system to meet an actual need.

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The first step p in the design g process p consists of establishing the system goals. The second step is to identify the variables that we desire to control (for example example, the velocity of the motor). The third step is to write the specifications in of the accuracy you must attain. The fourth step is to configure a system that will result in the desired control performance. System configuration normally consist of a sensor, the control an actuator and a process under control, controller

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The fifth step consists of identifying a candidate f the for h actuator. This Thi will, ill off course, depend d d on the process, but the actuation chosen must be capable of effectively adjusting the performance of the process. The sixth step is is the selection of a controller, which often consists of a summing amplifier that will compare the desired response and the actual response and then forward this error measurement signal to an amplifier. The seventh step of the p is the adjustment j parameters of the system in order to achieve the desired performance.

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Control systems are designed and analyzed using quantitative mathematical models of physical systems

Ta( t ) − Ts( t)

Ta( t ) ω( t )

Ta( t )

0

Ts ( t ) ωs( t ) − ωa( t ) = through - variable

angular rate difference = across-variable

Electrical Inductance

Energy or Power 1 2

Describing Equation

v 21

d L⋅ i dt

v 21

1 d ⋅ F k dt

E

2

⋅ L⋅ i

Translational Spring

2

E

1 F ⋅ 2 k

E

1 T ⋅ 2 k

Rotational Spring ω21

1 d ⋅ T k dt

P21

d I⋅ Q dt

2

Fl id IInertia Fluid ti E

1 2

2

⋅ I⋅ Q

Electrical Capacitance i

C⋅

d v 21 dt

E

1 2

⋅ M ⋅ v 21

2

Translational Mass d v2 dt

F

M⋅

T

J⋅

Q

Cf ⋅

q

Ct⋅

E

1 2

⋅M ⋅v2

2

Rotational Mass d ω2 dt

E

1 2

⋅ J⋅ ω 2

2

Fluid Capacitance

Thermal Capacitance

d P 21 dt

d T2 dt

E

E

1 2

⋅ C f ⋅ P 21

Ct⋅ T 2

2

Electrical Resistance 1

1

⋅ v 21

P

F

b ⋅ v 21

P

b ⋅ v 21

2

T

b ⋅ ω 21

P

b ⋅ ω 21

2

i

Translational Damper

R

R

⋅ v 21

2

Rotational Damper

Fluid Resistance Q

1 Rf

⋅ P 21

P

⋅ T 21

P

1 Rf

⋅ P 21

Thermal Resistance q

1 Rt

1 Rt

⋅ T 21

2

M⋅

d

2

d y ( t ) + b ⋅ y ( t ) + k⋅ y ( t) 2 dt dt

r( t)

t

1 ⌠ d + C⋅ v ( t) + ⋅ ⎮ v ( t ) dt R L ⌡0 dt

v ( t)

y( t) y(

K 1⋅ e

− α 1⋅ t

(

r( t)

⋅ sin β 1⋅ t + θ 1

)

ELECTRIC SHIP CONCEPT Vision Integrated Power System

All Electric Ship

Electrically Reconfigurable Ship Š Technology Insertion Š Warfighting Capabilities

Š Reduced manning Š Electric Drive Š Automation Š Reduce # of Prime Š Eliminate auxiliary Movers systems (steam, Š Fuel savings hydraulics, compressed Š Reduced maintenance air) i)

Increasing Affordability and Military Capability

Propulsion Motor

Motor Drive

Power Conversion Module

Main Power Distribution

Generator

Ship Service P Power

Prime Mover

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Control C t lS Systems t E Engineering i i b by N Norman S S. Nise Th El The Electronics t i E Engineers i H Handbook, db k 5th Edition Editi Laplace Transform and its Application by Sarina Adhikari Control Systems Engineering a Practical Approach by Frank Owen Owen, PhD PhD, P P.E. E

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