ContSys1 L1 Intro(1)

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Mechanical Engineering Science 8

Dr. Daniil Yurchenko

Introduction to Systems

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Assessment20% Test (week 6)30% Exam

If you have any questionsJN 1.23Email: d.yurchenko@hw.ac.uk

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Books

Modern Control EngineeringK. OgataPrentice-Hall.

----------------------------------------------------Automatic Control SystemsF. Golnaraghi, B. KuoJohn Wesley & Sons

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What is a system?

We define a system as a set of interactingcomponents making up a whole machine whichcan be isolated from its surroundings.It has a set of prescribed inputs and outputs.The process of isolating the system requires a

boundary to be defined which helps to identify

the system inputs and outputs.

SYSTEM

INPUT OUTPUT

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System definition examples

WIND

TURBINE

INPUT OUTPUT

WindElectricity

Single Input Single Output

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System definition examples

CARENGINE

INPUT OUTPUT

Throttle angle

Load TorqueEngine Speed

Multiple Input Single Output

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System definition examples

STEAMTURBINE

INPUT OUTPUT

SteamElectrical Power

Steam to Condenser

Single Input Multiple Output

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System definition examples

Airplane

INPUT OUTPUT

Current PositionFuel Left

Distance to Destination

Multiple Input Multiple Output

Current Velocity

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B-2 and F-117 areaerodynamically unstable in all three axes and

require constant flightcorrections from a fly-by-wire system to maintaincontrolled flight

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Wind turbines withadjustable blades or

pitch control.

This control is essential because sometimes thewind's speed puts toomuch stress on theturbine, causing safetycontrols to kick-in andapply brakes to the rotorto prevent it fromdamage or use pitch

control

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To manage traffic in largecities traffic light controlssystems are used.

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Robots

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CNC Machines

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Example

We wish to hold the tank level h constantregardless of the flow through valve V

1

This could be achieved through irregularadjustment of valve V 2

V1

h

V2

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Open-loop Control

Tank level control

manuallycontrolledValve V 2

OBJECTIVE RESULT

Maintain constantlevel of water

V1h

V2

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Closed-loop Control (Feedback)

Tank level control

BARRELwith

automaticallycontrolled

ValveMaintain constantlevel of water

V1h

V2

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Closed-loop Control (Feedback)

Tank level control

V1h

V2

Computer Objective/processReferenceinput

Output

Measurement

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Closed-loop Control (Feedback)ProcessOutput

Comparison

MeasurementController

Give examples of a feedback control used: In a car In an airplane

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Components of a closed-loop control

system

Measurement component

ComparatorAmplifierActuator

Corrector (or compensator)

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Basic requirement to control system

Stability: the ability to maintain stablestate

Accuracy: stable steady-state accuracy

Dynamic characteristics: response timeand damping characteristics

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Systems

In this course we will normally considersingle input/single output systems

The input is turned into the output via thesystem transfer process.This transfer process will be modelled by a

linear differential equation with constantcoefficients which will be presented as atransfer function

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Linear dynamic systems

These are modelled by a linear differentialequation. A generic example is shown

below

For a linear system the transfer propertiesrelate the system to the output

System TransferProperties

System Output,xo(t)

System Input,xi(t)

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Linear dynamic systems

The transfer properties take the generalform:

Coefficients a k , k = 1,2,…n are constants

xi(t) is a specified function of time

t xt xadt

t xd a

dt

t xd a

iOO

n

nn

On

n 0

1

1 .....

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Properties of linear systems

Linear differential equations exhibit the properties of superposition and homogeneity.

Conversely a system which exhibits these properties is a linear system.

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Principle of superposition

This states that if the system input is broken down into two elements

which individually generate outputsthen when the inputs are appliedsimultaneously (added) then the output isthe sum of the individual outputs.This can be expressed:

B

i

A

i x x

,

BO

AO x x ,

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Homogeneity

A linear system is said to be homogeneouswhen a constant scale factor applied to the

input generates the same scaling of theoutput. i.e. -application of an input

-application of the scaledinput

t xt xOi

t xt xOi

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Order of a linear system

The order of a linear differential equationand hence of the system which it describesis the value of the highest derivative in thedifferential equation.

is a an example of a first order

system

is an example of an n-order system

iOO x

T

x

dt

dx

iOn

O

n

nn

O

n

n xa xa

dt

xd a

dt

xd a

011

1

1 .......