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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: [email protected]
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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 .......