mechanical engineering department automatic control dr. talal mandourah 1 lecture 1 automatic...
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Mechanical Engineering DepartmentAutomatic Control
Dr. Talal Mandourah
Lecture 1
Automatic Control
Applications:Missile controlBehavior controlAircraft controlMachine controlAeronautic control
Engineering is control and control is engineering
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Mechanical Engineering DepartmentAutomatic Control
Dr. Talal Mandourah
What Control is About???!!!
Control= compensate= manipulate=Adjust= correct= desire= less error
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Mechanical Engineering DepartmentAutomatic Control
Dr. Talal Mandourah
What Control is About???!!!
Indeed all modern systems (aircrafts, CD player, speed trains, cruise control system, …) couldn’t operate without the aid of sophisticated control systems.
Improved control is the key enabling technology underpinning- Enhanced product quality- Waste minimization- Environmental protection- Greater throughput for a given installed capacity- Greater yield- Deferring costly plant upgrades- Higher safety margins
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Mechanical Engineering DepartmentAutomatic Control
Dr. Talal Mandourah
Close loop with sensor
PlantController
Measurement(sensor)
r(t)y(t)
my(t)
y(t)
u(t)Reference input
output
output
output
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Mechanical Engineering DepartmentAutomatic Control
Dr. Talal Mandourah
System Integration
Important Issues in control: Plant: the physical object to be controlled.Process: a series of operations acting toward the endSensors: machines which measure system output.Actuator: the muscles or the part which does the action.Disturbance: signals which affect the output.Feedback: the measure of the output compared to target.Open-loop system: the output is neither measured nor fed-back.Closed-loop system: the output is measured and compared with the desired value.
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Mechanical Engineering DepartmentAutomatic Control
Dr. Talal Mandourah
What should we do?
Study the process
Mathematical Model
Simulate with MATLAB and SIMULINK
Design a controller
Apply in real-time
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Mechanical Engineering DepartmentAutomatic Control
Dr. Talal Mandourah
Types of Control
Classical Control Time Domain (Root-locus, Laplace Transform)Frequency Domain (Bode, Nyquest)
Modern ControlState Space (work for linear systems, have much control on it)
Digital ControlZ-transform
Stochastic ControlKalman Filters (estimate the variables that can’t be measured)
Adaptive Control Optimal Control
Riccatti Equation (minimize the cost function) Robust ControlIntelligent Control
Neural NetworkFuzzy logic
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Mechanical Engineering DepartmentAutomatic Control
Dr. Talal Mandourah
Laplace Transform
Laplace transform: is a mathematical tool used to solve linear ordinary Differential equations ODEIt converts linear ODE into algebraic equation in “s”Homogenous (transient equation +particular Integral (steady state) of the sol.Obtained in one operationObtain the s-domain solution, use the inverse transform to find the time domain solution.
f(t)= a function of timeS= a complex variable₤= Laplace F(s)= Laplace transformed
0 0
)()]([)()]([ dtetftfdtesFtfL stst
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Mechanical Engineering DepartmentAutomatic Control
Dr. Talal Mandourah
Laplace Transform
)0()0(...)0()0()()]([
)0()0()()]([
)0()()]([
)1()2(21
22
2
nnnnn
n
n
ffsfsfssFstfdt
dL
fsfsFstfdt
dL
fssFtfdt
dL
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Mechanical Engineering DepartmentAutomatic Control
Dr. Talal Mandourah
Laplace Transform Properties
Properties of Laplace Transform1- Multiplication by constant
2- Superposition principal
3- Differentiation
4- Integration
)()]([ skFtkfL
)()()]()([ 2121 sFsFtftfL
)0()(])(
[ fsSFdt
tdfL
)(1
])([ sFs
dfL
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Mechanical Engineering DepartmentAutomatic Control
Dr. Talal Mandourah
Laplace Transform Properties
5- Time Shift6- Time Scaling7- Frequency Shift
8- Convolution:Convolution in time domain= multiplication in frequency domain
)()(
])()([
)(*)()](*)([
21
0 0
21
0
2121
sFsF
dtedtff
dtetftftftfL
tst
st
Convolution in time domain is multiplication in Frequency domain
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Mechanical Engineering DepartmentAutomatic Control
Dr. Talal Mandourah
Laplace Transform Properties
ssFtfst
(lim)(lim0
)(lim)(lim0
ssFtfst
9- Time product10- multiply by time11-Initial Value Theorem
12-Final Value Theorem
)()]([ sFtfL
Not valid if sF(s) contains a pole whose real part or zero is positive
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Mechanical Engineering DepartmentAutomatic Control
Dr. Talal Mandourah
Laplace Transform
Exponential function:
0.............
0..,........0)(
tforAe
tfortft
0
st-f(t)e ])([)( dttfLsF
Step function:
0.................
0..,........0)(
tforA
tfortf
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Mechanical Engineering DepartmentAutomatic Control
Dr. Talal Mandourah
Laplace Transform
0
st-f(t)e ])([)( dttfLsF
0................
0..,........0)(
tforAt
tfortf
Ramp function: Sinusoidal function:
)(2
1sin tjtj ee
jt
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Mechanical Engineering DepartmentAutomatic Control
Dr. Talal Mandourah
Problems
0...............
0.......0)(3
tte
tfortft
Find the Laplace transform: Find the Laplace transform:
0...)..sin(........
0...................0)(
tfort
tfortf
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Mechanical Engineering DepartmentAutomatic Control
Dr. Talal Mandourah
Problems
0......sin........
0............0)(2
ttt
tfortf
Find the Laplace transform