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7/31/2019 Gee 514 Lecture 1
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GEE 514 Solar Energy Institute,Dr.Mutlu BOZTEPE 1
Introduction to Control
Systems
G(s)+
_
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Course Objectives
To provide a general understanding of thecharacteristics of dynamic systems and feedbackcontrol.
To teach classical methods for analysing controlsystem accuracy, stability and dynamicperformance.
To teach classical control system designmethods.
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Course Contents
Introduction to control systems Modelling of the physical systems Time domain analysis, Laplace transforms, Transfer
functions, System Responses Closed loop control systems Classical design in the s-domain Classical design in the frequency domain
Digital control systems Nonlineer control systems, on/off control Design examples
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Course Book
Advanced Control Engineering
Roland S. Burns
Butterworth-HeinemanPaperback, 464 pages, publication date: OCT-2001
ISBN-13: 978-0-7506-5100-4ISBN-10: 0-7506-5100-8
http://www.elsevier.com/wps/find/bookdescription.cws_home/677158/description#description
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Introduction to Control
Systems
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Control System Concepts
A system is a collection of components whichare co-ordinated together to perform a function.
Systems interact with their environment across aseparating boundary.
The interaction is defined in terms ofvariables.
system inputs
system outputs
environmental disturbances
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Systems
Disturbance Inputs
Control Inputs
System Outputs
Engineering systems
Biological systems
Information systems
Subsystem
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System Variables
The systems boundarydepends upon thedefined objective function of the system.
The systems function is expressed in terms of
measured output variables.The systems operation is manipulated through
the control input variables.
The systems operation is also affected in anuncontrolled manner through the disturbanceinput variables.
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Car and Driver Example
Objective function: to control the direction andspeed of the car.
Outputs: actual direction and speed of the car
Control inputs: road markings and speed signs
Disturbances: road surface and grade, wind,
obstacles. Possible subsystems: the car alone, power
steering system, braking system, . . .
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Antenna Positioning Control System
Original system: the antenna withelectric motor drive systems.
Control objective: to point theantenna in a desired reference direction.
Control inputs: drive motor voltages.
Outputs: the elevation and azimuth of theantenna.
Disturbances: wind, rain, snow.
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Antenna Control System
Functional Block Diagram
Physical VariablesInformation Variables
AntennaMotorPoweramp
Diff.amp
Ref.
input
Angle
sensor
volts volts
volts
+
_
power torqueAngular
position
Antenna System
Wind force
Feedback Path
Error
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Control System Components
System or process (to be controlled)Actuators (converts the control signal to a power
signal)
Sensors (provides measurement of the systemoutput)
Reference input (represents the desired output)
Error detection (forms the control error) Controller (operates on the control error to form the
control signal, sometimes called compensators)
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Feedback System Characteristics
Consider the following speed control system
Load
KlMotor
Km
Amp
Ka
Speed sensorKs
Reference
speed
u+
_
Disturbance
torque
wo
Open loop system
Feedback Path
wr+
+
Td
Tm
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Open Loop System Characteristics
The accuracy of the open loop system depends upon the calibrationof the gains and prior knowledge of the disturbance (choose thecontrol uto give the desired w
o).Problems:
nonlinear or time varying gains
unknown and varying disturbances
Load
KlMotor
Km
Amp
Ka
u
Disturbance
torque
wo
Open loop system
+
+
Td
Tm
dllma
dmlo
TKuKKK
TTK
)(w
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Closed Loop Characteristics
IfKa
is very large such that,
then,
Ksis the sensor gain in units of volts per rad/s.
The input/output relationship is not verysensitive todisturbances or changes in the system gains
slmaslmaKKKKKKKK 1
d
sma
r
s
oT
KKKK
11 ww
rad/s volts 0
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Closed Loop Characteristics
System Error
The control error is
Again, if the loop gain, KaK
mK
lK
sis large, then the
error is small.
d
slma
sl
r
slma
d
slma
slr
slma
slma
osr
TKKKK
KK
KKKK
TKKKK
KK
KKKK
KKKK
Ke
11
1
111
)(
w
w
ww
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Note: Gain Definitions
forward gain: KaK
mK
l
feedback gain: Ksloop gain: K
aK
mK
lK
s
closed loop gain: forward gain1 + loop gain
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System Dynamics
Consider a sudden change in the speed reference,w
r.
The output speed, wowill not respond
instantaneously due to the inertial characteristics ofthe motor and load, i.e. their dynamiccharacteristics.
The motor and load need to be represented by
dynamic equations rather than simple gains. The output response will generallylagthe input and
may be oscillatory.
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System Dynamics
Step Responses
0 2 4 6 8 100
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1Step Response, Ka=2
0 2 4 6 8 10-0.5
0
0.5
1
1.5
2Step Response, Ka=20
wo wowr
wr
Tm
Tm
Ka
= 2 Ka = 20
Assume Ks
= 1.0
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Control System Design Objectives
Primary Objectives:
1. Dynamic stability
2. Accuracy
3. Speed of response
Addition Considerations:
4. Robustness (insensitivity to parameter variation)
5. Cost of control
6. System reliability
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Control System Design Steps
Define the control system objectives.
Identify the system boundaries.
define the input, output and disturbance variables
Determine a mathematical model for thecomponents and subsystems.
Combine the subsystems to form a model forthe whole system.
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Control System Design Steps
Applyanalysis and design techniques todetermine the control system structure andparameter values of the control components, to
meet the design objectives.
Test the control design on a computersimulation of the system.
Implement and test the design on the actualprocess or plant.
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Control System Design Steps
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Examples of Control SystemsRoom Temperature Control System
Proportionalmode: Betteraccuracy,complex
On/Off controlmode:
Thermostaticcontrol, simple,
low accuracy
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Examples of Control SystemsAircraft Elevator Control System
Hydraulicservomechanismshave a goodpower/weight
ratio, and are idealfor applicationsthat require largeforces to be
produced by smalland light devices.
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Examples of Control SystemsComputer Numerically Controlled (CNC) Machine
The purpose ofthis latter device,
which produces ananalog signal
proportional tovelocity, is to forman inner, or minorcontrol loop inorder to dampen,
or stabilize theresponse of thesystem.
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Examples of Control SystemsShip Autopilot Control System
Actual heading ismeasured by a gyro-compass (or magneticcompass), compared
with desired value.Error are send toautopilot (Course-keeping system)
Actual rudder angle is
sensed, and autopilotcontrols the shipcourse by steering-gear.