Introduction to Control Systems

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GEE 514 Solar Energy Institute,
Dr.Mutlu BOZTEPE

1

Introduction to Control
Systems

G(s)

+


_

Course Objectives


To provide a general understanding of the
characteristics of dynamic systems and feedback
control.


To teach classical methods for analysing control
system accuracy, stability and dynamic
performance.


To teach classical control system design
methods.


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


Course Book

Advanced Control Engineering


Roland S. Burns

Butterworth
-
Heineman

Paperback, 464 pages, publication date: OCT
-
2001

ISBN
-
13: 978
-
0
-
7506
-
5100
-
4

ISBN
-
10: 0
-
7506
-
5100
-
8

http://www.elsevier.com/wps/find/bookdescription.cws_home/677158/description#description

Introduction to Control
Systems

Control System Concepts


A
system

is a collection of components which
are co
-
ordinated together to perform a function.


Systems interact with their
environment

across a
separating boundary.


The interaction is defined in terms of
variables
.


system inputs


system outputs


environmental disturbances


Systems

Disturbance Inputs

Control Inputs

System Outputs

Engineering systems

Biological systems

Information systems

Subsystem

System Variables


The system’s
boundary
depends upon the
defined objective function of the system.


The system’s function is expressed in terms of
measured output variables
.


The system’s operation is manipulated through
the
control input variables
.


The system’s operation is also affected in an
uncontrolled manner through the
disturbance
input variables
.


Car and Driver Example


Objective function
: to control the direction and
speed 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, . . .


Antenna Positioning Control System


Original system
: the antenna with

electric motor drive systems.


Control objective
: to point the

antenna in a desired reference direction.


Control inputs
: drive motor voltages.


Outputs
: the elevation and azimuth of the
antenna.


Disturbances
: wind, rain, snow.



Antenna Control System

Functional Block Diagram

Physical Variables

Information Variables

Antenna

Motor

Power

amp

Diff.

amp

Ref.

input

Angle

sensor

volts

volts

volts

+

_

power

torque

Angular

position

Antenna System

Wind force

Feedback Path

Error

Control System Components


System or process
(to be controlled)


Actuators
(converts the control signal to a power
signal)


Sensors
(provides measurement of the system
output)


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)


Feedback System Characteristics


Consider the following speed control system

Load

K
l

Motor

K
m

Amp

K
a

Speed sensor

K
s

Reference

speed

u

+



_

Disturbance

torque

w
o

Open loop system

Feedback Path

w
r


+


+

T
d

T
m

Open Loop System Characteristics

The accuracy of the open loop system depends upon the calibration
of the gains and prior knowledge of the disturbance (choose the
control
u

to give the desired
w
o

).

Problems:


nonlinear or time varying gains


unknown and varying disturbances

Load

K
l

Motor

K
m

Amp

K
a

u

Disturbance

torque

w
o

Open loop system


+


+

T
d

T
m

d
l
l
m
a
d
m
l
o
T
K
u
K
K
K
T
T
K




)
(
w
Closed Loop Characteristics

Now consider the case with feedback

d
s
l
m
a
l
r
s
l
m
a
l
m
a
o
d
l
o
s
r
l
m
a
d
m
l
o
T
K
K
K
K
K
K
K
K
K
K
K
K
or
T
K
K
K
K
K
T
T
K









1
1
)
(
)
(
w
w
w
w
w
Load

K
l

Motor

K
m

Amp

K
a

Speed sensor

K
s

Reference

speed

u

+



_

Disturbance

torque

w
o

Open loop system

Feedback Path

w
r


+


+

T
d

T
m

Closed Loop Characteristics

If
K
a

is very large such that,



then,




K
s

is the sensor gain in units of volts per rad/s.

The input/output relationship is not very
sensitive

to
disturbances or changes in the system gains


s
l
m
a
s
l
m
a
K
K
K
K
K
K
K
K


1
d
s
m
a
r
s
o
T
K
K
K
K
1
1


w
w
rad/s volts


0

Closed Loop Characteristics


System Error

The control error is







Again, if the
loop gain
,
K
a
K
m
K
l
K
s

is large, then the
error is small.

d
s
l
m
a
s
l
r
s
l
m
a
d
s
l
m
a
s
l
r
s
l
m
a
s
l
m
a
o
s
r
T
K
K
K
K
K
K
K
K
K
K
T
K
K
K
K
K
K
K
K
K
K
K
K
K
K
K
e



















1
1
1
1
1
1
)
(
w
w
w
w
Note: Gain Definitions


forward gain:


K
a
K
m
K
l

feedback gain:


K
s


loop gain:



K
a
K
m
K
l
K
s


closed loop gain:


forward gain






1 + loop gain


System Dynamics


Consider a sudden change in the speed reference,
w
r

.


The output speed,
w
o

will not respond
instantaneously due to the inertial characteristics of
the motor and load, i.e. their
dynamic
characteristics
.


The motor and load need to be represented by
dynamic equations

rather than simple gains.


The output response will generally
lag

the input and
may be
oscillatory
.


System Dynamics


Step Responses

0
2
4
6
8
10
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Step Response, Ka=2
0
2
4
6
8
10
-0.5
0
0.5
1
1.5
2
Step Response, Ka=20
w
o

w
o

w
r

w
r

T
m

T
m

K
a

= 2

K
a

= 20

Assume
K
s

= 1.0

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


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 the
components and subsystems.


Combine the subsystems

to form a model for
the whole system.


Control System Design Steps


Apply
analysis and design

techniques to
determine the control system structure and
parameter values of the control components, to
meet the design objectives.


Test

the control design on a computer
simulation of the system.


Implement and test

the design on the actual
process or plant.


Control System Design Steps

Examples of Control Systems

Room Temperature Control System


Proportional
mode:

Better
accuracy,
complex



On/Off control
mode:

Thermostatic
control, simple,
low accuracy

Examples of Control Systems

Aircraft Elevator Control System


Hydraulic
servomechanisms
have a good
power/weight
ratio, and are ideal
for applications
that require large
forces to be
produced by small
and light devices.

Examples of Control Systems

Computer Numerically Controlled (CNC) Machine


The purpose of
this latter device,
which produces an
analog signal
proportional to
velocity, is to form
an inner, or minor
control loop in
order to dampen,
or stabilize the
response of the
system.

Examples of Control Systems

Ship Autopilot Control System


Actual heading is
measured by a gyro
-
compass (or magnetic
compass), compared
with desired value.
Error are send to
autopilot (Course
-
keeping system)


Actual rudder angle is
sensed, and autopilot
controls the ship
course by steering
-
gear.