INTRODUCTION TO CONTROL SYSTEM

✓ System ✓ Open & Closed Loop System

✓ Control System ✓ Feedback Characteristics
✓ Examples of Control System ✓ System Representations
✓ History Of Control System ✓ Block Diagram
✓ Input & Output ✓ Control Laws/Algorithms
✓ SISO & MIMO

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TOPIC OBJECTIVES
• To identify control systems and its applications
• To identify the parts of a control system.
• To distinguish between an open-loop and closed loop control
system and identify their advantages and disadvantages.

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 SYSTEM
✓An arrangement, set, or collection of things
connected or related in such a manner as to form
an entirety or whole.
✓An arrangement of physical components
connected or related in such a manner as to form
and/or act as an entire unit.

CONTROL SYSTEM
✓ An arrangement of physical components
connected or related in such a manner as to
command, direct, or regulate itself or
another system.
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EXAMPLES OF A CONTROL SYSTEM
BATHROOM TOILET TANK
FLOAT WATER
SOURCE

WATER
LEVEL VALVE

STOPCOCK

TANK

As the tank is emptied through a stopcock, the valve opens filling

the tank. When the tank becomes full, the float gets closer to the
top, closing the valve and so shutting the flow of water. 4
BLOCK DIAGRAM OF A BATHROOM
TOILET TANK
PRESET VALVE
WATER ERROR ACTUAL
SIGNAL POSITION
LEVEL WATER
(e) (u) LEVEL
(r)
(c)

+ CONTROL
CONTROLLED
LOGIC ACTUATOR
− ELEMENTS
SYSTEM

SOURCE WATER
& VALVE TANK

FLOAT &
LINKAGE DISTURBANCE
FLOW (n)

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 STEAM ENGINE WITH
CENTRIFUGAL GOVERNOR
PIVOT
POINTS

BALL BALL
SLIDE
ON
SHAFT
TO SLIDE ON
STEAM SHAFT
ENGINE

SHAFT DRIVEN
BY ENGINE 6
BLOCK DIAGRAM OF A STEAM ENGINE
WITH A CENTRIFUGAL GOVERNOR
ANGULAR
ERROR VALVE VELOCITY
DESIRED
SIGNAL POSITION
VELOCITY (c)
(r) (e) (u)

+ CONTROLLED
CONTROLLER
− SYSTEM

STEAM
ENGINE
CENTRIFUGAL
GOVERNOR

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HISTORY
✓300 B.C.-LIQUID-LEVEL CONTROL. A water clock
invented by Ktesibios, operated by having water trickle
into a measuring container at a constant rate. For a water
to trickle at a constant rate, the supply tank had to be kept
at a constant level. This was accomplished using a float
valve similar to the water level control in today’s flush
toilets.
✓1681-STEAM PRESSURE CONTROL. Denis Papin
invented the safety valve. The concept was further
elaborated on by weighting the valve top. If the upward
pressure from the boiler exceeded the weight, steam was
released and the pressure was decreased. If it did not
exceed the weight, the valve did not open and the
pressure inside the boiler increased. Thus the weight on
the valve top set the internal pressure of the boiler.
✓1745-SPEED CONTROL. Applied to a windmill by Edmund
Lee. Increasing winds pitched the blades further back so
that less area was available. 8
 HISTORY
✓1788-STEAM ENGINE SPEED CONTROL. James Watt
invented the flyball speed governor to control the speed of
steam engines. In this device, two spinning flyballs rise as
rotational speed increases. A steam valve connected to the
flyball mechanism closes with the ascending flyballs and
opens with the descending flyballs, thus regulating the
speed.
✓1868-STABILITY CRITERION FOR A THIRD-ORDER
SYSTEM. James Clerk Maxwell published the stability criterion
for a third-order system based on the coefficients of the
differential equation.
✓1874-STABILITY CRITERION FOR FIFTH-ORDER
SYSTEM. Edward John Routh extended the stability criterion
to fifth-order systems.
✓1892-NONLINEAR SYSTEMS-A.M.Lyapunov extended the
work of Routh to nonlinear systems in his doctoral thesis
entitled “The General Problem of Stability of Motion”.
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 HISTORY
✓1922-AUTOMATIC CONTROLLERS FOR STEERING
SHIPS. Minorsky worked on automatic controllers for steering
ships and showed how stability could be determined from the
differential equations describing the system.
✓1932-STABILITY OF CLOSED LOOP SYSTEM BY
SINUSOIDAL INPUTS. Nyquist developed a relatively
simple procedure for determining the stability of closed-loop
systems on the basis of open-loop response to steady-state
sinusoidal inputs.
✓1934-SERVOMECHANISM. Hazen introduced the term
servomechanisms for position control systems, discussed the
design of relay servomechanisms closely following a changing
input.
✓1940s-FREQUENCY RESPONSE. Bode made it possible for
engineers to design linear closed-loop control systems that
satisfied the performance requirements
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 INPUT OUTPUT
✓stimulus, excitation or ✓ actual response
command applied to a obtained from a control
control system, typically
from an external energy system. It may or may
source, usually in order to not be equal to the
produce a specified response specified response implied
from the control system. by the input.
Examples:
▪ Preset water level for a
bathroom toilet tank. Examples:
▪ Desired velocity for a steam ▪ Actual water level for a
engine governor. bathroom toilet tank.
▪ Thermostat setting for an ▪ Actual velocity for a steam
airconditioner. engine governor.
▪ Actual room temperature.
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SINGLE-INPUT,
SINGLE OUTPUT SYSTEM

✓a single output is controlled by a single input.

f (t ) SISO y (t )

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EXAMPLE OF SISO SYSTEM
DESIRED POSITION ACTUAL LATERAL POSITION

PILOT AIRCRAFT

+ CONTROLLED
COMPENSATOR ACTUATOR
− SYSTEM

AILERONS AIRCRAFT
AND BODY
MECHANISM

SENSORS

AIRCRAFT LANDING SYSTEM 13

MULTIPLE-INPUT,
MULTIPLE OUTPUT SYSTEM

✓more than one controlled output and command

input.
✓also called multivariable system

f1 (t ) y1 (t )
f 2 (t ) y2 (t )
f 3 (t ) MIMO y3 (t )
f n (t ) y m (t )
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EXAMPLE OF MIMO SYSTEM
STEERING WHEEL
POSITION
DIRECTION EYES
OF HANDS
HIGHWAY HEADING
ACTUATOR
ERROR CONTROL
VEHICLE
DETECTOR LOGIC
ACTUATOR
SPEED SPEED
LIMITS
BRAIN FOOT
ACCELERATOR/BRAKE
POSITION

AUTOMOBILE DRIVING CONTROL SYSTEM

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DECOUPLING MIMO SYSTEM INTO TWO
SISO SYSTEMS
STEERING WHEEL
EYES POSITION
DIRECTION
OF HANDS
HIGHWAY + HEADING
− ACTUATOR
CONTROL
+ LOGIC
VEHICLE
ACTUATOR
SPEED
LIMITS
− SPEED
BRAIN FOOT
ACCELERATOR/BRAKE
ERROR POSITION
DETECTOR

AUTOMOBILE DRIVING CONTROL SYSTEM

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OPEN-LOOP CONTROL SYSTEMS
✓the control action is independent of the output.

FEATURES OF OPEN-LOOP CONTROL

SYSTEMS
1. Their ability to perform accurately is determined
by their calibration. To calibrate means to
establish or reestablish the input-output relation
to obtain a desired system accuracy.
2. They are not usually troubled with the problems
of instability. 17
OPEN-LOOP CONTROL SYSTEM
OVEN TOASTER

PRESET TEMPERATURE
TIME ON - OFF

TIMER HEATER

ELECTRONIC HEATING
OR SPRING ELEMENT
TIMER

The time required for a well done cooking must be

first estimated by the user. 18
CLOSED-LOOP CONTROL SYSTEMS
✓the control action is somehow dependent on the
output.
PRESET VALVE
WATER ERROR ACTUAL
SIGNAL POSITION
LEVEL WATER
(e) (u) LEVEL
(r)
(c)

+ CONTROL
CONTROLLED
LOGIC ACTUATOR
− ELEMENTS
SYSTEM

SOURCE WATER
& VALVE TANK

FLOAT &
LINKAGE DISTURBANCE
FLOW (n) 19
 FEEDBACK
✓ property of a closed-loop system which permits the
output (or some other controlled variable) to be compared
with the input to the system (or an input to some other
internally situated component or subsystem) so that the
appropriate control action may be formed as some
function of the output and input.

CHARACTERISTICS OF FEEDBACK
1. Increased accuracy.
2. Reduced sensitivity of the ratio of output to input to
variations in system parameters and other
characteristics.
3. Reduced effects of nonlinearities.
4. Reduced effects of external disturbances or noise.
5. Increased bandwidth.
6. Tendency toward oscillation or instability. 20
CONTROL SYSTEM MODELS OR
REPRESENTATIONS
1. Mathematical models, in the form of differential equation
(difference equation), and/or other mathematical relations,
for example, Laplace transform (z-transform).
2. Block diagrams.
3. Signal flow graphs.

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BLOCK DIAGRAM
• shorthand, pictorial representation of the
cause-and-effect relationship between the input
and output of a physical system.

Block
Input Output

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BLOCK DIAGRAM
Arrows represent the
direction of information or
signal flow. y=
dx
dt

x d
dt
Block contains the description of or name of
the element, or the symbol for the mathematical
operation to be performed on the input to yield
the output. 23
SUMMING POINT
✓use in adding or subtracting signals
z
+
x + x+ y x + x+ y+z
+ +
y x + x− y y
−
y 24
TAKE-OFF POINT
✓use to have the same signal or variable be an
input to more than one block or summing point.
x

Takeoff Point Takeoff Point

x x
x x
x x
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BLOCK DIAGRAM OF A FEEDBACK CONTROL
SYSTEM
CONTROL
ACTUATING
SIGNAL
REFERENCE (ERROR)
OR CONTROLLED
INPUT SIGNAL
MANIPULATED
(r) (e) OUTPUT (c)
VARIABLE (u)

+ FEEDFORWARD PLANT
(CONTROL OR
g
2 ELEMENTS) PROCESS

g1 FORWARD PATH

PRIMARY
FEEDBACK
SIGNAL
(b) FEEDBACK
ELEMENTS

h 26
FEEDBACK PATH
PLANT
(PROCESS OR CONTROLLED SYSTEM)
(g2)
✓system, subsystem, process, or object
controlled by the feedback control system.

FEEDFORWARD ELEMENTS
(CONTROL ELEMENTS)
(g2)
✓ components of the forward path that generate the
control signal u or m applied to the plant. Typically
include controllers, compensators (or
equalization elements), and/or amplifiers. 27
FEEDBACK ELEMENTS
(h)
✓ establish the functional relationship between the
controlled output c and the primary feedback signal
b. Typically include sensors of the controlled c,
compensators, and/or controller elements.

REFERENCE INPUT
(r)
✓ an external signal applied to the feedback control
system, usually at the first summing point, in order
to command a specific action of the plant. It
usually represents ideal (or desired) plant output
behavior. 28
 ACTUATING (ERROR SIGNAL) (e)
✓reference input signal r plus or minus the
primary feedback signal b. The control action is
generated by the actuating (error signal in a
feedback control system.
Note: In an open-loop system the actuating signal is equal to r.

CONTROL SIGNAL (u)

(MANIPULATED VARIABLE) (m)
✓output signal of the feedforward elements g1
applied as input to the plant g2.
CONTROLLED OUTPUT (c)
✓is the output variable of the plant, under the
control of the feedback control system. 29
PRIMARY FEEDBACK SIGNAL
(b)
✓ a function of the controlled output c,
algebraically summed with the reference
input r to obtain the actuating (error)
signal e, that is e=r  b.

Negative feedback means the summing point is a subtractor

e=r-b.
Positive feedback means the summing point is an adder
e=r+b

Note: An open-loop system has no primary feedback signal. 30

FORWARD PATH
✓The transmission path from the
summing point to the controlled output c.

FEEDBACK PATH
✓The transmission path from the
controlled output c back to the summing
point.
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 CONTROLLER/COMPENSATOR
✓Elements of the forward path, between the
actuating (error signal e and the control variable u).
CONTROL LAWS (ALGORITHMS)
✓On-off controller
umax , e(t )  0
u (t ) = 
umin , e(t )  0
✓Proportional controller

u (t ) = K P e(t )
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CONTROLLER/COMPENSATOR
CONTROL LAWS (ALGORITHMS)
✓Derivative controller
de(t )
u (t ) = K D
dt
✓Integral controller

u (t ) = K I  e(t )dt
o

✓Phase-Lead/Lag compensator
du (t )  de(t ) 
+ pu (t ) = K  + ze(t )
dt  dt 
z p Lead
z  p Lag 33
REFERENCES:
• Schaum’s Outline Series “Feedback and Control Systems”,
2nd edition, by DiStefano III, J.J., Stubberud A.R., and Williams
I.J.
• Control Systems Principle and Design, 2nd ed., by Gopal M.,
• Control Systems Engineering, 3rd edition, by Nise N.S.
• Feedback Control Systems, 4th edition, by Philips C.L., and
Harbor R.D.
• Control System Design Lecture Notes for ME 155A, by
Åstrom K.J.

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