FEEDBACK AND CONTROL
SYSTEMS
INTRODUCTION
System
• An arrangement, set, or collection of things connected or
related in such 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.
INPUT
How do I change this?
SYSTEM
OUTPUT
To get what I want
Control System
• An arrangement of physical components connected or related in
such a manner as to command, direct, or regulate itself or another
system.
• A control system is a system of devices or set of devices, that
manages, commands, directs or regulates the behavior of other
device(s) or system(s) to achieve desire results.
• Position, velocity, acceleration, temperature, voltage, pressure,
current, etc.
“A control system is a system, which controls other system.”
“A control system is a mechanism that alters the future state of a system.”
Why do we build control systems?
• Power Amplification
• Remote control
• Convenience of input form
• Compensation of disturbances
Examples of a Control System
Bathroom Toilet Tank
*As the tank is emptied through the 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 the water.
Input
• Stimulus, excitation or command applied to a control system,
typically from an external energy source, usually in order to produce
a specified response from the control system
Examples:
Input
• Preset water level for a bathroom toilet tank
• Desired velocity for a steam engine governor
• Thermostat setting for an air conditioner
Output
• Actual response obtained from a control system. It may or
may not be equal the specified response by the input.
Examples:
Input
Output
• Actual water level for a bathroom toilet tank
• Actual velocity for a steam engine governor
• Actual room temperature
“System”
Input
System
Output
• A system is an arrangement of or a combination of different
physical components connected or related in such a manner so
as to form an entire unit to attain a certain objective.
Control
• It means to regulate, direct or command a system so that the
desired objective is attained.
System + Control = Control System
Control System
Input
Control
System
Output
• It is an arrangement of different physical elements connected in
such a manner so as to regulate, direct or command itself to
achieve a certain objective.
Difference between System and Control System
Input
System
Proper
Output
May or may
not be
desired
Input
Control
System
Desired
Output
Difference between System and Control System
A Fan: Can't Say System
• A fan without blades cannot be a “SYSTEM” Because it cannot provide a desired/proper
output i.e. airflow
A Fan: Can be a System
• A Fan with blades but without regulator can be a “SYSTEM” because it can provide a
proper output i.e. airflow
• But it cannot be a “Control System” Because it cannot provide desired output i.e.
controlled airflow
A Fan: Can be a Control System
• A Fan with blades and with regulator can be a “CONTROL SYSTEM” because it can
provide a desired output.
i.e. Controlled airflow
SINGLE-INPUT
SINGLE OUTPUT SYSTEM
MULTIPLE-INPUT
MULTIPLE OUTPUT SYSTEM
• A single output is controlled by a single input
f(t)
SISO
y(t)
• More than one controlled output and command
input
• Also called multivariable system
f1(t)
y1(t)
f2(t)
y2(t)
f3(t)
f4(t)
MIMO
y3(t)
y4(t)
Open-Loop Control Systems
• The control action is independent of the output
FEATURES OF AN 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.
Open loop systems
• Electric Hand Drier - Hot air (output) comes out as long
as you keep your hand under the machine, irrespective
of how much your hand is dried.
• Automatic Washing Machine - This machine runs
according to the pre-set time irrespective of washing is
completed or not.
• Bread Toaster - This machine runs as per adjusted time
irrespective of toasting is completed or not.
• Automatic Tea/Coffee Maker - These machines also
function for pre adjusted time only.
• Timer Based Clothes Drier - This machine dries wet
clothes for pre-adjusted time, it does not matter how
much the clothes are dried.
• Light Switch - Lamps glow whenever light switch is on
irrespective of light is required or not.
• Volume on Stereo System - Volume is adjusted manually
irrespective of output volume level.
CLOSED LOOP SYSTEM
• Compensated for disturbances
TRANSDUCER
• Converts the input/output to the form used by the controller
(example: potentiometer, thermistor)
Closed loop Control Systems
• The control action is somehow dependent on the
output.
Input
transducer
• Automatic Electric Iron - Heating elements are controlled by
output temperature of the iron.
• Servo Voltage Stabilizer - Voltage controller operates
depending upon output voltage of the system.
• Water Level Controller - Input water is controlled by water
level of the reservoir.
• Missile Launched and Auto Tracked by Radar - The direction
of missile is controlled by comparing the target and position of
the missile.
Output
transducer
• An Air Conditioner - An air conditioner functions depending
upon the temperature of the room.
• Cooling System in Car - It operates depending upon the
temperature which it controls.
Difference Between OLCS & CLCS
• Open Loop Control System
• The open loop systems are
simple & economical.
• They consume less power.
• The OL systems are easier to
construct because of less number
of components required.
• The open loop systems are
inaccurate & unreliable
• Closed Loop Control System
• The closed loop systems are
complex and costlier
• They consume more power.
• The CL systems are not easy to
construct because of more
number of components required.
• The closed loop systems are
accurate & more reliable.
Difference Between OLCS & CLCS
• Open Loop Control System
• Stability is not a major problem
in OL control systems. Generally
OL systems are stable.
• Small bandwidth.
• Feedback element is absent.
• Output measurement is not
necessary.
• Closed Loop Control System
• Stability is a major problem in
closed loop systems & more care
is needed to design a stable
closed loop system.
• Large bandwidth.
• Feedback element is present.
• Output measurement is
necessary.
Difference Between OLCS & CLCS
• Open Loop Control System
• The changes in the output due to
external disturbances are not
corrected automatically. So they
are more sensitive to noise and
other disturbances.
• Examples:
• Coffee Maker,
• Automatic Toaster,
• Hand Drier.
• Closed Loop Control System
• The changes in the output due to
external disturbances are
corrected automatically. So they
are less sensitive to noise and
other disturbances.
• Examples:
• Guided Missile,
• Temp control of oven,
• Servo voltage stabilizer.
Classification of Control System
• Linear Control System
A system is called linear system, if the output is proportional to its input and the
principle of superposition can be applied.
• Non Linear Control System
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 of
subsystem) so that the appropriate control action may be formed as some function of the output and
input.
CHARACTERISTICS OF FEEDBACK
• Increased accuracy
• Reduced sensitivity of the ratio of the output to input to variations in system parameters and other
characteristics
• Reduced effects of nonlinearities
• Reduced effects of external disturbances or noise
• Increased bandwidth
• Tendency toward oscillation or instability.
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 (ztransform)
2. Block diagrams
3. Signal flow graphs
Block Diagram
Shorthand, pictorial
representation of the causeand-effect relationship
between the input and
output of a physical system.
Arrows represent the
direction of information or
signal flow
x
input
Block
d/dt
y = dx/dt
output
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.
Summing Point
• Used in adding or subtracting signals
z
+
x
x+y
+
y
+
x
x-y
+
y
-
x
x+y+z
+
y
+
Take-off Point
• Used to have the same signal or variable be an input to more than
one block or summing point.
Takeoff Point
Takeoff Point
x
x
x
x
x
x
x
Block Diagram of a Feedback Control System
Control Signal or
Manipulated
Variable
(u)
Actuator
(Error)
Signal
(e)
Reference
Input
(r)
+
Plant
or
Process
Feedforward
(Control Elements)
±
g1
Primary
Feedback
Signal
(b)
Controlled Output
(c)
FORWARD PATH
Feedback
Elements
h
FEEDBACK PATH
g2
Block Diagram of a Feedback Control System
PLANT
(PROCESS OR CONTROLLED SYSTEM)
(g2)
System, subsystem, process, or object controlled by the feedback control system.
FEEDFORWARD ELEMENTS
(CONTROL ELEMENTS)
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
Block Diagram of a Feedback Control System
• 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.
Block Diagram of a Feedback Control System
• ACTUATIONG (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.
• 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.
Block Diagram of a Feedback Control System
• 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.
Block Diagram of a Feedback Control System
• 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.
Block Diagram of a Feedback Control System
• CONTROLLER / COMPENSATOR
• Elements of the forward path, between the actuating (error signal e and the control variable
u)
• CONTROL LAWS (ALGORITHMS)
• ON-OFF CONTROLLER
𝑢 𝑡 =
𝑢
𝑢
,𝑒 𝑡 > 0
,𝑒 𝑡 < 0
• PROPORTIONAL CONTROLLER
𝑢 𝑡 = K 𝑒(𝑡)
Block Diagram of a Feedback Control System
• CONTROLLER / COMPENSATOR : CONTROL LAWS / ALGORITHMS
• Derivative controller
𝑢 𝑡 =𝐾
𝑑𝑒(𝑡)
𝑑𝑡
• Integral controller
𝑢 𝑡 = 𝐾 𝑒(𝑡)𝑑𝑡
• Phase-Lead/Lag compensator
𝑑𝑢 𝑡
𝑑𝑒(𝑡)
+ 𝑝𝑢(𝑡) = 𝐾
+ 𝑧𝑒(𝑡)
𝑑𝑡
𝑑𝑡
𝑧 < 𝑝 Lead
𝑧 > 𝑝 Lag
• Analysis – is the process by which a system’s performance is
determined.
• Design – is the process by which a system’s performance is created or
changed.
• Main objectives of Control System Analysis and Design
• Transient response
• Steady-state error
• Stability
• Note
• Transient response and Steady-state error can be controlled
• often by a simple adjustment of gain (amplification)
• Sometimes by redesigning the controller
• (Redesign – compensating the system;
• Redesigned Hardware – compensator )
Manual control system
Automatic control system