Automatic control: Chapter 1
OBJECTIVES
The objectives of this subject/course are to enable you to:
•
Define a control systems.
• Two major measure of performance of control systems.
• Advantages of control systems.
• Difference between Open-Loop and Closed-Loop Control
systems .
• Advantages of Closed-Loop control systems.
• Discuss three major objectives of design and analysis of
control systems.
• Go through all the review questions.
• Go through problem 1, 2, 8, 10,and 23.

Control systems: Control systems as an integral part
of modern society and its numerous applications all
around us. A control system consists of subsystems
and processes (or plants) assembled for the purpose
of controlling the outputs of processes (Nise, 2004).

History of control systems: Read

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
Terminology:
Control system.
Open-loop systems.
Closed loop systems.
Transfer function and characteristic equation.
System.
Discuss how a specific open-loop system can be
altered to form a closed-loop system.
INTRODUCTION
1. What is a Control System?
 Daily life requires numerous objectives that need
to be accomplished through control e.g:
◦ Regulation of temperature and humidity to make our
homes and buildings comfortable to live in.
◦ Control automobiles and planes to reach our
destinations safely.
◦ Control of industrial processes to achieve satisfactory
precision and cost-effectiveness.
◦ Human beings have in-built senses which control their
own actions, the actions of others, and also the actions
of machines.
INTRODUCTION
The control mechanism is based on the ability
to measure the output of a system, and to take
corrective action if its value deviates from some
desired value.
 This necessitates the need for a sensing
device.
Definition: We define a control system as a
system with the ability to measure the output
and to regulate any deviations from the desired
value.
 Alternatively, we define a control system as a
device or set of devices to manage, command,
direct or regulate the behavior of other

INTRODUCTION
2.What are the benefits of Control?
 Some of the benefits of control are:

◦
◦
◦
◦
Path following.
Stabilization.
Performance improvement.
Robustness to plant uncertainty: be able to
maintain system response and error signals
within prescribed tolerances (despite
disturbance effects on plant, noise, modeling
errors due to nonlinearities and time-varying
parameters).
INTRODUCTION
3. Concept of System
 a. What is a System?
 System means different things integrated
together for a common purpose.
 Systems normally perform tasks through
coordinated actions.
 All systems have certain things in common:
◦ They require inputs and outputs to be specified.
◦ They have boundaries.

A typical system is as shown on next slide.
INTRODUCTION
Inputs
System
Outputs
Boundary
Fig.1 Components of a System
 A system may have many inputs and
outputs (Multi-variable system).
INTRODUCTION
In control Engineering the way in which the
outputs responds to the system inputs
(system response) is important.
 A control system design Engineer attempts to
evaluate
the
system
response
by
determining a MATHEMATICAL MODEL for
the system.
 Conventionally, we refer to the system that is
being controlled as the PLANT or PROCESS
and is usually represented by a block
diagram.

INTRODUCTION
In control engineering, there are some
inputs an engineer will have direct control
over, which he can use to control the plant
outputs.
 Such inputs are called Control Inputs.
 Those inputs to a control system which an
engineer has no control over and they tend
to deflect plant outputs from desired values,
are called Disturbance Inputs.
 The diagram on the next slide is an
example of a multivariable system

INTRODUCTION
Rudder
Engines
Wind
Waves/Turbulence
s
Current


Position
Ship/Airplane
Forward velocity
Heading
Ship/Aircraft Motion
(Roll, pitch, yaw, heave)
Fig.2. Multivariable System
The rudder and engines are controlled
inputs(values are adjustable).
Wind, waves, turbulences and current are
disturbance inputs and will induce errors in the
outputs(controlled variables) of position,
heading and forward velocity.
INTRODUCTION
In addition, the disturbance will introduce
increased ship or aircraft motion (roll,
pitch, yaw or heave) which is not
desirable.
 Pitch-motion in vertical plane
 Roll-rock from side to side.
 Yaw-Motion about vertical axis (deviate
temporarily from straight line).
 Heave-to cause to rise and fall with
swelling motion.

INTRODUCTION

The relationship between control input,
disturbance input, plant and controlled
variables is as shown below.
Fig. 3 Plant inputs and outputs
INTRODUCTION
b. Control System Applications
 Many examples of control application exist
and these include:
◦ i. Smart transportation systems
◦ ii. Intelligence Systems
◦ iii. Virtual Prototyping and Hardware in the Loop
◦ iv. Steering Control of Automobile
◦ v. Idle-Speed Control
◦ vi. Sun Tracking Control of Solar Collectors
INTRODUCTION
(i). Smart transportation systems
 Intelligent cars that provide maximum levels of
comfort, safety and fuel efficiency. Intelligent
systems may include climate control, cruise
control, anti-lock brake system (ABS), active
suspension that reduce vehicle vibration over
rough terrain.
◦ (ii). Intelligence Systems
 Newly developed materials provide unique
opportunities for highly efficient actuation and
sensing.
 State-of -the –art actuators and sensors are
implemented in locomotion, material
handling, defence, robotics, aeronautics,
space industry and biological applications.
INTRODUCTION
◦ (iii) Control in Virtual Prototyping and Hardware in
the Loop
 Virtual prototyping is where manufacturers design and test the
entire system in the computer environment (simulation) before
a physical prototype is made.
 This phenomenon is widely applicable in automotive,
aerospace, defence and space industries.
 Design tools such as MATLAB and Simulink (a highperformance language for technical computing) enable
designers to design and test controllers for different
components (suspension, steering, ABS, engines, flight
control mechanisms, landing gears, and other specialized
devices).
 Hardware in the loop technology is a new approach of testing
individual components by attaching them to the virtual and
controller prototypes. The physical controller is interfaced with
the computer and replaces its mathematical model within the
computer.
INTRODUCTION
◦ (iv).Steering Control of Automobile
 This is a simple example of a control system where the
direction of the two front wheels can be regarded as the
controlled variables or the output.
 The direction of the steering wheel is the actuating
signal or input.
 The control system in this case is composed of the
steering mechanism and the dynamics of the entire
automobile.
◦ (v). Idle-Speed Control
 The objective is to control the idle-speed of the engine
of an automobile at relatively low value (for fuel
economy), regardless of the applied engine loads.
 The aim of controlling the engine idle-speed is to
eliminate or minimize the speed droop when engine load
is applied (transmission, power steering, air-conditioning
INTRODUCTION
 The diagram below shows the idle-speed control
system.
Fig. 4. Idle-Speed Control System
 By adjusting the throttle angle, you control the
engine speed.
INTRODUCTION
◦ (vi) Sun Tracking Control of Solar Collectors
 Solar power conversion methods include the solar-cell
conversion technique which involves tracking the sun to
generate non-fossil fuel electrical power.
 In these systems, sun tracking has to be achieved
efficiently.
 The figure below show such a typical system used for
water extraction from underground..
Fig. 5. Solar tracking for Electric power generation for water extraction
INTRODUCTION
 The collector dish must track the sun accurately.
 The movement of the collector dish has to be controlled
by a sophisticated control system(s).
 The controller uses the sun’s rate and sun sensor
information as inputs to generate proper motor commands
to adjust the controller.
◦ The important components of sun-tracking control
system are shown below.
Fig. 6. Important Components of Sun-Tracking Control System
INTRODUCTION
4. Open-Loop Control Systems (Non-feedback
systems)
 This is a system that does not have information
feedback.
 A very simple system.
 The elements of this system can be divided into
two parts:
◦ the controller , and
◦ the controlled process/plant

An input signal or command applied to the
controller, whose output acts as actuating signal,
controls the controlled process so that the
controlled variables will perform according to
INTRODUCTION
In a simple case, the controller can be an Amplifier,
Mechanical linkage, filter, or any other control
elements, depending on the nature of the system.
 In more sophisticated systems, the controller can be
a computer, such as Microprocessor.

Control Input
(Ref Signal) CONTROLLER
Actuating Signal CONTROLLED
PROCESS
(PLANT)
Controlled
Variable
or
Output
Fig. 7. Elements of an Open-Loop Control System

Challenge: This system is very sensitive to changes
in the disturbance input.
INTRODUCTION

Examples of Open-Loop Control Systems
include:
◦ a.Idle-speed control system:-adjust throttle angle
manually, to increase or reduce engine speed.
◦ b. An electric washing machine:-the amount of
washing time is entirely determined by judgment of
its operator.
◦ c. A central heating system without a
thermostat/thermo-switch:- it has to be turned off or
adjusted manually to reduce excessive room
temperature.
INTRODUCTION
5. Closed-Loop Control Systems
 This is a system that has information feedback
which is compared with the desired output and
corrects the output automatically if there are
deviations.
 The closed-loop control system has got a link or
feedback from the output to the input of the
system.
 To obtain more accurate control, the controlled
signal is fed back and compared with the
reference or desired output, and an actuating
signal proportional to the difference of the input
INTRODUCTION
A closed-loop control system is therefore an
automatic control system which does not
require manual intervention to correct for output
deviations.
 The diagram below is an example of a closedloop control system.

or
Desired
output
(Actual)
Fig. 8. Closed-Loop Control System
INTRODUCTION
It is important to note that feedback can be
negative or positive.
 Closed-Loop control systems with feedback
(negative) are not sensitive to changes in the
controlled variables as does open-loop
systems.
 Closed-loop control systems are generally
stable systems.

INTRODUCTION
Practical Examples of Closed-Loop Control
Systems
 a. Room temperature control system with
thermocouple/thermostat:
 The output signal from a temperature sensing
device such as thermocouple or a resistance
thermometer (thermistor) is compared with the
desired temperature.
 Any difference or error causes the controller to
send a control signal to the heat control source
(gas solenoid valve) which produces a linear
movement to adjust the flow of the gas to the gas
burner.
INTRODUCTION
The diagram below shows the room temperature
control system and its block diagram
representation.
Fig.9. Room temperature control system
INTRODUCTION
b. Aircraft Elevator control system:
Control is achieved by power-assisted devices or
servomechanisms that provide the large forces
necessary to operate control surfaces.
 Movement of the control column produces a signal
from the input angular sensor which is compared
with the measured elevator angle by the controller
which generates a control signal that is proportional
to the error.
 The error signal is fed to the electro-hydraulic servovalve which generates a valve movement that is
proportional to the control signal, thereby allowing
high pressure fluid to enter the hydraulic cylinder.

INTRODUCTION

The diagram below illustrates how elevator
control is achieved.
Fig. 10. Aircraft elevator control system
INTRODUCTION
c. Aircraft/Ship Autopilot Control System:
 The system is designed to maintain a vessel
or aircraft on a set heading while being subject
to a series of disturbances such as wind,
waves (turbulences) and current.
 The autopilot can also be used for course
changing.
 The actual heading is measured by a
gyrocompass(or a magnetic compass in small
vessels) and then compared with the desired
heading, dialed/fed into the autopilot by the
ship or aircraft master.

INTRODUCTION

The diagram below demonstrates how this
control is achieved.
Fig. 11. Autopilot control system
INTRODUCTION
The autopilot or controller computes the
demanded rudder angle and sends a control
signal to the steering gear.
 The actual rudder angle is monitored by a
rudder angle sensor, and compared with the
demanded rudder angle to form a control loop.
 The rudder provides a control moment on the
hull to drive the actual heading towards the
desired heading, while the wind, waves and
currents produce moments that may help or
hinder this action.

INTRODUCTION
6. Requirements of a Control System
 The following are the basic requirements of a
control system:
◦ a. Knowledge of the desired value:-What is it you
are trying to control, to what accuracy, and over what
range of values (performance specs).
◦ b. Knowledge of the output or actual value:-This
must be measured by a feedback sensor, in a form
suitable for the controller to understand. Sensor must
also have the necessary resolution and dynamic
response for accuracy of the measured values and
required performance specifications.
INTRODUCTION
◦ c. Knowledge of the controlling device:-The controller
must be able to accept measurements of desired and actual
values and compute a control signal in a suitable form to
drive an actuating element. Controllers can be a range of
devices including mechanical levers, pneumatic elements,
amplifiers, filters, microcomputers, analogue or digital
circuits.
◦ d. Knowledge of the actuating device:- This unit amplifies
the control signal and provides the effort to move the output
of the plant towards the desired value. For example, a gas
solenoid in a room temperature control system is an example
of an actuator device.
◦ e. Knowledge of the plant (process):- Most control
strategies require some knowledge of the static and dynamic
characteristics of the plant or process. These can be
measured or obtained from application of fundamental
INTRODUCTION
7. Design Process of Feedback Control
Systems
The design process of a negative feedback
control system can be achieved in 6 basic
steps:
a. Step 1:-Transform Requirements into a
Physical System.
◦ Identify system performance specifications.
◦ Identify the system components.
◦ Describe such features as weight and physical
dimensions.
◦ Using the requirements, design specifications
INTRODUCTION

b. Step2: Draw a functional block diagram
◦ Translate a qualitative description of the system into a
functional block that describes the component parts of the
system (function and hardware) and show their
interconnection.
◦ Indicate input functions such as transducers and controllers
(with description such as amplifier and motor).
◦ Produce a detailed layout of the system from which the next
stage of developing a schematic can be launched.

c. Step 3: Create a schematic
◦ Transform the physical system into a schematic diagram.
◦ Make approximations about a system and neglect certain
phenomena (details about components) making certain
assumptions about system and the load.
INTRODUCTION

d. Step 4: Develop a Mathematical Model
(Block Diagram) (Model behavior of plant).
◦ Use physical laws such as Kirchhoff’s laws for electrical
networks and Newton’s laws for mechanical systems.
◦ Make simplifying assumptions.
◦ Model the system mathematically.
◦ Develop a mathematical model that describes the
relationship between the input and output of the system eg.
d n y(t )
d n1 y(t )
d m x(t )
d m1 x(t )
a0
 a1
 ...  an y(t )  b0
 b1
 ...  bm x(t )
n
n 1
m
m 1
d t
dt
d t
dt
◦ NB. Many systems can approximately be described by this
equation.
INTRODUCTION
◦ The transfer function, also derived from the above equation,
can be used to model the system. The model is derived from
linear time-invariant differential equation using the Laplace
transform e.g.y ( s ) b0 s m  b1s m1  ...  bm
G( s) 
x( s )

a0 s n  a1s n1  ...  an
◦ However, the transfer function is meant for modeling linear
systems, but yields more information about the system than
the differential equation.
◦ Transfer function can also be used to model interconnection
of subsystems by forming block diagrams.
◦ State-space representation can also be used for modeling
systems especially for simulation on the digital computer.
.
◦ The system
x  Ax can
Bu be represented in state space by the
equations:
y  Cx  Du
INTRODUCTION
t  t0
x(t )
where by assuming initial conditions
and that
:
.
x=state
vector
x
=derivative of the state vector with respect to
time
y=output vector
u=input or control vector
A=system matrix
B=input matrix
C=output matrix
D=feed forward matrix
0
INTRODUCTION

Step 5: Reduce the Block Diagram
◦ Need to reduce large systems block diagram to a
single block with mathematical description that
represents the system from its input to its output.

Step 6: Analyze and Design
◦ Analyze the system to see if the response
specifications and performance requirements can
be met by simple adjustment of system
parameters. If not, you may need to design
additional hardware to achieve the desired
performance.
◦ Use test input signals (step, impulse, ramp,
parabolic, sinusoidal) and check the transient
INTRODUCTION
8. System
We defined a system as a network of components
integrated together to form a common purpose entity.
 For simplicity, a system(whether open-loop or
closed-loop), can be represented by a box with at
least an input and output terminal.
 Systems can be linear or non-linear.


The block diagram below represents a system.
x(t )
Syste
m
y (t )
Fig. 12. System Representation
INTRODUCTION
◦ a. Linear System
◦ A system is called linear if:
 (i). Magnitude of output follows that of input:
ax(t )  ay(t )
 (ii). System satisfies additive (superposition) property:
x1 (t )  x2 (t )  y1 (t )  y2 (t )
 A system that is non-linear does not meet the above
conditions.
◦ b. Time Invariant System
 A system is called time-invariant if the output follows the
same time shift in the input:
 (x(t+τ)=y(t+ τ)).
 E.g. When the parameters of a control system are
stationary w.r.t. time.

c. Time Variant System:
◦ A system is time variant if the inputoutput characteristics vary with time:
(x(t+τ)≠y(t+τ)).
System is time variant when the
parameters of a system vary with time e.g.
 Resistance of a coil that tends to change with
time of current flow and therefore heat
generated by the current.
 Parameters of guided missile changes as
it travels and burns the fuel.
INTRODUCTION
d. Linear Time Invariant (LTI) Systems
 We may define a Linear Time Invariant
System as follows:
◦ Let y(t) be the output of the system for an input
x(t) so that L[x(t)]=y(t).
◦ The system is LTI when it satisfies the
following conditions:
 (a) L[x(t+ τ)]=y(t +τ) (Time invariance)
 (b) L[a x (t )  a x (t )]  a y (t )  a y (t ) (Superposition or
1 1
2 2
1 1
2 2
additive property)

It should be noted that many processes of
interest can be approximated by LTI
models.
INTRODUCTION
9. System Transfer Function

When a signal passes through a system, the
following may occur to it:
◦ a. Amplification or attenuation (Proportional or Identity
operator function).
◦ b. Differentiation (Differentiator function)
◦ c. Integration (Integrator operator function)
This behavior of the system when a signal is
transferred through the system to the output is
referred to as the Transfer Characteristics of the
system.
 The characteristic is also referred to as the
Transfer Function of the system.

INTRODUCTION
Amplification/Attenuation
x(t )
Gain/
Attenuation
A
Ax(t )
System
Differentiation
x(t )
Differential
d/dt
System
dx(t ) / dt
INTRODUCTION
Integration
x(t )
Integral
 x(t )dt

System
Fig. 13. Effects of a system on a Signal
• The transfer function relates the output to the input.
•It characterizes the behavior of the system it represents.
•We shall call the transfer function of a system G(s).
•Remember that we said the transfer function is developed from a system
modeled by a set of linear differential equations, transformed by Laplace
transforms.
•The transfer function depends only on the system and not upon the form of
input.
•We should remember however that the transfer function is derived by
assuming linearity and zero initial conditions.
INTRODUCTION

The mathematical model relating the input and
output of a linear and time invariant system is:
d n y(t )
d n1 y(t )
d m x(t )
d m1 x(t )
a0
 a1
 ...  an y(t )  b0
 b1
 ...  bm x(t )
n
n 1
m
m 1
d t
dt
d t
dt

where n≥m-1, a condition for a system to be
realizable.
 Assuming all initial conditions to be zero, and
applying
a0 s n y(sLaplace
)  a1s n1 y(stransforms
)  ...  an y(s) we
b0 s mget;
x(s)  b1s m1x(s)  ...  bm x(s)

m 1
Re-arranging the above
we obtain;
b0 s m  b1srelationship
 ...  bm
y( s) 
a0 s  a1s
n
n 1
 ...  an
x( s )  G ( s ) x( s )
INTRODUCTION
The overall transfer function of the system
becomes:
y ( s) b0 s m  b1s m1  ...  bm
G( s) 

n
n 1
x( s) a0 s  a1s  ...  an
 We model such a system by a single block
diagram with one input and one output as
follows:

x( s )
y( s)
G(s)
Fig.14. Transfer Function Representation of a System

Now, suppose g(s) represents the denominator of
INTRODUCTION

We can rewrite the relationships as:
f ( s)  b0 s m  b1s m1  ...  bm
g ( s)  a0 s n  a1s n1  ...  an
We can find roots of these two equations by
equating each one of them to zero.
 The roots of f(s) are called Zeros.
 The roots of g(s) are called Poles.
 These roots have a bearing on the stability
and steady-state gain of a system.

INTRODUCTION
Stability and Steady-State Gain
 The stability of the system is determined by
its characteristic equation:
d n y(t )
d n1 y(t )
d m x(t )
d m1 x(t )
a0
 a1
 ...  an y(t )  b0
 b1
 ...  bm x(t )
n
n 1
m
m 1
d t
dt
d t
dt
This is identical to setting the denominator of
the system transfer function equal to zero:
g(s)=0.
 For system stability, the roots of g(s)=0, must
be negative real parts and where they are
complex, they occur as conjugate pairs
(poles are real negative, complex and in

INTRODUCTION
Recall that these roots of g(s)=0 are called
poles of G(s).
 The roots of the numerator f(s)=0 are called
zeros of G(s).
 Note that when counting the roots, repeated
roots (zeros) are counted as separate roots.

INTRODUCTION
Cascaded Control Systems
G ( s)
 Consider 2 systems with transfer functions
and G (s) connected in series.

1
2
x( s )
q( s)
G1 ( s)
y( s)
G2 ( s)
Fig. 14. Cascaded Systems

Assume that there is no interaction or loading
between the blocks and that the individual
transfer functions remain unaltered when the
blocks are linked together.
INTRODUCTION
Then,q(s)  x(s)G1 (s) andy(s)  q(s)G2 (s) .
 It follows that;

◦
◦ and
◦

y(s)  x(s)G1 ( s)G2 (s)
y( s)
 G1 ( s)G2 ( s) .
x( s )
In general, for n blocks in cascade;
y( s)
 Gn ( s)Gn 1 (s)...G2 (s)G1 (s)
x( s )
INTRODUCTION
Paralleled Control Systems
G ( s)
 Assume thatG (s) and
are connected in
parallel.

2
1
G1 ( s)
q1 ( s)
y( s)
x( s )
G2 ( s)
q2 ( s)
Fig. 15. Paralleled Control Systems
x( s )

Since
is common to the two systems;
INTRODUCTION
q1 ( s)  x( s)G1 ( s)
q2 ( s)  x( s)G2 ( s)
y ( s)  q1 ( s)  q2 ( s)  x( s)G1 ( s)  x( s)G2 ( s)

Therefore, the overall transfer function is:
y(s)
 G1 ( s)  G2 ( s)
x( s )

In general, for n blocks in parallel;
y( s)
 G1 ( s)  G2 ( s)  ...Gn ( s) .
x( s )
INTRODUCTION

Closed-Loop Control System

Consider a closed-loop system with negative feedback loop
or control.
Let the forward transfer function be G(s).
Let H(s) be the transfer function of the feedback
network/system/device.


Error detector/
summing junction
x( s )
e( s )
+
G( s)
y( s)
z ( s)
H (s)
Fig.15.Closed-Loop Control System
INTRODUCTION
From the diagram above we can deduce the
overall transfer gain/function of the system as
follows:
e( s )  x ( s )  z ( s )
(1)
z (s)  y(s) H (s)
(2)
y ( s)  e( s)G ( s)
(3)
 We therefore need to come up with a
x(s), yincluding
(s), G(s)andH (s)
relationship
.
 Substituting (1) in (3) we get:
(4)
y(s)  [ x(s)  z (s)]G(s)

INTRODUCTION


Substituting for z(s) in (4), we get:
y(s)  [ x(s)  y(s) H (s)]G(s)
Equating and dividing we obtain:
y( s)
G(s)

 G ' ( s)
x( s) 1  H ( s)G( s)

(5)
(6)
The overall transfer function/gain of the
( s)
closed loop controlG system
is given as:
'
G( s)
G ( s) 
1  H ( s)G( s)
'
(7)
INTRODUCTION

Note: The characteristic equation of this
system is:
1  H (s)G(s)  0

Now, for unity-feedback, H ( s)  1
G ' ( s) 
Therefore,
x( s )
G( s)
1  G( s)
G( s)
y( s)
INTRODUCTION

10. Effects of feedback in Control Systems
Feedback effects in control systems are more complex than
mere reduction of system error.
 Feedback also affects system performance characteristics
such as stability, bandwidth, overall gain, impedance and
sensitivity.
 a. Effects on overall Gain: Negative feedback reduces gain
of a non-feedback system due to the introduction of (1+GH) in
the denominator of the transfer function.
 In positive feedback, the gain of the system is increased due
to the introduction of (1-GH) in the denominator of the nonfeedback transfer function.
 Positive feedback causes the system to be unstable and may
drive the system into oscillations (regeneration).
 Feedback can increase the gain of a system in one frequency

INTRODUCTION

b. Effects on Stability: Feedback can improve stability or
be harmful to stability when not properly applied.
 Generally one of the conditions for instability is when GH=-1
and overall gain is infinity (favorable condition for
oscillations).
 There are many other conditions that may be used to
determine system stability, including the determination and
location of poles and zeros of the transfer function.
 c. Effects on Sensitivity: In general, a good control system
should be very insensitive to parameter variations but
sensitive to input commands.
 Since GH is a function of frequency, positive or negative
values of GH may cause the system to be sensitive to some
frequency range and less sensitive to others.
 Feedback, therefore, can increase or decrease sensitivity of
INTRODUCTION
d. Effect on External Disturbance or Noise:
 Physical systems are subject to some
extraneous signals or noise.
 Sources of noise include thermal noise
voltages in electronic circuits, and brush or
commutator noise in electric motors.
 External disturbances such as wind acting on
the antenna are quite common in control
systems.
 Control systems should be designed so that
they are insensitive to noise and disturbances
but sensitive to input commands.

INTRODUCTION
e. Effect on bandwidth, impedance,
transient and frequency response:
 In general, feedback has an effect on such
performance characteristics as bandwidth,
impedance, transient response and frequency
response.
 This is so because G and H are a function of
frequency.

Questions

Q1. Define the following:
◦
◦
◦
◦
◦
◦
◦

a. System
b. Linear System.
c. Linear Time Invariant System.
d. Control System.
e. Open-loop system.
f. Closed-loop system.
g. System transfer function.
Q2.What are the benefits of control in
systems?
Q3. How can an open-loop control system be
converted into a closed-loop system?
 Q4. What are the requirements of a control
system?
 Q5. List and briefly explain the design
process of a feedback control system.
 Q 6. For a system with transfer function
2
given by;
4s  15s  5

G( s) 
s(s 2  3s  2)
a. Determine if the system is stable or not.
b. Determine the number of zeros and
poles of the system.

Q7. Consider a servomechanism (closedloop control system) depicted by block
diagram below:
Error detector/
summing junction
Amplifier and
Control
e( s )
x( s )
+
System or Plant
(Includes actuator)
q( s)
K(s)
y( s)
G(s)
-
H(s)
Measuring Device

Show that the overall transfer function of the closed-loop
control servo control system is:G ' (s)  G(s) K (s)
1  G ( s) K ( s) H ( s)

What is the characteristic equation of the system?

Q8. Describe briefly the effects of feedback
on closed-loop control systems.