1. CONTROL SYSTEMS
ENGINEERING
Course Code: MEB 4101
Course Credit 4
Introduction
Prepared by;
Masoud Kamoleka Mlela
BSc, Electromechanical Eng. (UDSM)
MSc, Renewable Energy (UDSM)
PhD, Mechanical Engineering (HEU, CN).

2. 1. Control Systems Terminology and Definitions:
• Systems and control systems,
• classification of control systems,
• block diagram of a feedback control systems,
• terminology of the closed loop block diagram servomechanisms and
regulations,
• remote position control servomechanisms.
2. Modelling and performance of control systems:
• Overview on on/off and continuous control of mechanical,
• thermal and chemical systems,
• physical relationships of basic components,
• transfer functions,
• block diagrams and their reductions,
• sign flow graphs, overall system transfer function.
MODULE CONTENT

3. 3. Dynamic response:
• Time response – classical solution and lap lace transforms,
• transient response and steady – state error.
4. Stability criteria and Analysis:
• Stability definition,
• characteristic of root locus,
• Rourth – Hurwitz criteria,
• Nyquist criteria,
• Bode diagrams.
5. Analysis and Design of feedback control systems:
• Objectives of analysis,
• methods of analysis,
• design objectives,
• design methods.
MODULE CONTENT Cont…

4. 6. Practical Aspect:
• Machine tool systems,
• pneumatic and Hydraulic Systems,
• servomechanisms system components,
• A/D and D/A conversion.
7. Measuring Systems:
• Pressure,
• Speed, Level, and
• Temperature.
Integrated Methods of Assessment
• Continuous Assessment components: 40%
• End of Semester Examination: 60%
MODULE CONTENT Cont…

5. CONTROL SYSTEMS TERMINOLOGY
AND DEFINITIONS
CONTROL SYSTEMS ENGINEERING

6. Introduction to control systems
• A system is a collection of objects (components)
connected together to serve an objective, or
• A system is a combination of components that act
together to perform an objective
• A control system is that means by which any quantity of
interest in a machine, mechanism, or other equipment is
maintained or altered in accordance with a desired
manner,
or simply
• A control system is a system in which the output quantity
is controlled by varying the input

7. Classification of control systems
Control systems may be classified in a number of ways
depending on the purpose of classification
1. Depending on the hierarchy, control systems may be
classified as
»Open-loop control systems
»Closed-loop control systems
»Optimal control systems
»Adaptive control systems
»Learning control systems

8. Classification of control systems Cont...
1. Depending on the presence of human being as a
part of the control systems , control system may be
classified as
»Manually controlled systems
»Automatic control systems

9. Depending on the presence of feedback, control
systems may be classified as
»Open-loop control systems
»Closed-loop control systems or feedback
control systems

10. According to the main purpose of the system, control
systems may be classified as
»Position control systems
»Velocity control systems
»Process control systems
»Temperature control systems
»Traffic control systems etc.

11. Open-loop control systems

12. Open-loop control systems
• These systems in which the output has no effect on the
control action (on the input) are called open-loop
control systems.
• In other words, in an open-loop control system, the
output is neither measured nor feedback for
comparison with the input
• Open-loop control systems are not feedback systems

13. Open-loop control systems
• Examples of Open-loop control system
* One practical example of an open-loop control system is a washing
machine - soaking washing and rinsing in the washer operates on a time
basis.
The machine does not measure the output signal, i.e. the cleanliness of the
clothes
* A traffic control system that operates by means of signal on a time
basis; is another example of an open-loop control system
* A room heater without any temperature sensing device is also an example
of an open-loop control system

14. Closed-loop control systems
• Feedback control systems are often referred to as closed-
loop control system.
• In contrast to an open-loop control system, a closed-loop
control system utilities an additional measure of the actual
output to compare the actual output with the desired
output response.
• The measure of the output is called the feedback signal

15. • A simple closed-loop control system is shown in the
following figures.
Closed-loop control systems
Fig 2: general block diagram of a closed-loop control system

16. • The system operates under these simple principles
 Measure the variable to be controlled (output)
 Compare this measured value with the reference input
(commanded) value and determine the difference.
 Use this difference as a means of control i.e. this difference
adjust the controlled variable (output) to the desired value.
Closed-loop control systems

17. Open-loop vs Closed loop
Open-loop control system Closed-loop control system
1 The open-loop systems are simple and
economical.
1 The closed-loop systems are complex and
costlier.
2 They consume less power. 2 They consume more power.
3 The open-loop systems are easier to construct
because of less number of components
required.
3 The closed-loop systems are not easy to
construct because of more number of
components required.
4 Stability is not a major problem in open-loop
control systems. Generaly, the open-loop
systems are stable.
4 Stability is a major problem in closed-loop
control systems and more care is needed to
design a stable closed-loop system.
5 The open-loop systems are inaccurate and
unreliable.
5 The closed-loop systems are accurate and more
reliable.
6 The changes in the output due to external
disturbances are not corrected automatically. So
they are more sensitive to noise and other
disturbances.
6 The changes in the output due to external
disturbances are corrected automatically. So
they are less sensitive to noise and other
disturbances.
7 The feedback in a closed-loop system may lead
to oscillatory response, because it may over
correct errors, thus causing oscillations of
constant or changing amplitude.

18. Servomechanism
• In the modern usage, the term servomechanism is
restricted to feedback control systems in which the
controlled variable is mechanical position or time
derivatives of position, e.g. velocity and acceleration.
• servomechanisms are illustrated below.
Fig 3: Automatic Tank level control system

19. Servomechanism
• The purpose of this system is to maintain the liquid level
h (output) in the tank as close to desired liquid level H
as possible, even when the output flow rates is varied by
opening the valve V1. This has to be done by controlling
the opening of the valve V2.
Fig shows an
automatic tank
level control
system.

20. • The potentiometer acts as an error detector. The slider arm A is
positioned corresponding to the desired liquid level H (the
reference input). The power amplifier and the motor drive form
the control elements. The float forms the feedback path element.
The valve V2 is to be controlled in the plant.
Servomechanism

21. • The liquid level is sensed by a float and it positions the slider arm B on the
potentiometer. When the liquid level rises or falls, the potentiometer gives
an error voltage proportional to the change in liquid level. The error
voltage actuates the motor through a power amplifier which in turns
conditions the plant (i.e. decreases or increases the opening of the valve
V2) in order to restore the desired liquid level.
• Thus, the control system automatically attempts to correct any deviation
between the actual and the desired liquid levels in the tank
Servomechanism

22. Control Systems - Feedback
Types of Feedback
 There are two types of feedback
– Positive feedback
– Negative feedback
Positive Feedback
The positive feedback adds the reference input, R(s) and feedback output.
The following figure shows the block diagram of positive feedback
control system.
transfer function of positive feedback
control system is,
Where,
• T is the transfer function or overall gain of positive feedback
control system.
• G is the open loop gain, which is function of frequency.
• H is the gain of feedback path, which is function of frequency.

23.  Negative Feedback
Negative feedback reduces the error between the reference input, R(s)
and system output. The following figure shows the block diagram of the
negative feedback control system.
Transfer function of negative feedback control system is,
Where,
• T is the transfer function or overall gain of
negative feedback control system.
• G is the open loop gain, which is function of
frequency.
• H is the gain of feedback path, which is
function of frequency.
Control Systems - Feedback

24. Block Diagram
• Figure 4 shows an element of the block diagram. The arrow head
pointing towards the block indicates the input, and the arrow
head leading away from the block represents the output.
Fig 4: Element of block diagram
• The advantages of the block diagram representation of a system
lie in the fact that it is easy to form the overall block diagram of
the entire system by merely connecting the blocks of the
components according to the signal flow and that it is possible to
evaluate the contribution of each component to the overall
performance of the system.

25. • The plus or minus sign at each arrow head indicates
whether the signal is to be added or subtracted. It is
important that the quantities being added or subtracted
have the same dimensions and the same units.
• The block diagram elements used frequently in control
system and the related algebra are shown below in figure5.
One of the important components of a control system is the
sensing device that acts as a junction point for signal
comparisons. The physical components involved are: the
potentiometer, synchro, resolver, differential amplifier,
multiplier and other signal processing transducer
Block Diagram

26. Block Diagram
Fig5: (a), (b) and (c) addition and subtraction operations and (d) multiplication operation and
(e) take-off point
Branch point: A branch point or a take-off point is a point from which the signal from
a block goes concurrently to other blocks or summing point

27. • Figure 6 shows an example of a block diagram of a closed-loop system. The
output C(s) is fed back to the summing point where it compared with the
reference input. When the output is fed back to the summing point for
comparison with the input, it is necessary to convert the form of the output
signal. The role of the feedback element is to modify the output before it is
compared with the input. This conversion is accomplished by the feedback
element whose transfer function is H(s). The output of the block C(s) in this
case is obtained by multiplying the transfer function G(s) by the input to the
block E(s). The feedback signal that is fed back to the summing point for
comparison with the input is B(s) =C(s) H(s).
Block diagram of a Closed-Loop system
Fig 6: Block diagram of Closed-Loop System

28. The following terminology is defined with reference to the diagram of Fig 6:
r(t), R(s) = reference input (command)
c(t), C(s) = output (controlled variable)
b(t), B(s) = feedback signal
e(t), E(s) = error signal
G(s) = forward path transfer function
H(s) = feedback path transfer function
G(s) H(s) = L(s) = Loop transfer function or open-loop transfer function
= Closed-loop transfer function or system transfer function
Block diagram of a Closed-Loop system
)
(
)
(
)
(
s
R
s
C
s
T 

29. • The closed-loop transfer function T(s) can be expressed as a function of
G(s) and H(s).
From Figure 6
C(s) = G(s) E(s) ........ (i)
And B(s) = C(s) H(s) ........ (ii)
The error signal is
E(s) = R(s)-B(s) ....... (iii)
Substituting equation (iii) and (ii) in Eq (i), we get
C(s) = G(s) [R(s) ˗ B(s)]
= G(s) R(s) ˗ G(s) B(s)
= G(s) R(s) ˗ G(s) H(s) C(s)
Or C(s) [1+ G(s) H(s)] = G(s) R(s) ....... (iv)
Block diagram of a Closed-Loop system

30. In general, a control system may contain
more than one feedback loop, and
evaluation of transfer function from the block
diagram by means of the algebraic method
described above may be tedious. The
transfer function of any linear system can be
obtained directly from its block diagram by
use of the signal flow graph gain formula.
Block diagram of a Closed-Loop system

31. BLOCK DIAGRAM AND TRANSFER FUNCTIONS OF MULTIVARIABLE
SYSTEMS
• When multiple inputs are present in a
linear system, each input can be treated
independently of the others. The
complete output of the system can then
be obtained by superposition, i.e.
outputs corresponding to each input
alone are added together.
• Consider the two-input linear system
shown in Fig 7(a). The response to the
reference input can be obtained by
assuming U(s) = 0. The corresponding
block diagram shown in Fig 7(b) gives
CR(s) = output due to R(s) acting alone
...........(v)
Figure7: (a) Block diagram of a 2-input system, (b)
block diagram when U(s) is zero, and (c)
Block diagram when R(s) is zero
)
(
)
(
)
(
)
(
1
)
(
)
(
2
1
2
1
s
R
s
H
s
G
s
G
s
G
s
G



32. • Similarly, the response to the input U(s) is
obtained by assuming R(s) = 0. The block
diagram corresponding to this case is shown
in Fig 7(c) which gives
Cu(s) = output due to U(s) acting alone
.......(vi)
The response due to the simultaneous
application of R(s) and U(s) can obtained by
adding the two individual responses, i.e. Eqs. (v)
and (vi).
)
(
)
(
)
(
)
(
1
)
(
2
1
2
s
U
s
H
s
G
s
G
s
G


)]
(
)
(
)
(
[
)
(
)
(
)
(
1
)
(
1
2
1
2
s
U
s
R
s
G
s
H
s
G
s
G
s
G


 ....................... (Vii)
BLOCK DIAGRAM AND TRANSFER FUNCTIONS OF MULTIVARIABLE
SYSTEMS

33. • Consider now the case, where and
In this case, the closed-loop transfer function becomes
almost zero, and the effect of the disturbance is suppressed.
This is an advantage of the closed-loop system.
1
)
(
)
(
1 
s
H
s
G .
1
)
(
)
(
)
( 2
1 
s
H
s
G
s
G
)]
(
)
(
)
(
[
)
(
)
(
)
(
1
)
(
)
( 1
2
1
2
s
U
s
R
s
G
s
H
s
G
s
G
s
G
s
C 


BLOCK DIAGRAM AND TRANSFER FUNCTIONS OF MULTIVARIABLE
SYSTEMS

34. • Two block diagram representations of a multivariable
system with p inputs and q outputs are shown in Fig 8 . In
Figure 8(a), the individual input and output signals are
designated whereas in the block diagram of Figure 8(b), the
multiplicity of inputs and outputs is denoted by vectors. In
practice, the case of Figure 8(b) is preferable because of
simplicity
BLOCK DIAGRAM AND TRANSFER FUNCTIONS OF MULTIVARIABLE
SYSTEMS
Figure 8: Block diagram representation of a multivariable system.

35. • In the case of Multiple-input-multiple-output system shown
in Figure 8(a), the ith output Ci(s) is given by the principle of
superposition as
(viii)
Where Rj(s) is the jth input and Gij(s) is the transfer function
between the ith output and jth input with all other inputs
reduced to zero.




r
j
j
ij
i m
i
s
R
s
G
s
C
1
,...,
2
,
1
);
(
)
(
)
(
BLOCK DIAGRAM AND TRANSFER FUNCTIONS OF MULTIVARIABLE
SYSTEMS
The corresponding block
diagram can be drawn as
in Figure 8(b), where thick
arrows represent multi-
inputs and outputs.

36. This can be expressed in compressed matrix notation as
)
(
)
(
)
( s
R
s
G
s
C  ........... (ix)
Where, R(s) = Vector of inputs (In Laplace transform) (p)
G(s) = Matrix transfer function (q ×p)
C(s) = Vector of outputs (In Laplace transform)
BLOCK DIAGRAM AND TRANSFER FUNCTIONS OF MULTIVARIABLE
SYSTEMS
In matrix form, Eq (viii) can be expressed as

37. • The figure 9 shows the block diagram of a multivariable
feedback control system. When a feedback loop is present
as in Fig 9, each feedback signal is obtained by processing
in general all the outputs. Thus for ith feedback signal, we
can write
The ith error signal is then
BLOCK DIAGRAM AND TRANSFER FUNCTIONS OF MULTIVARIABLE
SYSTEMS
• The figure 9 shows the block diagram of a multivariable
feedback control system. When a feedback loop is present
as in Fig 9, each feedback signal is obtained by processing
in general all the outputs. Thus for ith feedback signal, we
can write
The ith error signal is then
BLOCK DIAGRAM AND TRANSFER FUNCTIONS OF MULTIVARIABLE
SYSTEMS



m
j
j
ij
i s
C
s
H
s
B
1
)
(
)
(
)
( ............................(x)
)
(
)
(
)
( s
B
s
R
s
E i
i
i 

Fig 9: Block diagram of multivariable feedback control system

38. Block Diagram Reduction
• It is important to note that blocks can be connected in
series, if the output of one block is not affected by the next
following block. If there are any loading effects between the
components, it is necessary to combine these components
into a single block.
• Any number of cascaded blocks can be replaced by a
single block, the transfer function of which is simply the
product of the individual transfer functions.
• A complicated block diagram involving many feedback
loops can be simplified by a step-by-step rearrangement,
using the rules of block diagram algebra.

39. • Some of these important rules are given below.
Block Diagram Reduction

40. Block Diagram Reduction

41. Block Diagram Reduction

42. Block Diagram Reduction

43. • Exercise:
Obtain the transfer function of the control system whose
block diagram is shown in Fig below
Block Diagram Reduction