The relationship between the input and output are mentioned in terms of transfer function, which is

1
The relationship between the input and output are
mentioned in terms of transfer function, which is
defined as the ratio between the Laplace
transform of the output and the Laplace transform
of the input. If the output is proportional to
the input, the plant is called a linear system.
2
An example of a block diagram of an open-loop
control system. The term open-loop comes from
the fact that the output only depends on the
inputs. This is a complete system by itself. The
control system takes the input from the
controller in order to produce output by the
action of the plant.
3
The overall transfer function of the system is
the product of individual transfer functions. In
general, in open-loop configuration,
mathematically, the overall transfer function of
the composite system is given by the following
formula.
4
A closed-loop control system, on the other hand,
uses input as well as some portion of the output
to regulate the output. The closed-loop systems
are also called feedback control systems. In
feedback control the variable required to be
controlled is measured. This measurement is
compared with a given setpoint. If the error
results, the controller takes this error and
decides what action should be taken to compensate
and hence to remove the error.
5
The closed-loop control schematic must have a
plant which is to be controlled. The plant is
referred to as the controlled system. The block
that controls the plant (i.e., the controlled
system) is called the controller. The controller
is not a physical controller that you studied in
the Chapter-8. It is a manipulation method that
controls and regulates the output through
feedback or closed-loop action. The algorithm of
the manipulation can be implemented in a physical
controller in order to achieve the objective,
i.e., to regulate the output.
6
The equivalent transfer function of the feedback
control system, shown in the figure- (b), is
called closed-loop transfer function, which can
be written as,
7
On-off controller
From closed-loop control point of view there are
commonly seven types of control actions which are
considered as the most fundamental because the
plant can adequately be controlled to attend the
reachability point by designing appropriate
controllers.

• On-off controller
• Proportional controller
• Integral controller
• Derivative controller
• PD controller
• PI controller
• PID controller

8
On-off controller with hysteresis or dead-band
The turn-ON and turn-OFF in case of ON/OFF
controller in many situation are deliberately
made to differ by a small amount, known as the
hysteresis or dead-band, to prevent noise from
switching the controller unnecessarily when the
output is nearly the setpoint. The sensitivity of
the On-Off controller depends on the hysteresis.
9
Proportional Control means that the plant input
is changed in direct proportion to the error,
e(t). This controls the output so that the
manipulated variable and the error has a
proportional relation. The advantage of
proportional controller is that it is relatively
easy to implement. However, the disadvantage is
that there always involves an offset in the
output response causing difference between the
set-point and the actual output.
10
When the controller controls the output by
integrating the error signal, then it is called
an integral control action. The offset in the
output, and hence the steady-state performance of
the system can be improved by employing integral
control action. But the integral action may lead
to oscillatory output resulting poor stability.
11
The transfer function of the PID controller is
12
Intelligent control incorporates biological
information processing method and Fuzzy theory.
Biological information processing method includes
Neural Network, Genetic Algorithm and Immune
Network. At the core of the neural
computation, there exist the concepts of
distributed, adaptive, and nonlinear computing.
13
All ANNs have a similar structure as far as
topology is concerned. Some of the neurons
interface the real world to receive its inputs,
and other neurons provide the real world with the
networks outputs. Besides input layer and output
layer there may be many middle layers, with a
variable number of nodes, depending upon the task
at hand.
14
Uncertainties are of two types stochastic
uncertainty and fuzziness. Stochastic uncertainty
has only two levels such as true or false. Where
the event is not well defined, the outcome may be
given by a quantity other than true or false, but
rather fuzzy. There comes fuzzy logic. The
outcome in presence of fuzziness is quantified by
a degree
of belief. FL system is called soft linguistic
system.
15
FL based strategy simplifies the design loop.
This results in some significant benefits, such
as reduced development time and simpler design.
16
A schematic diagram of a process is shown. The
mathematical description is expressed as,
Y Output U input N Noise X Process state
variables P Process parameters
17
Two main subtasks are involved within FDI
techniques. Failure detection that indicates that
something abnormal has happened in the system.
Failure isolation is the ability to distinguish
between specific faults and isolating the
component that has failed.
18
Implementation of FDI is achieved mainly through
statistical and model-based approach. Method
that relies on a quantitative mathematical
relation between the I/O is called model-based
technique. Model-based fault detection depends
only on the availability of a mathematical model
of the plant.
19
The digital control technology to some extend is
immune to noise. The effect of noise can be
efficiently reduced using error correcting codes
or distortion eliminator.
20
From implementation schematic an advanced digital
control system in its basic nature can be seen as
shown in the figure. Digital control technology
makes it easy to implement state feedback and
adaptive control.
21
A full-fledged advanced control system has to
incorporate auxiliary functions such as display,
storage, monitoring, protection, diagnostics and
prognostics as illustrated above. The blocks
drawn inside the dotted box shows the schematic
diagram of a typical control implementation
scenario.