intelligent control

1. Principles of feedback &
Intelligent Control

2. CONTROL SYSTEMS
• Control is the basis of a mechatronic system.
• Various ways of classifying the plant are
• Linear or non-linear
• Time-variant or time-invariant
• SISO, MIMO, MISO or SIMO (SISO and MIMO systems are commonly seen)
• Open-loop or Closed-loop configured plant

3. THE FEEDBACK CONTROLLERS
• characteristically the controller can be of one of the following types.
• On-off controller
• Proportional controller
• Integral controller
• Derivative controller
• Proportional-plus-derivative (PD) controller
• Proportional-plus-integral (PI) controller
• Proportional-plus-integral-plus-derivative (PID) controller

4. Automatic Control
• The methods are:
• PID Control
• Adaptive Control
• Robust Control
• Predictive Control
• Optimal Control and
• Intelligent Control

5. Adaptive Control
• Adaptive control is another feedback method, which is characterized by self-adjustment,
unlike PID, of its characteristics in a changing environment to operate the system in an
optimized manner.
• In the adaptive control method, the controller learns about the system dynamics by
acquiring data from the process itself and keeps on updating the existing mathematical
control model.
• To achieve this, a program, called parameter estimator, which continuously monitors the
process and estimates the process dynamics is run.

6. RobustControl
• The robust control design method assumes the knowledge of the
system dynamics and the range of variation.
• Robust control is applied in the application areas where the process
dynamics are known, and the variation ranges for uncertainty is
readily obtained

7. Predictive Control
• It is a method implements controller algorithm based on a typical predictive
model of the system.
• The algorithms compute a sequence of manipulated variables in order to
optimize the future behaviour of a plant.
• Based on historical knowledge, the model predicts the output, as well as the
input.
• Predictive control, is also called Model Predictive Control

8. The optimal control
• A method is based on the state equation and initial condition of the process/
plant. The control algorithm starts with the initial conditions, and arrives at the
objective setpoint.
• A transformation with regard to state is achieved in an optimized manner.
• The method can govern strategies for maximizing (optimizing) a performance
measure, as the transformation of the dynamic system evolves from the initial
condition

9. Intelligent control
• Intelligent control incorporates biological information processing method and
Fuzzy theory. Biological information processing method includes Neural
Network, Genetic Algorithm and Immune Network.
• The chapter deals with Artificial Neural Network (ANN) and Fuzzy logic (FL).
• ANN is a computing method that uses the principle of natural neural network
(NNN).
• Fuzzy control is built on mathematical foundations with Fuzzy Set Theory.

10. ARTIFICIAL NEURAL NETWORK
• Biological systems, such as human beings, can be regarded as the
ultimate distributed information processing system.
• The main information processing systems in the living organisms are
neural system and genetic system
• Natural brain consists of nerve cells, which together with the
dendrites and the axon, constitutes neuron, a small unit that provides
an output only when the sum total of the input exceeds its threshold
level.
• A neuron can receive and send out signals to neighbouring neurons in
the form of electrical pulses

11. ARTIFICIAL NEURAL NETWORK
• The dendrites and axon are like electrical links which serve to conduct
incoming and outgoing signals to the neurons respectively.
• A cut down description of the operation of a neuron is that it
processes the electric currents, which arrive on its dendrites and
transmits the resulting electrical currents to other connected neurons
using its axon.
• A simple explanation of the processing step is that the neuron sums
up the incoming signals and produces an output signal only if this sum
exceeds some threshold

12. Neural Networks
What is a Neural Network?
Similarity with biological network
Fundamental processing elements of a neural network
is a neuron
1.Receives inputs from other source
2.Combines them in someway
3.Performs a generally nonlinear operation on the
result
4.Outputs the final result
•Biologically motivated approach to
machine learning

13. Similarity with Biological Network
• Fundamental processing element of a
neural network is a neuron
• A human brain has 100 billion neurons
• An ant brain has 250,000 neurons

14. Synapses,
the basis of learning and memory

15. Neural Network
• Neural Network is a set of connected
INPUT/OUTPUT UNITS, where each connection has a WEIGHT
associated with it.
• Neural Network learning is also called CONNECTIONIST learning due to the
connections between units.
• It is a case of SUPERVISED, INDUCTIVE or CLASSIFICATION learning.

16. Neural Network
• Neural Network learns by adjusting the weights so as to be able to
correctly classify the training data and hence, after testing phase, to
classify unknown data.
• Neural Network needs long time for training.
• Neural Network has a high tolerance to noisy and incomplete data

17. Neural Network Classifier
• Input: Classification data
It contains classification attribute
• Data is divided, as in any classification problem.
[Training data and Testing data]
• All data must be normalized.
(i.e. all values of attributes in the database are changed to contain values in the internal [0,1] or[-1,1])
Neural Network can work with data in the range of (0,1) or (-1,1)
• Two basic normalization techniques
[1] Max-Min normalization
[2] Decimal Scaling normalization

18. One Neuron as a
Network
• Here x1 and x2 are normalized attribute value of data.
• y is the output of the neuron , i.e the class label.
• x1 and x2 values multiplied by weight values w1 and w2 are input to the neuron x.
• Value of x1 is multiplied by a weight w1 and values of x2 is multiplied by a weight w2.
• Given that
• w1 = 0.5 and w2 = 0.5
• Say value of x1 is 0.3 and value of x2 is 0.8,
• So, weighted sum is :
• sum= w1 x x1 + w2 x x2 = 0.5 x 0.3 + 0.5 x 0.8 = 0.55
•

19. One Neuron as a Network
• The neuron receives the weighted sum as input and calculates the output
as a function of input as follows :
• y = f(x) , where f(x) is defined as
• f(x) = 0 { when x< 0.5 }
• f(x) = 1 { when x >= 0.5 }
• For our example, x ( weighted sum ) is 0.55, so y = 1 ,
• That means corresponding input attribute values are classified in class 1.
• If for another input values , x = 0.45 , then f(x) = 0,
• so we could conclude that input values are classified to class 0.

20. Bias as extra input
Input
Attribute
values
weights
Summing function
Activation
function
v
Output
class
y
x1
x2
xm
w2
wm
W1
 
 )
(

w0
x0 = +1
b
w
x
w
v j
m
j
j



0
0

21. Neuron with Activation
• The neuron is the basic information processing unit of a NN. It
consists of:
1 A set of links, describing the neuron inputs, with weights W1,
W2, …, Wm
2. An adder function (linear combiner) for computing the
weighted sum of the inputs (real numbers):
3 Activation function : for limiting the amplitude of the
neuron output.



m
1
j
jx
w
u
j
)
(u
y b



22. k
O
jk
w
Output nodes
Input nodes
Hidden nodes
Output Class
Input Record : xi
wij - weights
Network is fully connected
j
O
A Multilayer Feed-Forward Neural Network

23. Neural Network Learning
• The inputs are fed simultaneously into the input
layer.
• The weighted outputs of these units are fed into
hidden layer.
• The weighted outputs of the last hidden layer are
inputs to units making up the output layer.

24. A Multilayer Feed Forward Network
• The units in the hidden layers and output layer are
sometimes referred to as neurodes, due to their symbolic
biological basis, or as output units.
• A network containing two hidden layers is called a three-
layer neural network, and so on.
• The network is feed-forward in that none of the weights
cycles back to an input unit or to an output unit of a
previous layer.

25. A Multilayered Feed – Forward Network
• INPUT: records without class attribute with normalized
attributes values.
• INPUT VECTOR: X = { x1, x2, …. xn}
where n is the number of (non class) attributes.
• INPUT LAYER – there are as many nodes as non-class
attributes i.e. as the length of the input vector.
• HIDDEN LAYER – the number of nodes in the hidden layer
and the number of hidden layers depends on
implementation.

26. 26
FUZZY CONTROL
Control Theory?
The term control is generally
defined as a mechanism used to
guide or regulate the operation
of a machine, apparatus or
constellations of machines and
apparatus.

27. 27
FUZZY CONTROL
CONTROL THEORY?
Feedback control' is thus a
mechanism for guiding or
regulating the operation of a
system or subsystems by
returning to the input of the
(sub)system a fraction of the
output.

28. 28
FUZZY CONTROL
CONTROL THEORY?
The machinery or apparatus etc., to be
guided or regulated is denoted by S, the
input by W and the output by y, and the
feedback controller by C. The input to the
controller is the so-called error signal e
and the purpose of the controller is to
guarantee a desired response of the
output y.

29. 29
FUZZY CONTROL
DEFINITIONS
'Feedback control' is thus a mechanism for guiding or regulating the
operation of a system or subsystems by returning to the input of the
(sub)system a fraction of the output.
The machinery or apparatus etc., to be guided or regulated is denoted
by S, the input by W and the output by y, and the feedback controller by
C. The input to the controller is the so-called error signal e and the
purpose of the controller is to guarantee a desired response of the
output y.
C S
y
e u
w

30. 30
FUZZY CONTROL
DEFINITIONS
C S
y
e u
w
One can intuitively argue that the control signal, u,
in part, is
(a) Proportional to the error;
(b) Proportional to the both the magnitude of the
error and the duration of the error
(c ) Proportional to the relative changes in the
error values over time

31. 31
FUZZY CONTROL
DEFINITIONS: Conventional Control and Fuzzy Control
•In the case of classical operations of
process control one has to solve the
non-linear function u. Furthermore,
it is very important that one also
finds the proportionality constants
KI, KD, and KP
•In the case of fuzzy controller, the
non-linear function is represented
by a fuzzy mapping, typically
acquired from human beings

32. 32
FUZZY CONTROL
DEFINITIONS
C S
y
e u
w
One can intuitively argue that the control signal, u, in part,
(a) Proportional to the error;
(b) Proportional to the both the magnitude of the error and the duration of the error
(c ) Proportional to the relative changes in the error values over time
The above intuition can be expressed more formally as an
algebraic equation involving three proportionality constants
–KP, KI and KD
 


t
D
I
P
dt
t
de
K
d
e
K
t
e
K
t
u 0
)
(
)
(
)
(
)
( 


33. 33
FUZZY CONTROL
DEFINITIONS
Value determines reaction to the
Proportional (Kp) current error
Integral (KI) sum of recent errors
Derivative (KD) rate at which the error has
been changing
C S
y
e u
w
 


t
D
I
P
dt
t
de
K
d
e
K
t
e
K
t
u
0
)
(
)
(
)
(
)
( 


34. 34
FUZZY CONTROL
DEFINITIONS
Value determines reaction to
the
Proportional current error
Integral sum of recent errors
Derivative rate at which the error
has been changing
C S y
e u
w
The weighted sum of these
three actions is used to
adjust the process via a
control element such as
the position of a control
valve or the power supply
of a heating element.
 


t
D
I
P
dt
t
de
K
d
e
K
t
e
K
t
u
0
)
(
)
(
)
(
)
( 


35. 35
FUZZY CONTROL
DEFINITIONS
S
C y
e u
w
dt
t
de
x
d
e
x
t
e
x
where
x
K
t
u
dt
t
de
K
d
e
K
t
e
K
t
u
D
t
I
p
i
I
D
P
i
i
t
D
I
P
)
(
;
)
(
);
(
)
(
)
(
)
(
)
(
)
(
0
,
,
0
















36. 36
FUZZY CONTROL
DEFINITIONS: Conventional Control and Fuzzy Control
•In the case of classical operations of
process control one has to solve the
non-linear function u. Furthermore,
it is very important that one also
finds the proportionality constants
KI, KD, and KP
•In the case of fuzzy controller, the
non-linear function is represented
by a fuzzy mapping, typically
acquired from human beings

37. 37
FUZZY CONTROL
DEFINITIONS: Conventional Control and Fuzzy Control
‘Conventional control theory uses a mathematical
model of a process to be controlled and specifications
of the desired closed-loop behavior to design a
controller. This approach may fall short if the model
of the process:
(a) is difficult to obtain, or
(b) is (partly) unknown, or
(c) is highly nonlinear.
(Babuska & Mamdani, accessed 16th
Nov. 2007*
)
*http://www.scholarpedia.org/article/Fuzzy_Control

38. 38
FUZZY CONTROL
DEFINITIONS: Conventional Control and Fuzzy Control
‘Conventional control theory uses a mathematical model
of a process to be controlled and specifications of the
desired closed-loop behavior to design a controller. This
approach may fall short if the model of the process is
difficult to obtain, (partly) unknown, or highly nonlinear.
The design of controllers for seemingly easy everyday
tasks such as driving a car or grasping a fragile object
continues to be a challenge for robotics, while these tasks
are easily performed by human beings. Yet, humans do
not use mathematical models nor exact trajectories for
controlling such processes.’ (Babuska & Mamdani,
accessed 16th
Nov. 2007*
)
*http://www.scholarpedia.org/article/Fuzzy_Control

39. 39
FUZZY CONTROL
FUZZY CONTROLLERS
•Here are some heuristics for making decisions in a
feedback control loop:
IF the error is positive (negative)
& the change in error is approximately zero
THEN the change in control is positive (negative);
IF the error is approximately zero
& the change in error is positive (negative)
THEN the change in control is positive (negative);
IF the error and change in error are approximately zero
THEN the change in control is approximately zero.

40. 40
FUZZY CONTROL
DEFINITIONS: Conventional Control and Fuzzy Control
•Logical rules with vague predicates
can be used to derive inference from
vague formulated data.
•The idea of linguistic control
algorithms was a brilliant
generalisation of the human
experience to use linguistic rules
with vague predicates in order to
formulate control actions.

41. 41
FUZZY CONTROL
DEFINITIONS: Conventional Control and Fuzzy Control
C S
y
e u
w
Conventional Control System
FLC
Internal
Structure
Z
-1
Z
-1
e(k)
e(k)
e(k)

u(k)
 u(k)
Fuzzy-logic based Control System

42. 42
FUZZY CONTROL
FUZZY CONTROLLERS
•A fuzzy controller is a
device that is intended to
modelise some vaguely
known or vaguely described
process.

43. 43
FUZZY CONTROL
FUZZY CONTROLLERS
•A knowledge-based system for closed-loop
control is a control system which enhances the
performance, reliability, and robustness of control
by incorporating knowledge which cannot be
accommodated in the analytic model upon which
the design of a control algorithm is based, and that
is usually taken care of manual modes of
operation, or by other safety and ancillary logic
mechanisms.
Driankov,D., Hellendoorn, H., & Reinfrank, M. (1996). An Introduction to
Fuzzy Control. (2nd
Edition). Heidelberg: Springer-Verlag

44. 44
FUZZY CONTROL
DEFINITIONS: Fuzzy Control
There are two types of fuzzy controllers:
*http://www.scholarpedia.org/article/Fuzzy_Control
Controller-type Typical Operation
Mamdani (linguistic)
controller with either
fuzzy or singleton
consequents.
Direct closed-loop
controller
Takagi-Sugeno (TS) or
Takagi-Sugeno-Kang
controller
Supervisory controller
– as a self tuning
device

45. 45
FUZZY CONTROL
FUZZY CONTROLLERS
•The controller can be used with the process in
two modes: Feedback mode when the fuzzy
controller will act as a control device; and
feedforward mode where the controller can be
used as a prediction device.
•All inputs to, and outputs from, the controller
are in the form of linguistic variables. In many
ways, a fuzzy controller maps the input variables
into a set of output linguistic variables.

46. 46
FUZZY CONTROL
FUZZY CONTROLLERS
•Usually, a plant, process,
vehicle, or any other object to be
controlled is called a system (S).
•The feedback controller is
expected to ‘guarantee a desired
response’, or output y.
Yager, R R & Filev, D P. (1994) Essentials of Fuzzy Modeling
and Control. Chichester: John Wiley & Sons Ltd

47. 47
FUZZY CONTROL
FUZZY CONTROLLERS
•Regulation is a process described in the
control theory literature as a process for
‘keeping the output y close to the setpoint
(reference input) w, despite the presence
of disturbances, fluctuations of the system
parameters, and noise measurements’.
(Error e=w-y)
•A controller is implemented using the
control algorithm.

48. 48
FUZZY CONTROL
FUZZY CONTROLLERS
A controller is implemented using the
control algorithm.
Vehicle dynamics: Vehicle moving with
velocity v(t) and control u(t):
τ dv(t)/dt+ v(t) = K u(t);
The solution of the above equation for
K=2km/hour and τ=15 seconds:
v(t) = 0.936 v(t-1) +0.128 u(t-1).

49. 49
FUZZY CONTROL
FUZZY CONTROLLERS
The principal message in the
fuzzy control literature is that
“the control algorithm is a
knowledge-based algorithm,
described by the methods of
fuzzy logic’ (Yager and Filev,
1994:111)

50. 50
FUZZY CONTROL
FUZZY CONTROLLERS
•A typical fuzzy logic controller is described
by the relationship between change of
control (u(k)) on the one hand and the error
(e(k)) and change in the error on the other
hand
e(k) = e(k) -e(k-1).
Such a control law is formalised as:
u(k) = F(e(k), e(k)).

51. 51
FUZZY CONTROL
FUZZY CONTROLLERS
•Here are some heuristics for making decisions in a
feedback control loop:
IF the error is positive (negative)
& the change in error is approximately zero
THEN the change in control is positive (negative);
IF the error is approximately zero
& the change in error is positive (negative)
THEN the change in control is positive (negative);
IF the error and change in error are approximately zero
THEN the change in control is approximately zero.

52. 52
FUZZY CONTROL
FUZZY CONTROLLERS
•Here are some heuristics for making decisions in a
feedback control loop:
System Responsiveness
IF the error is positive (negative)
& the change in error is approximately zero
THEN the change in control is positive (negative);
Reduction in overshooting
IF the error is approximately zero
& the change in error is positive (negative)
THEN the change in control is positive (negative);
Steady State Control
IF the error and change in error are approximately zero
THEN the change in control is approximately zero.

53. DIAGNOSTICS
• Diagnostics has become a fundamental requirement within the real-time
mechatronics technology. As target application (Target applications is a
plant/process/system) becomes more complex and more costly to build and
maintain, preventive maintenance measures become increasingly important.
• There is currently a great need for systems to automatically predict, detect, and
diagnose faults. Devices such as sensors, actuators, valves and switches are
integral parts of the target application
• The detection and isolation of fault is defined as diagnostics and prognostics
(DAP). Prognostic measure helps to estimate the time remaining before
machine breakdown occurs.
• In addition to control, if the Fault Detection and Isolation (FDI) features are
incorporated into the system then the system is said to be self-diagnostic
system.

54. DIAGNOSTICS
• The terms FDI and DAP are used interchangeably. FDI incorporates sophisticated
methods, techniques and tools for on-line, continuous monitoring of the target
application. FDI scheme involves continuous analysis of operational point and the
detection of problems before the unit or component fails to operate.
• The diagnostics is carried out by measuring the detection parameters by the use of
sensors, and other equipment.
• The detection parameters are vibration, thermal deformation, fracture, crack, bend,
lubrication, wear, degradation factor and so on.
• The effect of FDI implementation in the mechatronic systems is significant. In
particular,
• The location, type, time, size and the nature of the faults can be quickly identified.
• Reliability can be improved reducing maintenance requirements.
• Production loss becomes low and overall productivity becomes high.
• The life of the machine and the auxiliary comp

55. Mathematical Description of Process and Faults
A schematic diagram of a process is shown in the Fig. 12.16 and its mathematical description is
expressed

56. Mathematical Description of Process and Faults
where, U(t) and Y(t) are measurable input and output signals, N(t) is disturbance signal (noise), P(t) is
slowly varying process parameters and X(t) time dependant process state variables and are
nonmeasurable parameters. The faults make a change in P(t) and in X(t) to produce P(t) + d P(t) and
X(t) + d X(t) respectively.

57. FDI Phases
• Two main subtasks are involved in implementing 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.
• Concern in the design of fault detection algorithm is detection
performance, which implies first and accurate identification of
failures. The detection performance is measured in terms of
isolability, sensitivity and robustness.

58. FDI Approaches
• Two classes of faults are seen in the systems, additive and multiplicative. Additive faults are of two types,
additive measurement and additive process faults. Additive measurement faults result due to discrepancies
between the measured and true values of the I/O signal, where as additive process faults are zero during
normal operation, but entered unexpectedly and affect the operation.
• Multiplicative faults are those, which describe the deterioration of the units, components and equipments.
As far as design scenario of FDI is concerned, there exists three approaches such as:
• Statistical approach
• Model-based
• Other approaches

59. Statistical approach
• Statistical parameters such as mean value, standard deviation, variance, density
function etc. of the available output signals are used for the development of FDI
algorithm.
• The simplest approach is to measure the mean square value of the parameters
(vibrations for instance) with respect to time, since this is expected to increase. By
treating the parameters as a random variable, other higher order statistical
moments, cumulants and measures such as the crest factor are used as features.

60. Model-based
• The 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. The
procedure of using model information to generate
signals to be compared with the original
• measured quantities is known as analytical
redundancy, which implies that additional signals are
generated and compared with the measured
quantities.
• The primary objective of the model-based technique
is to generate residuals. Residuals are the image of the
fault, i.e. they possess the knowledge about the fault.

61. Other approaches
• Limit-checking,
• Hardware-installation of special sensors,
• Fusion,
• Spectrum comparison,
• Expert system based (H/W & S/W), and
• Artificial Immune Network (AIN)

62. Merits and Demerits
• Statistical methods work well within communication systems and are rarely
applied to dynamic machinery systems because the I/O signals of such systems
are not strongly stationary rather they are nearly stationary.
• The possible sources of errors and ambiguity in model-based approaches are:
• Formulation of mathematical model is quite complex.
• The modeling uncertainties and disturbances to the system must be encountered.
• Detection of relatively small faults, which develop over time is not so easy.
• The approach involves computation of transfer functions delaying the diagnostics.