Fuzzy Logic Controller

1. Fuzzy Logic Control
Lect 6 Fuzzy PID Controller

2. Contents
• PID
• PID Fuzzy
• Example
• Supervisory PID Fuzzy Control
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3. PID
 PID: Proportional Integral Derivative
 More than 90% of controllers used in industries are
PID or PID type controllers (the rest are PLC)
 PID controllers are simple, reliable, effective
 For lower order linear system PID controllers have
remarkable set-point tracking performance and
guaranteed stability.
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4. Convectional PID Controller
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5. Convectional PID Controller
 Time Domain
 Frequency Domain
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6. PID Controller
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7. PID Controller
Time Domain
Frequency Domain
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8. A comparison of different controller types
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9. General tips for designing a PID controller
• Obtain an open-loop response and determine what needs to be
improved
• Add a proportional control to improve the rise time
• Add a derivative control to improve the overshoot
• Add an integral control to eliminate the steady-state error
• Adjust each of Kp, Ki, and Kd until you obtain a desired overall
response. You can always refer to the table shown to find out which
controller controls what characteristics
• you do not need to implement all three controllers (proportional,
derivative, and integral) into a single system, if not necessary. Keep
the controller as simple as possible.
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10. General tips for designing a PID controller
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11. Tuning of PID Controller
There are methods for tuning PID controllers, for
example:
 hand-tuning,
 Ziegler–Nichols tuning,
 optimal design,
 pole placement design, and
 auto-tuning (A° stro¨m and H¨agglund 1995).
There is much to gain, if these methods are
carried forward to fuzzy controllers.
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12. Why use fuzzy with PID
• Although PID controllers are able to provide
adequate control for simple systems, they are unable
to compensate for disturbances.
• We will use Fuzzy Logic controllers to improve the
PID controllers ability to handle disturbances.
• PID Control works well for linear processes
• PID control has poor performance in nonlinear
processes.
• Fairly complex systems usually need human control
operators for operation and supervision
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13. Types of Fuzzy Controllers:
- Direct Controller -
Slide 13
The Outputs of the Fuzzy Logic System Are the Command Variables of the Plant:
Fuzzification Inference Defuzzification
IF temp=low
AND P=high
THEN A=med
IF ...
Variables
Measured Variables
Plant
Command
Fuzzy Rules Output
Absolute Values !

14. Types of Fuzzy Controllers:
- PID Adaptation -
Slide 14
Fuzzy Logic Controller Adapts the P, I, and D Parameter of a Conventional PID Controller:
Fuzzification Inference Defuzzification
IFtemp=low
AND P=high
THEN A=med
IF...
P
Measured Variable
Plant
PID
I
D
Set Point Variable
Command Variable
The Fuzzy Logic System
Analyzes the Performance of the
PID Controller and Optimizes It !

15. Types of Fuzzy Controllers:
- Fuzzy Intervention -
Slide 15
Fuzzy Logic Controller and PID Controller in Parallel:
Fuzzification Inference Defuzzification
IFtemp=low
AND P=high
THEN A=med
IF...
Measured Variable
Plant
PID
Set Point Variable
Command Variable
Intervention of the Fuzzy Logic
Controller into Large Disturbances !

16. Supervisory Control Systems
Most controllers in operation today have been
developed using conventional control methods. There
are, however, many situations where these controllers
are not properly tuned and there is heuristic knowledge
available on how to tune them while they are in
operation. There is then the opportunity to utilize fuzzy
control methods as the supervisor that tunes or
coordinates the application of conventional controllers.
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17. Fuzzy PID Control
Because PID controllers are often not properly tuned (e.g.,
due to plant parameter variations or operating condition
changes), there is a significant need to develop methods
for the automatic tuning of PID controllers. While there exist
many conventional methods for PID auto-tuning, here we
will strictly focus on providing the basic ideas on how you
would construct a fuzzy PID auto-tuner.
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18. Fuzzy PID Control
 A fuzzy PID controller is a fuzzified proportional-integral-
derivative (PID) controller. It acts on the same input
signals, but the control strategy is formulated as fuzzy
rules.
 If a control engineer changes the rules, or the tuning
gains, it is difficult to predict the effect on rise time,
overshoot, and settling time of a closed-loop step
response, because the controller is generally nonlinear
and its structure is complex.
 In contrast, a PID controller is a simple, linear combination
of three signals: the P action proportional to the error e,
the I-action proportional to the integral of the error 𝑒𝑑𝑡,
and the D-action proportional to the time derivative of the
error de/dt, or ˙e for short. 18

19. Fuzzy PID Control
Fuzzy PID controllers are similar to PID controllers under
certain assumptions about the shape of the membership
functions and the inference method (Siler and Ying 1989,
Mizumoto 1992, Qiao and Mizumoto 1996, Tso and Fung
1997).
A design procedure for fuzzy controllers of the PID type,
based on PID tuning, is the following:
Procedure Design fuzzy PID
1. Build and tune a conventional PID controller first.
2. Replace it with an equivalent fuzzy controller.
3. Fine-tune it.
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20. Fuzzy PID Control
The procedure is relevant whenever PID control is
possible, or already implemented. Our starting point is the
ideal continuous PID controller
The control signal u is a linear combination of the error e,
its integral and its derivative. The parameter Kp is the
proportional gain, Ti is the integral time, and Td the
derivative time.
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21. Fuzzy PID Control
To implement fuzzy PID control on the computer, one first
needs a digital version of analog one.
Discretization of PID controller:
To digitize the analog controller, the following can be used:
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22. Fuzzy PID Control
In digital controllers, the equation must be approximated.
Replacing the derivative term by a backward difference
and the integral by a sum using rectangular integration,
and given a constant – preferably small – sampling time
Ts , the simplest approximation is,
Index n refers to the time instant. By tuning we shall
mean the activity of adjusting the parameters Kp, Ti , and
Td in order to achieve a good closed-loop performance.
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23. Example
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24. Example
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25. Example
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26. Example
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27. Example
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Simulation result are shown , where red is system output, and green is error signal

28. Supervisory Control Systems
 Human operators in the process industry are faced with
nonlinear and time-varying behaviour, many inner
loops, and much interaction between the control loops.
Owing to sheer complexity it is impossible, or at least
very expensive, to build a mathematical model of the
plant, and furthermore the control is normally a
combination of sequential, parallel, and feedback
control actions.
 Operators, however, are able to control complicated
plants using their experience and training, and thus
fuzzy control is a relevant method within supervisory
control.
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29. Supervisory Control Systems
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Supervisory control is a multilayer (hierarchical) controller
with the supervisor at the highest level, as shown in
Figure

30. Supervisory Control Systems
 The supervisor can use any available data from the control
system to characterize the system’s current behavior so that
it knows how to change the controller and ultimately achieve
the desired specifications.
 In addition, the supervisor can be used to integrate other
information into the control decision-making process. It can
incorporate certain user inputs, or inputs from other
subsystems.
 Supervisory control is a type of adaptive control since it
seeks to observe the current behavior of the control system
and modify the controller to improve the performance
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31. Supervisory Control Systems
For example, in an automotive cruise control problem, inputs
from the driver (user) may indicate that she or he wants the
cruise controller to operate either like a sports car or more like
a sluggish family car. The other subsystem information that a
supervisor could incorporate for supervisory control for an
automotive cruise control application could include data from
the engine that would help integrate the controls on the vehicle
(i.e., engine and cruise control integration). Given
information of this type, the supervisor can seek to tune
the controller to achieve higher performance operation or
a performance that is more to the liking of the driver.
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32. Supervisory Control Systems
Conceptually, the design of the supervisory controller can
then proceed in the same manner as it did for direct fuzzy
controllers: either via the gathering of heuristic control
knowledge or via training data that we gather from an
experiment. The form of the knowledge or data is,
however, somewhat different than in the simple fuzzy
control problem.
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33. Supervisory Control Systems
the type of heuristic knowledge that is used in a
supervisor may take one of the following two forms:
1. Information from a human control system operator who
observes the behavior of an existing control system (often
a conventional control system) and knows how this
controller should be tuned under various operating
conditions.
2. Information gathered by a control engineer who knows
that under different operating conditions controller
parameters should be tuned according to certain rules.
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34. High-level control configurations
Fuzzy controllers are combined with other
controllers in various configurations. The PID
block consists of independent or coupled PID
loops, and the fuzzy block employs a high-level
control strategy. Normally, both the PID and the
fuzzy blocks have more than one input and one
output.
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35. Supervisory Fuzzy Control
There are four types of Fuzzy supervisory control:
1. Fuzzy replaces PID
2. Fuzzy replaces operator
3. Fuzzy adjusts PID parameters
4. Fuzzy adds to PID control
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36. Fuzzy replaces PID
In this configuration, the operator may select between a
high-level control strategy and conventional control
loops. The operator has to decide which of the two most
likely produces the best control performance.
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37. Fuzzy replaces operator
This configuration represents the original high level
control idea, where manual control carried out by a
human operator is replaced by automatic control.
Normally, the existing control loops are still active, and
the high-level control strategy makes adjustments of the
controller set points in the same way as the operator
does. Again it is up to the operator to decide whether
manual or automatic control will result in the best
possible operation of the process, which, of course, may
create conflicts.
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38. Fuzzy replaces operator
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39. Fuzzy adjusts PID parameters
In this configuration, the high-level strategy adjusts the
parameters of the conventional control loops. A common
problem with linear PID control of highly nonlinear
processes is that the set of controller parameters are
satisfactory only when the process is within a narrow
operational window. Outside this, it is necessary to use
other parameters or set points, and these adjustments
may be done automatically by a high-level strategy.
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40. Fuzzy adjusts PID parameters
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41. Fuzzy adds to PID control
Normally, control systems based on PID controllers are
capable of controlling the process when the operation is
steady and close to normal conditions. However, if
sudden changes occur, or if the process enters abnormal
states, then the configuration may be applied to bring the
process back to normal operation as fast as possible. For
normal operation, the fuzzy contribution is zero, whereas
the PID outputs are compensated in abnormal situations,
often referred to as abnormal situation management
(ASM).
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42. Fuzzy adds to PID control
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43. Homework
13.2, 13.4, 13.5
Due 20/11/2011
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