Intelligent Control and Fuzzy Logic

EE363 Mechatronics – 2014: Introduction to Intelligent Control & Fuzzy Logic Dr. Praneel Chand 1
Introduction to Intelligent Control & Fuzzy
Logic
Learning Outcomes
In this topic we shall look at the fundamentals of intelligent control
and fuzzy logic. At the end of this topic you should be able to:
 Define intelligent control.
 Define fuzzy logic.
 Explain the structure and operation of fuzzy logic
controllers/systems
 Create a fuzzy logic system in Matlab.
 Explain the application of fuzzy logic in mechatronic systems.

Introduction to Intelligent Control
What is Normal (Classical) Control?
 Open loop control system
o Signal is sent to plant (mechatronic device) in order to
make it move to a certain position
o No feedback to tell if the target has been reached
 Closed-loop control system
o Output of the plant is feedback to the input side
Controller
K
Process
G(s)
Input
R Output C

o Error between input and output is applied to a controller
which then controls the plant
 The whole idea behind classical control is that the system to
be controlled requires a model.
 The success of the system depends on the accuracy of this
model and controller parameters (e.g. PID controller gains).
 The model and the parameters are rigid (i.e. fixed) E.g. first
and second order systems and PID controller equation

First order system:
1
( )
1
G s
Ts


Second order system: 2 2
1
( )
2 n n
G s
s s 

 
PID controller TF:
What about Intelligent Control?
 The premise behind intelligent control is that the system to be
controlled does not have to be rigidly modelled.

 This is unlike classical control and is the biggest distinction
between the two approaches.
 Humans can perform complex tasks without knowing exactly
how they do them (and without using a rigid model).
 Therefore, one may say that an intelligent method solves
o A difficult (non-trivial, complex, usually large or
complicated) problem
o In a non-trivial human-like way
 Types of intelligent control include:
o Fuzzy logic
o Artificial neural networks
o Genetic programming
o Support vector machines
o Reinforcement learning
 We shall consider Fuzzy logic and artificial neural networks

Components of Intelligent Systems
Structure of intelligent system

 Two categories of components
o Software Elements
 Knowledge Base – similar to a database, stores
rules and relationships between data elements
 Inference Engine – is the processing (program)
element. Performs reasoning using knowledge base
content and inputs
 Knowledge base manager – resource and
consistency management of the knowledge base
and relationships between knowledge items
o Users
 Knowledge Engineer – design, implement, verify,
validate the system
 User – person or (process/plant/device) that
connects to the inference engine

Introduction to Fuzzy Logic
What is Fuzzy Logic?
 Fuzzy logic like most of the intelligent control methods
attempts to model the way of reasoning that goes on in the
human brain.
 It is based on the idea that human reasoning is approximate,
non-quantitative, and non-binary. In many cases, there is no
black and white answer, but shades of grey
 The simplest example is temperature. Usually when you as
someone the temperature they respond with “cool”, “warm”,
“hot”, “very hot” as opposed to telling the exact temperature
such as “28.5 degrees” or “33.1 degrees”

 Fuzzy logic is a convenient way to map input space to output
space. E.g. How much to tip at a hotel? Input space is the
quality of service and output space is the amount of tip.

Why use Fuzzy Logic?
Advantages over ‘conventional’ or ‘classical’ control:
 Don’t need a good mathematical model of process being
controlled.
 Control system requires less information
 Can be quicker to implement
 Rules (more details later) can be tested individually
Other advantages include:
1. Conceptually easy to understand – mathematical concepts
are simple
2. Flexible – easy to layer on more functionality to existing
system

3. Fuzzy logic is tolerant of imprecise data
Applications in Mechatronics include:
1. Speed and position control in mechatronic systems
(alternative to PID controllers)
2. Robot trajectory control and obstacle avoidance
3. Control of appliances such as washing machines
General Approach to Fuzzy Logic Control
The general approach to designing a fuzzy logic controller is
made up 5 steps. These steps are
1. Define the Input and Output Variables
2. Define the subsets (Fuzzy sets) intervals

3. Choose the Membership Functions
4. Set the IF-THEN rules
5. Perform calculations (using Fuzzy Inference) and adjust rules
The block diagram of a fuzzy controller is shown below.

It has several components:
1. The rule-base is a set of IF-THEN rules about how to control
2. Fuzzification is the process of transforming the numeric
inputs into a form that can be used by the inference
mechanism. This relies on fuzzy sets and membership
functions.
3. The inference mechanism uses information about the current
inputs (formed by fuzzification), decides which rules apply in
the current situation, and forms conclusions about what the
plant input should be.
4. Defuzzification converts the conclusions reached by the
inference mechanism into a numeric input for the plant.

We shall look at Fuzzy sets, Membership Functions, IF-THEN
rules, and Fuzzy Inference in the next section. Fuzzy Inference is
the combination of Fuzzification, the Inference Mechansim and
Defuzzification

Components of Fuzzy Logic
Fuzzy Sets
 Fuzzy logic relies on the notion of fuzzy sets
 A fuzzy set is a set without any crisp, clearly defined
boundaries.
 It can contain elements with a partial degree of membership.
 Classical sets either wholly include an element or wholly
exclude it. E.g. a set of the days of the week

 An example of a fuzzy set would the set of days that make up
the weekend
 Another example is age. If we were to ask “what is middle
age?, we would be inclined to classify middle age on grade
so that we classify middle age as fuzzy, rather than a crisp
set.

Crisp set Fuzzy set
The curve in the fuzzy set that defines middle age is a function
that maps the input space (age) to the output space (middle
agedness or grade). Specifically, this is known as a membership
function.

Membership Functions
 A membership function (MF) is a curve that defines how each
point in the input space is mapped to a membership value (or
degree of membership) between 0 and 1.
 The input space is sometimes referred to as the universe of
discourse.
 The output-axis is a number known as the membership value
between 0 and 1.
 The curve is known as a membership function and is often
given the designation of μ.
The only condition a membership function must satisfy is that it
must vary between 0 and 1.

A classical set might be described as
A= { x | x>6 }
A fuzzy set is an extension of a classical set. If X is the universe
of discourse and its elements are denoted by x, then the fuzzy set
A in X is defined as a set of ordered pairs.
A= { x, A (x) | xX}
A (x) is called the membership function (or MF) of x in A. The
membership function maps each element of X to a membership
value between 0 and 1.
The fuzzy logic toolbox includes membership function types such
as, triangular membership function (trimf), trapezoidal
membership function (trapmf), simple Gaussian curve (gaussmf)

and a two-sided composite of two different Gaussian curves
(gauss2mf), sigmoid membership function (sigmf) and others.

Fuzzy Logic Operators
 Fuzzy logic is a superset of standard Boolean logic
 If we keep the fuzzy values to the extremes of 1 (completely
true) and 0 (completely false), standard logical operators will
hold.
Standard truth tables

Fuzzy truth tables
Note some books use ‘intersection’ or ‘ ’ for the min operator and
‘union’ or ‘ ’ for the max operator
The standard and fuzzy truth tables are illustrated in figure below

If-Then Rules
 If-Then rules are fuzzy rules that are defined as a conditional
statement in the form:
IF x is A
THEN y is B
Where x and y are linguistic variables; and A and B are linguistic
values determined by fuzzy sets on the universe of discourses X
and Y, respectively
 The “IF” part of the rule is called the antecedent
 The “THEN” part is called the consequent

 Classical IF-THEN rules use binary logic, for example,
Rule: 1
IF speed is > 100
THEN stopping_distance is long
Rule: 2
IF speed is < 40
THEN stopping_distance is short
The variable speed can have any numerical value, but the
linguistic variable stopping_distance can take either value long or
short.
 Fuzzy IF-THEN rules example,

Rule: 1
IF speed is fast
THEN stopping_distance is long
Rule: 2
IF speed is slow
THEN stopping_distance is short
In this case the linguistic variable speed includes fuzzy sets such
as slow, medium and fast. The linguistic variable
stopping_distance may include fuzzy sets as short, medium and
long. Thus fuzzy rules relate to fuzzy sets.

 Note that the antecedent is an interpretation that returns a
single number between 0 and 1.
 On the other hand, the consequent is an assignment that
assigns the entire fuzzy set B to the output variable y.
The Fuzzy Inference Process (from MATLAB Fuzzy Logic
Toolbox)
There are five parts to the fuzzy inference process (in the
MATLAB Fuzzy Logic Toolbox)
1. Fuzzification of the input variables
i. Takes the inputs and determines the degree to which
they belong to each of the appropriate fuzzy sets via
membership functions.

ii. The input is always a crisp numerical value limited to
the universe of discourse of the input variable and the
output is a fuzzy degree of membership (always in
interval between 0 and 1).
2. Application of the fuzzy operator (AND or OR or NOT) in
the antecedent
i. If the antecedent of a given rule has more than one part,
the fuzzy operator is applied to obtain one number that
represents the result of the antecedent for that rule. This
number will then be applied to the output function.
ii. Any number of well-defined methods can fill in for the
AND operation or the OR operation.
iii. In fuzzy logic toolbox, two built -in AND methods are
supported: min (minimum) and prod (product). Two built-

in OR methods are also supported: max(maximum),
and the probabilistic OR method probor.
3. Implication from the antecedent to the consequent
i. The implication method is defined as the shaping of the
consequent (a fuzzy set) based on the antecedent ( a
single number).
ii. The input for the implication process is a single number
given by the antecedent, and the output is a fuzzy set.
iii. Implication occurs for each rule.
iv. Two built-in methods are supported, min (minimum)
which truncates the output fuzzy set, and prod (product)
which scales the output fuzzy set.
4. Aggregation of the consequents across the rules
i. Unify the outputs of each rule
5. Defuzzification

i. Input for defuzzification phase is unified fuzzy set
formed by aggregation of consequents and output is
crisp number.
ii. If there are more than one output variables, final output
for each variable is a crisp number.
iii. The most popular defuzzification method is the centroid
calculation, which returns the center of area under the
curve.
iv. There are five built-in methods supported: centroid,
bisector, middle of maximum ( the average of the
maximum value of the output set), largest of maximum,
and smallest of maximum.
The centroid defuzzification method is briefly explained below:

The centroid technique finds a point where a vertical line would
slice the aggregate set into two equal masses. In the figure below,
a centroid defuzzification finds a point representing the centre of
gravity of the fuzzy set, A, on the interval, ab. In practice, a
reasonable estimate is obtained by calculating over a sample of
points as shown below
( )
( )
b
A
x a
b
A
x a
x x
COG
x








If you recall the block diagram of a fuzzy controller on page 12,
you will notice that the Inference Mechanism consists of steps
2,3,4 of the fuzzy inference process.

Examples
The Basic Structure of Mamdani-style Fuzzy Inference
Lets examine a simple two-input one-output problem that includes
three rules:
Rule: 1
IF x is A3
OR y is B1
THEN z is C1
Rule: 2
IF x is A2
AND y is B2
THEN z is C2

Rule: 3
IF x is A1
THEN z is C3
Where x, y, z are linguistic variables; A1, A2 and A3 are linguistic
values determined by fuzzy sets on universe of discourse X; B1
and B2 are linguistic values determined by fuzzy sets on universe
of discourse Y; C1, C2, C3 are linguistic values determined by
fuzzy sets on universe of discourse Z.
The basic structure of the Mamdani-style fuzzy inference is shown
below:

For the defuzzification process, we calculate the centre of gravity
(centroid) of the output as:

Hence, the result of defuzzification, crisp output z1 is 67.4.

Controlling the Distance Between Two Cars
Design a fuzzy controller/system for controlling the distance
between two cars.
Recall that the general approach to designing a fuzzy logic
controller is made up 5 steps (pages 11 and 12).
First, define the inputs and outputs. There are two inputs: D, the
distance between the cars, and v, the velocity of the following car.
There is one output: B, the amount of braking to apply to the
following car (force). The inputs and outputs are shown in the
figure below.

Second, define the subsets’ intervals. To simplify things, 3 subset
intervals will be chosen for each variable. These are low, medium
and high for distance and velocity, and small, medium and big for
braking force. These subset intervals are illustrated in the figure
below.

Third, choose the membership functions. In this example, the
shape of the membership functions are fairly simple, just a linear
transition between the various subsets (see above figure). To
illustrate, in the figure above, the membership function for low
distance goes down linearly from 1 to 0 as distance goes from 0
to 5 meters.

Fourth, set the IF-THEN rules. This is how combinations of the
input determine the output. For example, IF the distance, D,
between the cars is low AND the velocity, v, of the following car is
high, THEN the braking to apply, B, is big. Similarly, the other
rules are defined. This is where the non-quantitative human
reasoning comes in. A simple two-rule system could be:
Rule: 1
IF D is Low
AND v is High
THEN B is Big
Rule: 2
IF D is Medium
AND v is High

THEN B is Medium
Fifth, perform calculations and adjust the rules. Since the rules
are non-exact some adjustments may be necessary to more
optimally control the vehicles’ distance.
As an example, say the distance between the vehicles is 2.5
meters and the speed of the following car is 100 km/h. From the
distance subset in Figure 8, the 2.5 meter distance translates into
0.25 medium distance plus 0.5 low distance. Likewise, the 100
km/h speed translates into 0.75 high speed. A process similar to
the Mamdani Fuzzy Inference Example (previous example) is
used to compute the final crisp braking percentage.

Question
If the distance between the vehicles is 4 metres and the speed of
the following car is 60 km/hr what percentage braking will be
applied?
Using the Fuzzy Logic Toolbox GUI to Build a Fuzzy System
Refer to the document “Building Fuzzy System using GUI” in
Moodle. We shall build a fuzzy system for the previous example in
class.
Water Level Control (Simulink Example)
Refer to the document “Water Level Control” in Moodle

Further Mechatronic Systems Related Examples
Please refer to the papers in the reading resources folder on
Moodle.
Fuzzy knowledge-based controller design for autonomous
robot navigation
In this study a fuzzy logic controller for mobile robot navigation
has been designed. The designed controller deals with the
uncertainty and ambiguity of the information the system receives.
The technique has been used on an experimental mobile robot
which uses a set of seven ultrasonic sensors to perceive the
environment. The designed fuzzy controller maps the input space

(information coming from ultrasonic sensors) to a safe collision-
avoidance trajectory (output space) in real time. This is
accomplished by an inference process based on rules (a list of IF-
THEN statements) taken from a knowledge base. The technique
generates satisfactory direction and velocity maneuvers of the
autonomous vehicle which are used by the robot to reach its goal
safely. Simulation and experimental results show the method can
be used satisfactorily by wheeled mobile robots moving on
unknown static terrains
Fuzzy Logic Controller for Mechatronics and Automation
Conventional car suspensions systems are usually passive, i.e
have limitation in suspension control due to their fixed damping
force. Semi-active suspension system which is a modification of

active and passive suspension system has been found to be
more reliable and robust but yet easier and cheaper than the
active suspension system.
In semi active damping, the damper is adjustable and may be set
to any value between the damper-allowable maximum and
minimum values. Semi active control systems are a class of
active control systems for which external energy is needed like
active control systems.
In this paper a fuzzy logic controller and hybrid controller were
applied to a car Active suspension system. The fuzzy logic
controller was applied to the car suspension system with different
types of disturbances.

The five general steps to design a fuzzy controller were followed
and a block diagram of the system is shown below:

Mechatronic Design and Control of Hybrid Electric Vehicles
The work in this paper presents techniques for design,
development, and control of hybrid electric vehicles (HEV’s).
Toward these ends, four issues are explored. First, the
development of HEV’s is presented. This synopsis includes a
novel definition of degree of hybridization for automotive vehicles.
Second, a load-leveling vehicle operation strategy is developed.
In order to accomplish the strategy, a fuzzy logic controller is
proposed. Fuzzy logic control is chosen because of the need for a
controller for a nonlinear, multidomain, and time-varying plant with
multiple uncertainties. Third, a novel technique for system
integration and component sizing is presented. Fourth, the system
design and control strategy is both simulated and then
implemented in an actual vehicle. The controller examined in this

study increased the fuel economy of a conventional full-sized
vehicle from 40 to 55.7 mi/h and increased the average efficiency
over the Federal Urban Driving Schedule from 23% to 35.4%. The
paper concludes with a discussion of the implications of intelligent
control and mechatronic systems as they apply to automobiles.

Summary
 Intelligent control methods do not require rigid modelling of
the system that is to be controlled.
 An intelligent method solves a difficult problem in a non-trivial
human-like way.
 There are several types of intelligent control methods and we
considered fuzzy logic in this section.
 Fuzzy logic like most of the intelligent control methods
attempts to model the way of reasoning that goes on in the
human brain.
 It is based on the idea that human reasoning is approximate,
non-quantitative, and non-binary. In many cases, there is no
black and white answer, but shades of grey

 The general approach to designing a fuzzy controller
consists of 5 steps
o Define input and output variables
o Define the subsets intervals
o Choose membership functions
o Set IF-THEN rules
o Perform calculations (using Fuzzy Inference) and adjust
rules
 There are five parts to the fuzzy inference process
o Fuzzification of the input variables
o Application of the fuzzy operator (AND or OR or NOT) in
the antecedent
o Implication from the antecedent to the consequent
o Aggregation of the consequents across the rules
o Defuzzification

 Fuzzy logic can be used in mechatronic applications such
as speed, position, level control, robot trajectory control and
obstacle avoidance, hybrid electric vehicles, vehicle active
suspension systems, control of appliances such as washing
machines etc.
Sources
B. Smith, “Classical vs Intelligent Control”, in EN9940 Special Topics in Robotics Notes, Memorial
University, 2002. (http://www.engr.mun.ca/~baxter/Publications/ClassicalvsIntelligentControl.pdf )
K.M. Hangos, R. Lakner and M. Gerzson, “Intelligent Control Systems: An Introduction with
Examples”, Kluwer Academic Publishers, New York, USA, 2004.
“Fuzzy Logic Toolbox”, in MATLAB Full Product Family Help, MATLAB 7.10.0 (Release 2010a), The
Math Works Inc., Natick MA, USA, 2010. (electronic resource)
“Fuzzy Logic Toolbox User’s Guide Version 2.2.11”, in MATLAB Release 2010a PDF Documentation,
CDROM, The Math Works Inc., Natick MA, USA, 2010.
D. Necsulescu, “Mechatronics”, Prentice Hall, New Jersey, USA, 2002.

M. Negnevitsky, “Artificial Intelligence: A Guide to Intelligent Systems”, Addison Wesley, Essex,
England, 2005.

Intelligent Control and Fuzzy Logic

Recomendados

Recomendados

Mais conteúdo relacionado

Mais procurados

Mais procurados (20)

Semelhante a Intelligent Control and Fuzzy Logic

Semelhante a Intelligent Control and Fuzzy Logic (20)

Mais de Praneel Chand

Mais de Praneel Chand (12)

Intelligent Control and Fuzzy Logic