2. Control systems are an arrangement of physical components designed to alter
or regulate the system based on control action.
Control system may be of two systems:
(1) Open loop control system – control action is independent of system output
(2) Closed loop control system – control action depends on system output
Controllers designed may be of two types:
(a) Regulatory type of control
(b) Tracking controllers
3. a) Regulatory type of control or regulator: object of the control system is to
maintain the physical variable at some constant value in the presence of
disturbances, it is a regulator.
Ex: Room temperature control, autopilot.
b) Tracking controllers: a physical variable is required to follow or track some
desired time function.
Ex: Automatic aircraft landing function.
4. SIMPLE FUZZY LOGIC CONTROLLER
The block diagram for simple fuzzy logic controller is shown in Figure:
5.
6. DESIGN OF A SIMPLE FUZZY LOGIC CONTROL
It involves the following steps:
(1) Identify the variables of the plant, i.e., inputs, states, and the outputs
(2) Partition the universe of discourse or the interval spanned by each variable
into a number of fuzzy subsets, assigning each a linguistic label
(3) Assign or determine a membership function for each fuzzy subset
(4) Assign the fuzzy relationships between the inputs’, states’ fuzzy subsets on the
one hand and the outputs’ fuzzy subsets on the other hand, to form the rule base
(5) Choose appropriate scaling factors for the input and output variables in order
to normalize the variables to the [0, 1] or the [−1, 1] interval
7. (7) Use fuzzy approximate reasoning to infer the output contributed from each
rule
(6) Fuzzify the inputs to the controller
(8) Aggregate the fuzzy outputs recommended by each rule
(9) Apply defuzzification to form a crisp output
8. GENERAL FUZZY LOGIC CONTROLLERS
The principal design elements in this case are:
(1) Fuzzification strategies and the interpretation of fuzzification operator or
fuzzifier
(2) Knowledge base
(a) Normalization of the universe of discourse
(b) Fuzzy partitions of input and output spaces
(c) Completeness of the partitions
(d) Choice of the membership function
9. (3) Rule base
(a) Choice of process of state and control variables (input and output)
(b) Source of derivation of fuzzy control rules
(c) Types of fuzzy control rules
(d) Completeness of fuzzy control rules
(4) Decision making logic
(a) Definition of fuzzy implication
(b) Interpretation of sentence connective
(c) Inference mechanism
10. (5) Defuzzification strategies and the interpretation of a defuzzification operator
(defuzzifier)
If all the five above are fixed, the fuzzy logic control system is simple
and nonadaptive. Adaptation or change in any of the five design parameters above
creates an adaptive fuzzy control system.
11. FUZZY LOGIC CONTROL SYSTEM MODELS
The fuzzy logic control system models are expressed in two different forms:
(1) Fuzzy rule based structure
(2) Fuzzy relational equations
12. (1) FUZZY RULE BASED STRUCTURE
There are five types of fuzzy rule based system models:
(1) If the input and the output restrictions are given in the form of Singletons
IF Ai : x = xi THEN Bi : y = yi
(2) If the input restrictions are in the form of crisp sets and output are given by
singleton
IF Ai : xi−1 < x < xi THEN Bi : y = yi
(3) If the input conditions are crisp sets and the output is a fuzzy set
IF Ai : xi−1 < x < xi THEN y = Bi
13. (4) If the input conditions are fuzzy sets and the outputs are crisp functions,
IF x = Ai THEN Bi : y = fi(x)
(5) If both the input and output restrictions are given by fuzzy sets
IF Ai THEN Bi
14. (2) FUZZY RELATIONAL EQUATIONS
The following are the fuzzy relational equations describing a number of
commonly used fuzzy control system models,
(1) For a discrete first-order system with input U, the fuzzy model is
xk+1 = xk o uk o R for k = 1, 2, . . .
(2) For a discrete Pth order system with single input U, the fuzzy system equation
is,
xk+p = xk o xk+1 o · · · o xk+p−1 o uk+p−1 o R
yk+p = xk+p
(3) A second-order system with full state feedback is described as
uk = xk o xk−1 o R
yk = xk
15. (4) A discrete Pth order SISO system with full state feedback is represented by the
following fuzzy relational equation,
uk+p = yk o yk+1 o · · · o yk+p−1 o R
In all the cases,
R = R1 U R2 U · · · , U Rr,
R = {R1,R2, . . . , Rr},
where R is a system transfer function.
R1 : IF x is A1, THEN y is B1
R2 : IF x is A2, THEN y is B2
.
.
.
Rr : IF x is Ar, THEN y is Br
