Fuzzy logic starts with and builds on a set of user-supplied human language
rules. The fuzzy systems convert these rules to their mathematical
equivalents. This simplifies the job of the system designer and the
computer, and results in much more accurate representations of the way
systems behave in the real world.
Additional benefits of fuzzy logic include its simplicity and its
flexibility. Fuzzy logic can handle problems with imprecise and incomplete
data, and it can model nonlinear functions of arbitrary complexity. "If you
don't have a good plant model, or if the system is changing, then fuzzy will
produce a better solution than conventional control techniques," says Bob
Varley, a Senior Systems Engineer at Harris Corp., an aerospace company in
Palm Bay, Florida.
You can create a fuzzy system to match any set of input-output data. The
Fuzzy Logic Toolbox makes this particularly easy by supplying adaptive
techniques such as adaptive neuro-fuzzy inference systems (ANFIS) and fuzzy
subtractive clustering.
Fuzzy logic models, called fuzzy inference systems, consist of a number
of conditional "if-then" rules. For the designer who understands the system,
these rules are easy to write, and as many rules as necessary can be
supplied to describe the system adequately (although typically only a
moderate number of rules are needed).
In fuzzy logic, unlike standard conditional logic, the truth of any
statement is a matter of degree. (How cold is it? How high should we set the
heat?) We are familiar with inference rules of the form p -> q (p implies
q). With fuzzy logic, it's possible to say (.5* p ) -> (.5 * q). For
example, for the rule if (weather is cold) then (heat is on), both
variables, cold and on, map to ranges of values. Fuzzy inference systems
rely on membership functions to explain to the computer how to calculate the
correct value between 0 and 1. The degree to which any fuzzy statement is
true is denoted by a value between 0 and 1.
Not only do the rule-based approach and flexible membership function
scheme make fuzzy systems straightforward to create, but they also simplify
the design of systems and ensure that you can easily update and maintain the
system over time.
DESIGN GOALS
Control of the environment for large computing systems is often a far
greater challenge than for rooms inhabited by people. Not only do the
systems themselves generate heat, but they are often specified by their
manufacturers to be maintained in as little as a plus-or-minus 1 degree
(Fahrenheit) range. Humidity is also a challenge, causing, for example,
corrosion and jamming of associated mechanical systems at high humidity
levels and the enhanced possibility of static discharge with low levels.
Humidity control is often specified to be 50% relative humidity, with a
maximum swing of plus-or-minus 3% per hour.
In addition, the design of a precision environmental control system also
faces nonlinearities, caused by such system behavior as air flow delay and
dead times, uneven airflow distribution patterns, and duct work layouts.
Uncertainties in system parameters are often present, for example, room size
and shape, location of heat-producing equipment, thermal mass of equipment
and walls, and amount and timing of external air introduction.
Recognizing these challenges, Liebert undertook the design of a control
system requiring (in general terms):
- Precision temperature and humidity control;
- Minimization of cycling times (i.e., the opening and closing of the
damper and turning on and off of the compressor), thereby increasing
reliability and component life, and also resulting in increased energy
efficiency;
- Straightforward and therefore inexpensive control electronics.
In short, Liebert wanted to precisely control with simple hardware a
nonlinear system with significant uncertainties. Several traditional linear
approaches were considered but proved inadequate. A fuzzy logic approach was
investigated and ultimately implemented. Design specifics - The LogiCool
control system has six fuzzy inputs, three fuzzy outputs, and 144 principles
(rules). It runs on a Motorola 6803 microprocessor, and is programmed in C.
LogiCool's fuzzy input variables are: e_temperature, the temperature
relative to a setpoint; delta_T/delta_t, the rate of temperature change;
e_humidity, the humidity relative to a setpoint; delta_H/delta_t, the rate
of humidity change; and two proprietary variables associated with the action
of the controllers.
Fuzzy outputs control: 1) amount of cooling, 2) amount of
dehumidification, and 3) heat. Outputs can also be treated as fedback input
variables, and time delays are treated as fuzzy outputs as well. Each fuzzy
variable is assigned seven membership functions as values, with the
traditional Large_Negative, Medium_Negative, Small_Negative, Near_Zero,
Small_ Positive, Medium_Positive, and Large_Positive as labels. Ranges for
the values of each variable are proprietary.
An example of a temperature control principle, using the as ...then ...
(rather than the if ... then ...) syntax, is:
as temperature relative to set point is small_positive and temperature rate
of change is medium_positive then amount of cooling is small_positive;
The Liebert design also incorporates time delays into their principles.
The following demonstrates both this as well as the use of a fuzzy output as
a feedback variable.
as temperature relative to setpoint is small_negative and amount of
cooling is small_positive then wait delay to cooling change is
medium_positive;
A fuzzy OR operator (maximizer) is used as the defuzzification technique,
avoiding the complicated calculations associated with a centroid approach.
Liebert has found that with the large number of principles, a more elaborate
approach is unnecessary. Inputs are sampled, the principle-base accessed,
and outputs are updated once a second. The "long" inter-sample delay allows
the 6803, a simple eight-bit microprocessor, to implement this rather large
fuzzy system.
FUZZY LOGIC OBJECTIONS
It would be remarkable if a theory as far-reaching as fuzzy systems did not
arouse some objections in the professional community. While there have been
generic complaints about the "fuzziness" of the process of assigning values
to linguistic terms, perhaps the most cogent criticisms come from Haack . A
formal logician, Haack argues that there are only two areas in which fuzzy
logic could possibly be demonstrated to be "needed," and then maintains that
in each case it can be shown that fuzzy logic is not necessary.
The first area Haack defines is that of the nature of Truth and Falsity:
if it could be shown, she maintains, that these are fuzzy values and not
discrete ones, then a need for fuzzy logic would have been demonstrated. The
other area she identifies is that of fuzzy systems' utility: if it could be
demonstrated that generalizing classic logic to encompass fuzzy logic would
aid in calculations of a given sort, then again a need for fuzzy logic would
exist.
In regards to the first statement, Haack argues that True and False are
discrete terms. For example, "The sky is blue" is either true or false; any
fuzziness to the statement arises from an imprecise definition of terms, not
out of the nature of Truth. As far as fuzzy systems' utility is concerned,
she maintains that no area of data manipulation is made easier through the
introduction of fuzzy calculus; if anything, she says, the calculations
become more complex. Therefore, she asserts, fuzzy logic is unnecessary.
Fox has responded to her objections, indicating that there are three
areas in which fuzzy logic can be of benefit: as a "requisite" apparatus (to
describe real-world relationships which are inherently fuzzy); as a
"prescriptive" apparatus (because some data is fuzzy, and therefore requires
a fuzzy calculus); and as a "descriptive" apparatus (because some
inferencing systems are inherently fuzzy).
His most powerful arguments come, however, from the notion that fuzzy and
classic logics need not be seen as competitive, but complementary. He argues
that many of Haack's objections stem from a lack of semantic clarity, and
that ultimately fuzzy statements may be translatable into phrases which
classical logicians would find palatable.
Lastly, Fox argues that despite the objections of classical logicians,
fuzzy logic has found its way into the world of practical applications, and
has proved very successful there. He maintains, pragmatically, that this is
sufficient reason for continuing to develop the field.
REFERENCES
[1] Daniel Mcneil and Paul Freiberger " Fuzzy Logic"
[2] http://www.ortech-engr.com/fuzzy/reservoir.html
[3] http://www.quadralay.com/www/Fuzzy/FAQ/FAQ00.html
[4] http://www.fll.uni.linz.ac.af/pdhome.html
[5] http://soft.amcac.ac.jp/index-e.html
[6] http://www.abo.fi/~rfuller/nfs.html
[7] L.A.Zadeh,"Making computer think like people, IEEE spectrum, 8/1984, pp
26-32 [8] S.Haack, " Do we need fuzzy logic? " Int .Jr nl .of Man-Mach.stud
, vol.11, 1979, pp 437-445
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