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INTRODUCTION
Temperature control is widely used in various processes. These
processes, no matter if it is in a large industrial plant, or in
a home appliance, share several unfavorable features. These
include non-linearity, interference, dead time, and external
disturbances, among others. Conventional approaches usually do
not result in satisfactory temperature control.
In this Application Note we provide examples of fuzzy logic used
to control temperature in several different situations. These
examples are developed using FIDE, an integrated fuzzy inference
development environment.
FUZZY CONTROL IN A GLASS MELTING FURNACE
A glass melting furnace has two rooms, a melter and a refiner.
Raw materials are melted into glass at high temperature in the
melter. The temperature of the melted glass is adjusted to a
suitable temperature for the glass forming process to follow. It
takes a long time to change the temperature in the furnace, which
is an example of dead-time in this process. The flow of melted
glass is not uniform, especially at the bottom of the furnace. In
addition to temperature, other factors also contribute to the
thermal characteristics of melted glass. Raw material mixing
procedure, glass color, and the amount of the glass are some of
the factors. Because there are many variables and the procedure
complex, it is very difficult to design an effective temperature
controller for this application using conventional control
approaches.
Control Objective
Control temperature in a dead time process such as in a glass
melting furnace.
Fuzzy Control System
The control block diagram for a glass melting furnace is shown in
Figure 1. Control value u is applied to the
process to adjust the temperature. This value is changed by two
compensators. The variation of u can be written
as u = ud + ue where ud is the output of
the dead time compensator, and ue is the output
of the error compensator. The dead time compensator is used to
reduce the effect dead time has on the process. Its output
(ud), an incremental change in control value, is
derived from the change in the current and previous control value
(u) and the time differential of output
temperature (y). The error compensator is used
to reduce the difference between the desired temperature and the
actual temperture of hte furnace. Its outpu (ue), also an
incremental change in control value, is inferred from the
difference(error) e and its time differential <20>. ud and ue are
combined to change the control value u.
Input/Output Variables of the Dead Time Compensator
Labels and membership functions of input/output variables of the
dead time compensator are shown in Figure 2a, 2b, 2c. The
membership functions can be created by using the MF editor in
FIDE.
FIU Source Code for the Dead Time Compensator
The following is the source code for the dead time compensator
written in FIL, the fuzzy inference language provided in FIDE.
$ FILENAME: temp/temp1_dt.fil
$ DATE: 08/31/1992
$ UPDATE: 09/02/1992
$ Temperature Controller : Part 1 : dead time compensator
$ Two inputs, one output
$ INPUT(S): Prev(ious)_Var(iationOf)_Ctrl, TimeDiff(erentialOf)_Output
$ OUTPUT(S): Var(iationOf)_Ctrl
$ FIU HEADER
fiu tvfi (min max) *8;
$ DEFINITION OF INPUT VARIABLE(S)
invar Prev_Var_Ctrl " " : -1 () 1 [
P_Large (@0.45, 0, @0.75, 1, @1.00, 1),
P_Medium (@0.15, 0, @0.45, 1, @0.75, 0),
P_Small (@-0.15, 0, @0.15, 1, @0.45, 0),
N_Small (@-0.45, 0, @-0.15, 1, @0.15, 0),
N_Medium (@-0.75, 0, @-0.45, 1, @-0.15, 0),
N_Large (@-1.00, 1, @-0.75, 1, @-0.45, 0)
];
invar TimeDiff_Output " " : -90 () 90 [
P_Large (@20, 0, @60, 1, @90, 1),
P_Small (@-20, 0, @20, 1, @60, 0),
N_Small (@-60, 0, @-20, 1, @20, 0),
N_Large (@-90, 1, @-60, 1, @-20, 0)
];
$ DEFINITION OF OUTPUT VARIABLE(S)
outvar Var_Ctrl " " : -1 () 1 * (
P_Large = 0.80,
P_Medium = 0.40,
P_Small = 0.20,
Zero = 0.00,
N_Small = -0.20,
N_Medium = -0.40,
N_Large = -0.80
);
$ RULES
if Prev_Var_Ctrl is P_Large and TimeDiff_Output is P_Large then
Var_Ctrl is N_Large;
if Prev_Var_Ctrl is P_Large and TimeDiff_Output is P_Small then
Var_Ctrl is N_Medium;
if Prev_Var_Ctrl is P_Large and TimeDiff_Output is N_Small then
Var_Ctrl is N_Small;
if Prev_Var_Ctrl is P_Large and TimeDiff_Output is N_Large then
Var_Ctrl is Zero;
if Prev_Var_Ctrl is P_Medium and TimeDiff_Output is P_Large then
Var_Ctrl is N_Medium;
if Prev_Var_Ctrl is P_Medium and TimeDiff_Output is P_Small then
Var_Ctrl is N_Small;
if Prev_Var_Ctrl is P_Medium and TimeDiff_Output is N_Small then
Var_Ctrl is Zero;
if Prev_Var_Ctrl is P_Medium and TimeDiff_Output is N_Large then
Var_Ctrl is Zero;
if Prev_Var_Ctrl is P_Small and TimeDiff_Output is P_Large then
Var_Ctrl is N_Small;
if Prev_Var_Ctrl is P_Small and TimeDiff_Output is P_Small then
Var_Ctrl is Zero;
if Prev_Var_Ctrl is P_Small and TimeDiff_Output is N_Small then
Var_Ctrl is Zero;
if Prev_Var_Ctrl is P_Small and TimeDiff_Output is N_Large then
Var_Ctrl is Zero;
if Prev_Var_Ctrl is N_Small and TimeDiff_Output is P_Large then
Var_Ctrl is Zero;
if Prev_Var_Ctrl is N_Small and TimeDiff_Output is P_Small then
Var_Ctrl is Zero;
if Prev_Var_Ctrl is N_Small and TimeDiff_Output is N_Small then
Var_Ctrl is Zero;
if Prev_Var_Ctrl is N_Small and TimeDiff_Output is N_Large then
Var_Ctrl is P_Small;
if Prev_Var_Ctrl is N_Medium and TimeDiff_Output is P_Large then
Var_Ctrl is Zero;
if Prev_Var_Ctrl is N_Medium and TimeDiff_Output is P_Small then
Var_Ctrl is Zero;
if Prev_Var_Ctrl is N_Medium and TimeDiff_Output is N_Small then
Var_Ctrl is P_Small;
if Prev_Var_Ctrl is N_Medium and TimeDiff_Output is N_Large then
Var_Ctrl is P_Medium;
if Prev_Var_Ctrl is N_Large and TimeDiff_Output is P_Large then
Var_Ctrl is Zero;
if Prev_Var_Ctrl is N_Large and TimeDiff_Output is P_Small then
Var_Ctrl is P_Small;
if Prev_Var_Ctrl is N_Large and TimeDiff_Output is N_Small then
Var_Ctrl is P_Medium;
if Prev_Var_Ctrl is N_Large and TimeDiff_Output is N_Large then
Var_Ctrl is P_Large
end
Input/Output Response of the Dead Time Compensator
Figure 3 shows the response surface of the dead time compensator.
This surface can be obtained by using the Analyzer tool provided
in FIDE.
Input/Output Variables of the Error Compensator
Labels and membership functions of input/output variables of the
Error Compensator are shown in Figure 4a, 4b, 4c.
FIU Source Code of Error Compensator
$ FILENAME: temp/temp1_er.fil
$ DATE: 09/02/1992
$ UPDATE: 09/03/1992
$ Temperature Controller : Part 2 : error compensator
$ Two inputs, one output
$ INPUT(S): Error, TimeDiff(erentialOf)_Error
$ OUTPUT(S): Var(iationOf)_Ctrl
$ FIU HEADER
fiu tvfi (min max) *8;
$ DEFINITION OF INPUT VARIABLE(S)
invar Error " " : -100 () 100 [
P_Large (@50, 0, @80, 1, @100, 1),
P_Medium (@20, 0, @50, 1, @80, 0),
P_Small (@0, 0, @20, 1, @50, 0),
Zero (@-20, 0, @0, 1, @20, 0),
N_Small (@-50, 0, @-20, 1, @0, 0),
N_Medium (@-80, 0, @-50, 1, @-20, 0),
N_Large (@-100,1, @-80, 1, @-50, 0)
];
invar TimeDiff_Error " " : -90 () 90 [
P_Large (@50, 0, @70, 1, @90, 1),
P_Medium (@30, 0, @50, 1, @70, 0),
P_Small (@0, 0, @30, 1, @50, 0),
Zero (@-30, 0, @0, 1, @30, 0),
N_Small (@-50, 0, @-30, 1, @0, 0),
N_Medium (@-70, 0, @-50, 1, @-30, 0),
N_Large (@-90, 1, @-70, 1, @-50, 0)
];
$ DEFINITION OF OUTPUT VARIABLE(S)
outvar Var_Ctrl " " : -1 () 1 * (
P_Large = 0.80,
P_Medium = 0.40,
P_Small = 0.20,
Zero = 0.00,
N_Small = -0.20,
N_Medium = -0.40,
N_Large = -0.80
);
$ RULES
if Error is Zero and TimeDiff_Error is P_Large then Var_Ctrl is
P_Large;
if Error is Zero and TimeDiff_Error is P_Medium then Var_Ctrl is
P_Medium;
if Error is Zero and TimeDiff_Error is P_Small then Var_Ctrl is
Zero;
if Error is Zero and TimeDiff_Error is Zero then Var_Ctrl is
Zero;
if Error is Zero and TimeDiff_Error is N_Small then Var_Ctrl is
Zero;
if Error is Zero and TimeDiff_Error is N_Medium then Var_Ctrl is
N_Medium;
if Error is Zero and TimeDiff_Error is N_Large then Var_Ctrl is
N_Large;
if Error is P_Large and TimeDiff_Error is Zero then Var_Ctrl is
P_Large;
if Error is P_Medium and TimeDiff_Error is Zero then Var_Ctrl is
P_Medium;
if Error is P_Small and TimeDiff_Error is Zero then Var_Ctrl is
Zero;
if Error is N_Small and TimeDiff_Error is Zero then Var_Ctrl is
Zero;
if Error is N_Medium and TimeDiff_Error is Zero then Var_Ctrl is
N_Medium;
if Error is N_Large and TimeDiff_Error is Zero then Var_Ctrl is
N_Large;
if Error is P_Medium and TimeDiff_Error is P_Medium then Var_Ctrl is
P_Large;
if Error is P_Small and TimeDiff_Error is P_Small then Var_Ctrl is
Zero;
if Error is P_Medium and TimeDiff_Error is N_Medium then Var_Ctrl is
Zero;
if Error is P_Small and TimeDiff_Error is N_Large then Var_Ctrl is
N_Medium;
if Error is N_Small and TimeDiff_Error is P_Large then Var_Ctrl is
P_Medium;
if Error is N_Medium and TimeDiff_Error is P_Medium then Var_Ctrl is
Zero;
if Error is N_Small and TimeDiff_Error is N_Small then Var_Ctrl is
Zero;
if Error is N_Medium and TimeDiff_Error is N_Medium then Var_Ctrl is
N_Large
end
Input/Output Response of Error Compensator
Figure 5 shows the response surface of the error compensator.
COMMENTS
Temperature control systems, using fuzzy controllers as shown
above, have been put into operation and provide performance
better than conventional control systems. Fuzzy controllers also
show robust response in the handling of dead time behavior in the
process.
(Weijing Zhang, Applications Engineer, Aptronix Inc.)
For Further Information Please Contact:
Aptronix Incorporated
2150 North First Street #300
San Jose, CA 95131
Tel (408) 428-1888
Fax (408) 428-1884
FuzzyNet (408) 428-1883 data 8/N/1
Aptronix Company Overview
Headquartered in San Jose, California, Aptronix develops and
markets fuzzy logic-based software, systems and development
tools for a complete range of commercial applications. The
company was founded in 1989 and has been responsible for a
number of important innovations in fuzzy technology.
Aptronix's product Fide (Fuzzy Inference Development
Environment) -- is a complete environment for the development of
fuzzy logic-based systems. Fide provides system engineers with
the most effective fuzzy tools in the industry and runs in
MS-Windows(TM) on 386/486 hardware. The price for Fide is $1495 and
can be ordered from any authorized Motorola distributor. For a
list of authorized distributors or more information, please
call Aptronix. The software package comes with complete
documentation on how to develop fuzzy logic based applications,
free telephone support for 90 days and access to the Aptronix
FuzzyNet information exchange.
Temperature Control
FIDE Application Note 004-080992
Aptronix Inc., 1992