Number 21 January 20,1992
The Huntington Technical Brief
By David Brubaker Ph.D.
A Fuzzy Web Tension Controller
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NOTE: This application is easier to follow
if you have the drawings. If the information
here is important please contact Dr. Brubaker
about a paper version of this issue.
INTRODUCTION
We shall start the year with a description of an application,
for which I thank OMRON Electronics. The application to be
discussed is an industrial control system, specifically a web
tension controller.
DESCRIPTION
A metal film is fed from a supply reel, over a number of pivot
and tension rollers, and onto a take-up reel. As the metal film
is wound from the supply reel to the take-up reel, the tension
rollers are used to keep the film appropriately taut. The
position of the pivot rollers is held constant - that is they
are allowed to rotate but not to move vertically or laterally.
Drive is applied by the controller to both the supply and the
take-up reels.
The system was initially modeled as being linear, and control
was applied using a PID (proportional-integral-derivative)
controller. Unfortunately, action of the film as it moved across
the pivot and tension rollers had significant nonlinearities,
especially during speed changes. The PID controller was forced
to operate at reduced system velocities - higher velocities
resulted in material damage.
With goals of increasing system velocities (and thereby
increasing overall system throughput) and significantly reducing
material damage, a fuzzy approach was implemented. FUZZY
IMPLEMENTATION - Actually a rather simple fuzzy system was
implemented, with eight defined inputs and two outputs. Four
input-output mappings were defined.
The first four inputs are the velocity and acceleration of the
film as it: a) leaves the supply reel (v1 and v1', respectively)
and, b) approaches the take-up reel (v2 and v2', respectively).
The second four inputs are the vertical position variations of
the two tension rollers (dS1 and dS2, respectively) and the
velocities of these two rollers (the derivatives of the position
terms: dS1' and dS2').
The controller generates two outputs, the drives, Dr1 and Dr2, to
the supply and take-up reels. The variables Dr1 and Dr2 are
defined as variations from commanded speed values. Each output is
derived using fuzzy rules from two sets of input values, as shown
below:
(v1, v1') maps to Dr1
(dS1, dS1') maps to Dr1
(v2, v2') maps to Dr2
(dS2, dS2') maps to Dr2
Membership functions for input and output values provide seven
ranges: negative large (NL), negative medium (NM), negative small
(NS), zero (ZE), positive small (PS), positive medium (PM),
positive large (PL). These labels are the same for all eight
inputs and both outputs. Of course each input/output range will
be scaled and defined in units appropriate to the particular
physical parameter.
Each input-to-output mapping (e.g., (v1, v1') maps to ½1) is
calculated independently, but all four mappings use the same
seven entry rule-base. Using the "as... do..." rule format and
the generic variables IN, IN', and OUT, the seven rules are:
1. as (IN is NL) do (OUT is PL)
2. as (IN is NM and IN' is ZE) do (OUT is PM)
3. as (IN is NS and IN' is NS) do (OUT is PS)
4. as ((IN is NS and IN' is PS)
or (IN is ZE and IN' is ZE)
or (IN is PS and IN' is NS) do (OUT is ZE)
5. as (IN is PS and IN' is PS) do (OUT is NS)
6. as (IN is PM and IN' is ZE) do (OUT is NM)
7. as (IN is PL) do (OUT is NL)
At each system time increment, each output will have several
designated actions, both as a result of overlapping input values
on a single rule mapping, and also because two sets of inputs
drive a single output. Multiple actions are combined using a
standard center-of-gravity, or centroid approach.
RESULTS
Although a straightforward design, in actual operation
the fuzzy system handles admirably. System throughput (resulting
in no material damage) was double that of the PID controller.
Important side benefits were:
*Set-up time was greatly reduced.
*Maintenance time was greatly reduced.
*Adjustments to the system could be made by in-house personnel,
rather than a PID expert, as had been the case with the previous
system.
My thanks to OMRON Electronics, and to Brent Schnell, OMRON
senior sales engineer, in particular.
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The Huntington Technical Brief is published, monthly and free
of charge, as part of the marketing effort of Dr. David Brubaker
of The Huntington Group. A full collection of past issues
(starting with number 5 -- issues 1 through 4 are unrelated to
fuzzy logic and are unavailable) may be obtained for $10.00. The
42-page report "Introduction to Fuzzy Logic Systems" is
available for $35.00.
For the past fifteen years Dr. Brubaker has provided
technical consulting services in the design of complex systems,
real-time, embedded processor systems, and for the past four
years, fuzzy logic systems. If you need out-of-house expertise
in any of these, please call 415-325-7554.
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Copyright 1992 by The Huntington Group
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