141 lines
6.1 KiB
Plaintext
141 lines
6.1 KiB
Plaintext
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Number 21 January 20,1992
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The Huntington Technical Brief
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By David Brubaker Ph.D.
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A Fuzzy Web Tension Controller
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---------------------------------------
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NOTE: This application is easier to follow
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if you have the drawings. If the information
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here is important please contact Dr. Brubaker
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about a paper version of this issue.
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INTRODUCTION
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We shall start the year with a description of an application,
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for which I thank OMRON Electronics. The application to be
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discussed is an industrial control system, specifically a web
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tension controller.
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DESCRIPTION
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A metal film is fed from a supply reel, over a number of pivot
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and tension rollers, and onto a take-up reel. As the metal film
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is wound from the supply reel to the take-up reel, the tension
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rollers are used to keep the film appropriately taut. The
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position of the pivot rollers is held constant - that is they
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are allowed to rotate but not to move vertically or laterally.
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Drive is applied by the controller to both the supply and the
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take-up reels.
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The system was initially modeled as being linear, and control
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was applied using a PID (proportional-integral-derivative)
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controller. Unfortunately, action of the film as it moved across
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the pivot and tension rollers had significant nonlinearities,
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especially during speed changes. The PID controller was forced
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to operate at reduced system velocities - higher velocities
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resulted in material damage.
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With goals of increasing system velocities (and thereby
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increasing overall system throughput) and significantly reducing
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material damage, a fuzzy approach was implemented. FUZZY
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IMPLEMENTATION - Actually a rather simple fuzzy system was
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implemented, with eight defined inputs and two outputs. Four
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input-output mappings were defined.
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The first four inputs are the velocity and acceleration of the
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film as it: a) leaves the supply reel (v1 and v1', respectively)
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and, b) approaches the take-up reel (v2 and v2', respectively).
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The second four inputs are the vertical position variations of
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the two tension rollers (dS1 and dS2, respectively) and the
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velocities of these two rollers (the derivatives of the position
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terms: dS1' and dS2').
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The controller generates two outputs, the drives, Dr1 and Dr2, to
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the supply and take-up reels. The variables Dr1 and Dr2 are
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defined as variations from commanded speed values. Each output is
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derived using fuzzy rules from two sets of input values, as shown
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below:
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(v1, v1') maps to Dr1
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(dS1, dS1') maps to Dr1
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(v2, v2') maps to Dr2
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(dS2, dS2') maps to Dr2
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Membership functions for input and output values provide seven
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ranges: negative large (NL), negative medium (NM), negative small
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(NS), zero (ZE), positive small (PS), positive medium (PM),
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positive large (PL). These labels are the same for all eight
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inputs and both outputs. Of course each input/output range will
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be scaled and defined in units appropriate to the particular
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physical parameter.
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Each input-to-output mapping (e.g., (v1, v1') maps to <20>1) is
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calculated independently, but all four mappings use the same
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seven entry rule-base. Using the "as... do..." rule format and
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the generic variables IN, IN', and OUT, the seven rules are:
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1. as (IN is NL) do (OUT is PL)
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2. as (IN is NM and IN' is ZE) do (OUT is PM)
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3. as (IN is NS and IN' is NS) do (OUT is PS)
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4. as ((IN is NS and IN' is PS)
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or (IN is ZE and IN' is ZE)
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or (IN is PS and IN' is NS) do (OUT is ZE)
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5. as (IN is PS and IN' is PS) do (OUT is NS)
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6. as (IN is PM and IN' is ZE) do (OUT is NM)
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7. as (IN is PL) do (OUT is NL)
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At each system time increment, each output will have several
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designated actions, both as a result of overlapping input values
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on a single rule mapping, and also because two sets of inputs
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drive a single output. Multiple actions are combined using a
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standard center-of-gravity, or centroid approach.
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RESULTS
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Although a straightforward design, in actual operation
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the fuzzy system handles admirably. System throughput (resulting
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in no material damage) was double that of the PID controller.
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Important side benefits were:
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*Set-up time was greatly reduced.
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*Maintenance time was greatly reduced.
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*Adjustments to the system could be made by in-house personnel,
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rather than a PID expert, as had been the case with the previous
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system.
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My thanks to OMRON Electronics, and to Brent Schnell, OMRON
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senior sales engineer, in particular.
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----------------------------------------------------------------
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The Huntington Technical Brief is published, monthly and free
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of charge, as part of the marketing effort of Dr. David Brubaker
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of The Huntington Group. A full collection of past issues
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(starting with number 5 -- issues 1 through 4 are unrelated to
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fuzzy logic and are unavailable) may be obtained for $10.00. The
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42-page report "Introduction to Fuzzy Logic Systems" is
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available for $35.00.
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For the past fifteen years Dr. Brubaker has provided
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technical consulting services in the design of complex systems,
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real-time, embedded processor systems, and for the past four
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years, fuzzy logic systems. If you need out-of-house expertise
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in any of these, please call 415-325-7554.
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----------------------------------------------------------------
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Copyright 1992 by The Huntington Group
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883 Santa Cruz Avenue,Suite 27 Menlo Park, CA 94025-4608
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This information is provided by
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Aptronix FuzzyNet
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408-428-1883 Data USR V.32bis
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