Programmed Union Utilizing Hereditary Programming of Enhanced PID Tuning Rules.


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Programmed Combination Utilizing Hereditary Programming of Enhanced PID Tuning Rules Martin A. Keane Econometrics, Inc. Chicago, Illinois martinkeane@ameritech.net Matthew J. Streeter Hereditary Programming, Inc. Mountain View, California mjs@tmolp.com John R. Koza Stanford College
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Programmed Synthesis Using Genetic Programming of Improved PID Tuning Rules Martin A. Keane Econometrics, Inc. Chicago, Illinois martinkeane@ameritech.net Matthew J. Streeter Genetic Programming, Inc. Mountain View, California mjs@tmolp.com John R. Koza Stanford University Stanford, California koza@stanford.edu ICONS 2003, Faro Portugal, April 8-11

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Outline Overview of Genetic Programming (GP) Controller Synthesis utilizing GP Improved PID Tuning Rules

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Overview of Genetic Programming (GP)

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Overview of GP Breed PC projects to take care of issues Programs spoke to as trees in style of LISP dialect Programs can make anything (e.g., controller, mathematical statement, controller+equations)

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Pseudo-code for GP 1) Create beginning irregular populace 2) Evaluate wellness 3) Select fitter people to recreate 4) Apply propagation operations (hybrid, transformation) to make new populace 5) Return to 2 and rehash until arrangement discovered

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Random introductory populace Function set: {+, *,/, - } Terminal set: {A, B, C} (1) Choose “+” (2) Choose “*” (3-5) Choose “A”, “B”, “C”

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Fitness assessment 4 arbitrary comparisons indicated Fitness is shaded region Target bend ( x 2 + x +1 )

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Crossover Picked subtree Subtrees are swapped to make posterity Picked subtree Parents Offspring

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Controller Synthesis Using GP Program tree specifically speaks to control piece graph Special capacities for inner criticism/departure focuses Fitness measured as far as ITAE, affectability, solidness

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Control issues comprehended Control of two and three slack plants, non-negligible stage plant, three slack plant w/5 second postpone Parameterized controllers for three slack plant with variable inward pick up, . . . Parameterized controllers for wide groups of plants

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Improved PID Tuning Rules

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Basis for Comparison: the Å str ö m-H ä gglund controller Applied overwhelming post outline to 16 plants from 4 agent groups of plants Used bend fitting to acquire summed up arrangement Equations are communicated as far as extreme addition ( K u ) and extreme period ( T u )

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The Å str ö m-H ä gglund controller Equation 3 ( K i ) : Equation 4 ( K d ) : Equation 1 ( b ): Equation 2 ( K p ) :

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Experiment 1: Evolving tuning tenets starting with no outside help 4-branch system speaking to 4 mathematical statements (for K , K i , K d , and b ) regarding K u & T u Different from other GP work in that we are advancing tuning, not topology Fitness as far as ITAE, affectability, solidness

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Function & terminal sets Function set: {+, *, - ,/, EXP, LOG, POW} Terminal set: {KU, TU,  }

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Fitness measure ITAE punishment for setpoint & aggravation dismissal Penalty for least sensor commotion weakening (affectability) Penalty for most extreme affectability to clamor (steadiness) Evaluation on 30 plants (superset of A-H’s 16 plants) Controllers recreated utilizing SPICE

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Fitness measure: ITAE punishment Six blends of reference and unsettling influence signal statures Penalty is given by: B and C are normalizing components

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Fitness measure: security punishment 0 reference signal, 1 V commotion signal Maximum affectability is greatest adequacy of commotion sign + plant reaction Penalty is 0 if M s < 1.5 2( M s - 1.5) if 1.5  M s  2.0 20( M s - 1.0) is M s > 2.0

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Fitness measure: affectability punishment 0 reference signal, 1 V commotion flag A min is least lessening of plant reaction Penalty is 0 if A min > 40 db (40-A min )/10 if 20 db  A min  40 db 2+(20-A min ) if A min < 20 db

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Experimental setup 1000 hub Beowulf bunch with 350 MHz Pentium II processors Island model with nonconcurrent subpopulations Population size: 100,000 70% hybrid, 20% consistent transformation, 9% cloning, 1% subtree change

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Å str ö m-H ä gglund mathematical statements K i K d b

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Evolved comparisons K i K d b

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Experiment 1: Conclusions Evolved tuning standards are preferable all things considered over A-H, however not consistently better Dominant shaft configuration gives ideal answer for individual plants Maybe we can enhance A-H bend fitting

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Experiment 2: Evolving augmentations to A-H mathematical statements Same project structure, wellness measure, and so on. Estimations of advanced mathematical statements are presently added to A-H comparisons

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Evolved acclimations to A-H mathematical statements K i K d b

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Results 91.6% of setpoint ITAE of Å str ö m-H ä gglund (89.7% out-of-test) 96.2% of aggravation dismissal ITAE of A-H (95.6% OOS) 99.5% of 1/(least lessening) of A-H (99.5% OOS) 98.5% of greatest affectability of A-H (98.5% OOS)

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Conclusions Evolved controller is marginally superior to anything Å str ö m-H ä gglund Not much opportunity to get better (as far as our wellness measure) with PID topology We have become better results developing t

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