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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

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

Overview of Genetic Programming (GP)

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)

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

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

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

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

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

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

Improved PID Tuning Rules

Basis for Comparison: the Ã str Ã¶ m-H Ã¤ 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 )

The Ã str Ã¶ m-H Ã¤ gglund controller Equation 3 ( K i ) : Equation 4 ( K d ) : Equation 1 ( b ): Equation 2 ( K p ) :

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

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

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-Hâs 16 plants) Controllers recreated utilizing SPICE

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

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 ï£ M s ï£ 2.0 20( M s - 1.0) is M s > 2.0

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 ï£ A min ï£ 40 db 2+(20-A min ) if A min < 20 db

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

Ã str Ã¶ m-H Ã¤ gglund mathematical statements K i K d b

Evolved comparisons K i K d b

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

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

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

Results 91.6% of setpoint ITAE of Ã str Ã¶ m-H Ã¤ 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)

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