Real time optimization and constrained multivariable control
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REAL TIME OPTIMIZATION AND CONSTRAINED MULTIVARIABLE CONTROL. CHARLES R.CUTLER, Ph.D. PRESENTED AT THE NORDIC PROCESS CONTROL WORKSHOP ON AUGUST 23, 2001. REAL TIME OPTIMIZATION AND CONSTRAINED MULTIVARIABLE CONTROL HAS BEEN FOUND TO ADD 5 TO 10 PERCENT TO THE VALUE

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REAL TIME OPTIMIZATION AND CONSTRAINED MULTIVARIABLE CONTROL

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Real time optimization and constrained multivariable control

REAL TIME OPTIMIZATIONAND CONSTRAINED MULTIVARIABLE CONTROL

CHARLES R.CUTLER, Ph.D.

PRESENTED AT THE NORDIC PROCESS

CONTROL WORKSHOP ON AUGUST 23, 2001


Real time optimization and constrained multivariable control

REAL TIME OPTIMIZATION AND CONSTRAINED MULTIVARIABLE

CONTROL HAS BEEN FOUND TO ADD 5 TO 10 PERCENT TO THE VALUE

ADDED BY THE PROCESS.

A PLANT MUST BE OPERATED AT 70 TO 80 PERCENT OF DESIGN CAPACITY

TO PAY FOR THE COST OF CAPITAL, THE 5 TO 10 PERCENT FROM REAL

TIME OPTIMIZATION AND CONTROL IS RELATIVE TO THE 20 TO 30

PERCENT WHEN LOOKING FOR OPPORTUNITIES TO IMPROVE

PROFITABILITY.

THE REAL TIME OPTIMIZATION REFERRED TO IN THIS PAPER IS ONE

WHICH HAS A COMPREHENSIVE STEADY STATE ENGINEERING MODEL OF

THE PROCESS THAT IS BEING UPDATED IN REAL TIME.

CONSTRAINED MULTIVARIABLE CONTROL CONSIDERS ALL THE

RELAVENT PAST HISTORY, TO PREDICT THE FUTURE, SUCH THAT IT CAN

PLAN A SET OF CHANGES IN THE MANIPULATED VARIABLES TO HONOR

ALL THE CONSTRAINTS ON THE PROCESS.


Real time optimization and constrained multivariable control

  • FOR A LINEAR SYSTEM, ALL THE DEGREES OF FREEDOM FOR THE OPTIMIZATION WILL BE TIED UP AT SOME SET OF CONSTRAINTS TAKEN FROM THE INDEPENDENT AND DEPENDENT VARIABLES FROM A CONTROL POINT OF VIEW, THE INDEPENDENT VARIABLES ARE THE CONTROL HANDLES AN OPERATOR HAS; I.E. THE SET POINTS FOR PID CONTROLLERS OR MANUAL LOADING STATIONS FOR VALVES.

  • THE NUMBER OF POSSIBLE PERMUTATIONS OF CONSTRAINTS FOR A LINEAR SYSTEM IS GIVEN BY THE FOLLOWING EQUATION:

    (NUMBER OF LIMITS ON VARIABLES) !_________________

    (DEGREES FREEDOM) ! (NUMBER LIMITS - DEGREES FREEDOM) !

    WHERE THE DEGREES OF FREEDOM ARE EQUAL TO THE NUMBER OF INDEPENDENTVARIABLES

  • FOR A CONTROLLER WITH 25 INDEPENDENT VARIABLES AND 40 DEPENDENT VARIABLES WITH ONLY ONE LIMIT POSSIBLE ON EACH VARIABLE, THERE ARE 6.5 * 10 TO THE 17 TH POWER POSSIBLE COMBINATION OF CONSTRAINTS.


Overview

OVERVIEW

WE WILL REVIEW WHERE WE ARE IN THE EVOLUTION OF REAL

TIME OPTIMIZATION IN THE PROCESS INDUSTRIES.

WE WILL TALK ABOUT THE CONNECTION BETWEEN REAL TIME

OPTIMIZATION AND CONSTRAINED MULTIVARIABLE CONTROL.

WE WILL DISCUSS THE FEATURES A CONTROLLER MUST HAVE TO

SUPPORT REAL TIME OPTIMIZATION.

WE WILL OUTLINE THE REQUIREMENTS OF IDENTIFICATION

SOFTWARE FOR FINDING THE DYNAMIC MODEL OF THE PROCESS.

WE WILL DISCUSS THE ISSUES AROUND OPERATOR TRAINING FOR A

PROCESS THAT IS BEING CONTROLLED AND OPTIMIZED IN REAL

TIME.

WE WILL CONCLUDED WITH THE MANAGEMENT PROBLEMS

ASSOCIATED WITH MAINTENANCE OF REAL TIME OPTIMIZATION

AND CONTROL SYSTEMS.


The evolution of real time optimization in the process industries

THE EVOLUTION OF REAL TIME OPTIMIZATION IN THE PROCESS INDUSTRIES

THE GREAT ENTHUSIASM OF MID 1960S FOR REAL TIME

OPTIMIZATION GAVE WAY TO FRUSTRATION IN THE 1970S.

MOST OF THE EARLY REAL TIME OPTIMIZATION PROJECTS FAILED

FOR ONE OR MORE REASONS.

COMPUTERS WERE SLOW, NOT RELIABLE, AND WERE DIFFICULT TO PROGRAM

MODELING TOOLS WERE INADEQUATE, I.E. ONLY CLOSED MODELS

WERE USED

SOME PEOPLE USED ONLY REGRESSION MODELS RATHER THAN

FIRST PRINCIPLE ENGINEERING MODELS

MANY PEOPLE DID NOT PROVIDE FEED BACK FROM THE PROCESS

MEASUREMENTS TO UPDATE THE PARAMETERS IN THEIR MODELS


Real time optimization and constrained multivariable control

THE CONTROL TOOL OF THE TIME WAS SOME VARIATION TO THE

PID ALGORITHM WHICH WAS INADEQUATE FOR CONTROL AT A

LARGE NUMBER OF CONSTRAINTS

INORDINATE NUMBERS OF HIGHLY SKILLED MODELING AND

CONTROL ENGINEERS WERE REQUIRED TO MAINTAIN THE REAL

TIME OPTIMIZATION AND CONTROL SYSTEMS THAT SOLVED THE

PRECEDING PROBLEMS

THE GOOD NEWS FROM THE EARLY EXPERIENCES WITH REAL TIME

OPTIMIZATION WAS THE POTENTIAL PROFIT WAS HIGH IF THE

PROBLEMS COULD BE SOLVED.

THE DMC CONTROLLER WAS CONCEIVED TO CONTROL A PROCESS

AT A LARGE NUMBER OF CONSTRAINTS.

OPEN EQUATION MODELING TECHNIQUES EVOLVED TO SOLVE

LARGE OPTIMIZATION PROBLEMS WITH MANY INTERNAL RECYCLE

LOOPS.

HARDWARE TECHNOLOGY CONTINUED TO EVOLVE, PRODUCING

FASTER AND MORE RELIABLE COMPUTERS AND COMMUNICATION

DEVICES.


Real time optimization and constrained multivariable control

DCS INSTRUMENT SYSTEMS SIMPLIFIED THE INTERFACE OF THE

PROCESS COMPUTER TO THE PROCESS.

BY THE EARLY 1980S SOME PEOPLE WERE SUCCESSFULLY

OPTIMIZING AND CONTROLLING LARGE PROCESS UNITS IN REAL

TIME.

BY THE EARLY 1990S COMMERCIAL SOFTWARE WAS AVAILABLE TO

SOLVE THE REAL TIME OPTIMIZATION AND MULTIVARIABLE

CONTROL PROBLEMS.

OPEN EQUATION MODELS WITH OVER 200,000 EQUATIONS WERE

BEING SOLVED AND MULTIVARIABLE CONTROLLERS WITH 40

MANIPULATED VARIABLES AND 60 CONTROL VARIABLES WERE

BEING USED.

MANY OF THESE OPTIMIZATION AND CONTROL PROJECTS HAVE

PROVEN TO BE VERY PROFITABLE WITH PAYOUT TIMES MEASURED

IN MONTHS.

THE FAILURE OF AN OPTIMIZATION AND CONTROL PROJECT

TODAY CAN USUAL BE TRACED TO PERSONNEL PROBLEMS OR TO

MANAGEMENT PROBLEMS.


Real time optimization and constrained multivariable control

  • FOR A LINEAR SYSTEM, ALL THE DEGREES OF FREEDOM FOR THE OPTIMIZATION WILL BE TIED UP AT SOME SET OF CONSTRAINTS TAKEN FROM THE INDEPENDENT AND DEPENDENT VARIABLES.

  • FOR NON-LINEAR SYSTEMS, EXPERIENCE HAS SHOWN THAT OVER NINETY PERCENT OF THE TIME, ALL THE DEGREES OF FREEDOM FOR THE OPTIMIZATION WILL BE TIED UP AT SOME SET OF CONSTRAINTS.

  • CONSTRAINED MULTIVARIABLE CONTROL IS REQUIRED IF THE RESULTS OF THE REAL TIME OPTIMIZATION ARE TO BE ACHIEVED.

  • TO HOLD A PROCESS AT MULTIPLE CONSTRAINTS REQUIRES THAT ALL THE INTERACTIONS BETWEEN THE VARIABLES BE ACCURATELY DESCRIBED.

  • TRADITIONAL PID CONTROL HAS PROVEN TO BE INADEQUATE FOR LARGE MULTIVARIABLE PROBLEMS. THE DYNAMIC MODELS USED BY THE MULTIVARIABLE CONTROLLER MUST HAVE THE CORRECT STEADY STATE GAINS FOR CONTROL AT MULTIPLE CONSTRAINTS.


Real time optimization and constrained multivariable control

THE MULTIVARIABLE CONTROLLER FOR A REAL TIME

OPTIMIZATION WILL IN GENERAL HAVE MANY MORE CONTROLLED

VARIABLES THAN MANIPULATED VARIABLES.

EACH CONTROL VARIABLE CAN OPERATE BETWEEN AN UPPER

LIMIT AND A LOWER LIMIT; FOR A SET POINT, THE TWO LIMITS

ARE SET TO THE SAME VALUE.

THE CONNECTION BETWEEN THE REAL TIME OPTIMIZATION AND

THE CONTROLLER IS MADE WHEN THE OPTIMIZER SPECIFIES ITS

ACTIVE CONSTRAINTS AS SET POINTS FOR THE CONTROLLER.

THE LOCAL OPTIMIZER IN THE CONTROLLER IS TURNED OFF WHEN

THE REAL TIME OPTIMIZER WRITES THE SET POINTS DOWN TO THE

CONTROLLER.

WITH MANY MORE CONSTRAINT VARIABLES THAN MANIPULATED

VARIABLES, IT IS HIGHLY DESIRABLE FOR THE CONTROLLER TO

IGNORE VARIABLES THAT ARE NOT CLOSE TO THEIR CONSTRAINTS.

EXPERIENCE HAS SHOWN THAT AN OPERATOR USING A REAL

TIME OPTIMIZATION WILL REALIZE SIGNIFICANTLY LESS THAN 50

PERCENT OF THE POTENTIAL VALUE OF THE OPTIMIZATION.


Real time optimization and constrained multivariable control

IDENTIFICATION OF THE PROCESS DYNAMICS IS THE MAJOR TASK

FACING THE CONTROL ENGINEER.

TESTING THE PROCESS REQUIRES AN ENGINEER OR A PROCESS

CONTROL TECHNICIAN BE PRESENT FOR THE TEST TO WATCH FOR

UNMEASURED DISTURBANCES, THAT CAN BE OBSERVED, BUT NOT

QUANTIFIED.

THE TEST MAY RUN DAY AND NIGHT FOR SEVERAL WEEKS.

PRELIMINARY ANALYSIS OF THE DATA USUALLY OCCURS DURING

THE TEST PERIOD.

THERE ARE NO MAGIC BULLETS TO SHORTEN TESTING IF THE

CORRECT MODEL FORM AND STEADY STATE GAIN ARE REQUIRED.

CONVENTIONAL WISDOM IN SOME QUARTERS INDICATES PRBS

TESTING AND/OR PARAMETRIC MODELS WILL REDUCE TEST TIME.

UNMEASURED DISTURBANCES, THAT ARE NOT KNOWN, ARE THE

PRIMARY CAUSE OF MODEL ERROR.

COMMERCIAL SOFTWARE FOR THE IDENTIFICATION OF LARGE

PROBLEMS IS LINEAR, WHICH REQUIRES TRANSFORMATIONS BE

FOUND TO LINEARIZE THE NON-LINEAR ELEMENTS.


Real time optimization and constrained multivariable control

AUTOMATIC TESTING WITH THE COMPUTER MOVING THE

MANIPULATED VARIABLES MAKES THE TEST PERIOD EASIER IF THE

PROCESS IS NOT BEING OPERATED NEAR CONSTRAINTS.

COMMERCIAL MULTIVARIABLE SOFTWARE EMBEDS THE PID

CONTROLLER TUNING AND CONFIGURATION INTO THE DYNAMIC

MODELS OF THE PROCESS.

IF A CONFIGURATION CHANGE OR RETUNING OF PID CONTROLLERS

OCCUR, A RETEST OF THE PROCESS IS REQUIRED.

A PRETEST OF THE PROCESS IS USUALLY DONE TO MINIMIZE THE

PROBLEM OF CONTROLLER TUNING.

ALSO A GOOD UNDERSTANDING OF THE PROCESS ECONOMICS MAY

LEAD TO A CONFIGURATION CHANGE PRIOR TO THE TESTING, I.E.

PLACING ONE OR MORE PID CONTROLLERS ON MANUAL.

IT WOULD BE HIGHLY DESIRABLE TO HAVE SOFTWARE AVAILABLE

THAT WOULD PERMIT THE PROCESS CONTROL SYSTEM TO BE

RECONFIGURED AND RETUNED WITH OUT HAVING TO RETEST OR

TO BE ABLE TO TEST THE SYSTEM IN ONE STATE, KNOWING THE

CONTROL CONFIGURATION WOULD CHANGE FOR THE

MULTIVARIABLE CONTROLLER.


Real time optimization and constrained multivariable control

DESIRABLE FEATURES FOR IDENTIFICATION SOFTWARE ARE:

BETTER TOOLS FOR IDENTIFYING WHEN A PARTICULAR INPUT /

OUTPUT RELATION IS ADEQUATE FOR CONTROL AT CONSTRAINTS.

CONTINUOUS ANALYSIS OF THE PROCESS MODELS, SO MINIMUM

MOVES IN THE MANIPULATED VARIABLES ARE NOT MADE THAT

SHORTEN THE TEST.

THAT CONTINUOUSLY MONITORS PROCESS CONSTRAINTS AND

USES A PRELIMINARY MODEL TO AVOID EXCEEDING THE CONSTRAINTS.

TOOLS THAT IDENTIFY NON-LINEARITIES IN THE REGION OF

OPERATION AND BUILDS TRANSFORMATIONS THAT LINEARIZE THE

VARIABLES.

IN THE MORE DISTANT FUTURE, COMPREHENSIVE DYNAMIC

MODELS BASED ON FIRST PRINCIPLE ENGINEERING WILL BE

BUILT AND ADAPTED ON LINE IN THE SAME MANNER AS STEADY

STATE REAL TIME OPTIMIZATION MODELS ARE TODAY


Real time optimization and constrained multivariable control

OPERATOR TRAINING IS A SIGNIFICANT PROBLEM FOR PLANTS

THAT HAVE BEEN OPTIMIZED AND CONTROLLED FOR YEARS.

NEW OPERATORS DO NOT HAVE OPPORTUNITY TO RUN THE UNIT

AND THE OLDER OPERATORS LOSE THE FEEL FOR THE PROCESS.

TAKING THE PROCESS AWAY FROM THE COMPUTER IS AN

EXPENSIVE SOLUTION WHICH MANAGEMENT WILL RESIST

.

GOOD QUALITY DYNAMIC SIMULATORS ARE VERY EXPENSIVE AND

MOST DO NOT REPRESENT THE DYNAMICS OF THE PLANT WELL

ENOUGH FOR THE EXPERIENCED OPERATOR TO FEEL HE CAN FINE

TUNE HIS SKILLS BY USING THE SIMULATOR.


Real time optimization and constrained multivariable control

DYNAMIC SIMULATORS HAVE PROVEN USEFUL FOR TRAINING NEW

OPERATORS THAT DO NOT KNOW WHICH DIRECTION THE

DEPENDENT VARIABLES IN THE SYSTEM WILL MOVE WHEN A

SETPOINT OR A VALVE ARE CHANGED.

FURTHER, SIMULATORS HAVE BEEN VERY USEFUL WHEN A NEW

PLANT IS BEING COMMISSIONED AND NONE OF THE OPERATORS

ARE FAMILIAR WITH THE PROCESS.

MY EXPERIENCE INDICATES THAT MOST PEOPLE WITH SIMULATORS

STOP USING THEM AFTER A TIME.

THE TWO REASONS USUALLY GIVEN ARE; THEY DON’T MATCH THE

PLANT OR THE UNIT HAS CHANGED AND THE SIMULATOR HASN’T

BEEN UPDATED.

AN IDEAL SIMULATOR FOR OPERATOR TRAINING IS THE DYNAMIC

MODEL USED BY THE MULTIVARIABLE CONTROLLER.

THE INTEGRITY OF THE DYNAMIC MODEL IN THE CONTROLLER

WHICH IS SUFFICIENT TO CONTROL THE PROCESS AT MULTIPLE

CONSTRAINTS, SHOULD SATISFY THE MOST DEMANDING OPERATOR.


Real time optimization and constrained multivariable control

THE CURRENT GENERATION OF IDENTIFICATION SOFTWARE

EMBEDS THE PID CONTROLLER CONFIGURATION IN THE DYNAMIC

MODEL, WHICH PREVENTS THE MODEL FROM BEING USED

EFFECTIVELY AS A TRAINING SIMULATOR.

TO BE AN EFFECTIVE TRAINER ANY PERMUTATION OF THE PID

CONTROLLERS IN AUTOMATIC OR MANUAL SHOULD BE POSSIBLE.

SAFETY OF THE PROCESS UNIT AND THE OPERATORS WILL

PROBABLY BECOME AN ISSUE WITH FEDERAL REGULATORY

AGENCIES IN THE NEAR FUTURE, WHEN THEY REALIZE THE SKILLS

THAT ARE BEING LOST WHEN A PROCESS HAS BEEN OPTIMIZED

AND CONTROLLED FOR AN EXTENDED TIME.

THE FEDERAL AGENCIES WILL MANDATE PROFICIENCY TESTS FOR

OPERATORS THAT INCLUDE HANDS ON DEMONSTRATION OF THEIR

SKILLS.


Real time optimization and constrained multivariable control

THE MAINTENANCE PROBLEMS FOR REAL TIME OPTIMIZATION

SYSTEMS ARE GREATER THAN THOSE FOR MULTIVARIABLE

CONTROL.

MANY TIMES A GOOD TECHNICIAN CAN MAINTAIN A CONTROL

SYSTEM, SINCE THE PROBLEMS THAT OCCUR ARE USUALLY

ASSOCIATED WITH BAD INPUTS OR MECHANICAL PROBLEMS THAT

GET FIXED BY CRAFTSMEN IN THE PLANT.

THE ENGINEER MAINTAINING THE REAL TIME OPTIMIZATION

SYSTEM MUST KNOW THE MODEL EQUATIONS AS WELL AS THE

PEOPLE WHO DEVELOPED THE ORIGINAL MODELS, HE MUST KNOW

HOW THE OPTIMIZATION SOFTWARE FITS INTO THE COMPUTER

OPERATING SYSTEM AND HOW THE OPTIMIZATION SOLUTION IS

PUT INTO THE CONTROL SYSTEM.

TO BUILD AND MAINTAIN REAL TIME OPTIMIZATION SYSTEMS

REQUIRES THE BEST ENGINEERS IN A COMPANY, I.E. THE TOP 20

PERCENT FROM A TECHNICAL POINT OF VIEW.

MANY TIMES, OPERATIONS MANAGEMENT DOES NOT UNDERSTAND

THE VALUE OF THE OPTIMIZATION SYSTEM AND WILL NOT GIVE IT

THE REQUIRED PRIORITY


Real time optimization and constrained multivariable control

AS INDICATED ABOVE THE ENGINEERS SUPPORTING THE

OPTIMIZATION SYSTEM MUST BE AN OUTSTANDING PROCESS

ENGINEER, CONTROL ENGINEER, AND COMPUTER ANALYST.

A PERSON WITH THESE SKILLS IS USUALLY AN OUTSTANDING

MANAGEMENT PROSPECT.

MOST ENGINEERS WITH A HIGH POTENTIAL ARE NOT WILLING TO

SACRIFICE THE MONEY AND PRESTIGE ASSOCIATED WITH MOVING

UP THE CORPORATE LADDER.

FURTHER, MANAGEMENT MAY NOT PERMIT THE ENGINEER TO

STAY IN THE MAINTENANCE JOB.

IT HAS BECOME APPRARENT TO ME THAT MOST LARGE CORPORATION

ARE NOT ORGANIZED TO MAINTAIN LARGE SCALE REAL TIME

OPTIMIZATION SYSTEMS.

RE-ENGINEERING OF THE TECHNICAL WORK FORCE HAVE MOST

PLANTS OPERATING WITH SKELETON CREWS OF TECHNICAL PEOPLE.


Real time optimization and constrained multivariable control

  • REAL TIME OPTIMIZATION AND CONSTRAINED MULTIVARIABLE

  • CONTROL WILL ADD 5 TO 10 PERCENT TO THE VALUE ADDED BY THE

  • PLANT.

  • THE PLANT MUST BE OPERATED AT 70 TO 80 PERCENT OF DESIGN

  • CAPACITY TO PAY FOR THE COST OF CAPITAL, THE 5 TO 10 PERCENT

  • FROM REAL TIME OPTIMIZATION AND CONTROL IS RELATIVE

  • TO THE 20 TO 30 PERCENT WHEN LOOKING FOR OPPORTUNITIES TO

  • IMPROVE PROFITABILITY.

  • HOWEVER,WITH LIMITED MANPOWER, THE DECISION TO USE THE

  • TECHNICAL MANPOWER TO KEEP THE PLANT OPERATING IS THE RIGHT

  • DECISION, SINCE CONTINUOUS OPERATION AT NOMINAL CAPACITY

  • BRINGS IN 80 TO 90 PERCENT.

  • THE SENIOR MANAGEMENT OF A CORPORATION MUST BE WILLING TO

  • ADD TECHNICAL PEOPLE AND CHANGE THE CULTURE IN THEIR

  • CORPORATION, IF THE FULL BENEFITS OF REAL TIME OPTIMIZATION

  • AND CONTROL ARE TO BE REALIZED.


Real time optimization and constrained multivariable control

A SECOND OPTION FOR MANAGEMENT TO REALIZE THE BENEFITS OF REAL TIME OPTIMIZATION IS TO CONTRACT THE MAINTENANCE TO ENGINEERING COMPANIES WHO SPECIALIZE IN SIMULATION AND MODELING.

THE ADVANTAGE OF SUCH AN ARRANGEMENT IS THE SPECIALIST IN THE ENGINEERING COMPANIES CAN BE REWARDED FINANCIALLY IN A WAY THAT MAY BE IMPOSSIBLE IN AN OPERATING COMPANY THAT HAS STRUCTURED GUIDE LINES FOR SALARY ADMININSTRATION.

THE HIGHER QUALITY SPECIALIST IN THE ENGINEERING COMPANY CAN BE TIME SHARED OVER SERVERAL PROJECTS WITH THE MONITORING OF THE REAL TIME OPTIMIZATION BEING DONE OVER THE INTERNET.

THE JUNIOR SPECIALIST FROM THE ENGINEERING COMPANY SHOULD BE SITE RESIDENT. A PLAN SHOULD NEVER BE MADE THAT LEAVES

A REAL TIME OPTIMIZATION SYSTEM UNATTENDED.

.


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