REAL TIME OPTIMIZATION AND CONSTRAINED MULTIVARIABLE CONTROL

1
REAL TIME OPTIMIZATION AND CONSTRAINED
MULTIVARIABLE CONTROL

• CHARLES R.CUTLER, Ph.D.

PRESENTED AT THE NORDIC PROCESS CONTROL WORKSHOP
ON AUGUST 23, 2001
2
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.
3

• 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.

4
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.

5
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

6

• 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

7

• 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.

8

• 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.

9

• 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.

10

• 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

11

• 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

12

• 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

13

• 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.

14

• 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
  DONT MATCH THE
• PLANT OR THE UNIT HAS CHANGED AND THE
  SIMULATOR HASNT
• BEEN UPDATED.
• AN IDEAL SIMULATOR FOR OPERATOR TRAINING
  IS THE DYNAMIC
• MODEL USED BY THE MULTIVARIABLE
  CONTROLLER.

15
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.
16

• 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

17

• 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

18

• 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.

19
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. .