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 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.

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.

TIME OPTIMIZATION IN THE PROCESS INDUSTRIES. 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 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

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.

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.

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.

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.

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.

MANIPULATED VARIABLES MAKES THE TEST PERIOD EASIER IF THE 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.

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

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.

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.

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.

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

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 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.

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. .