CHE 185 PROCESS CONTROL AND DYNAMICS

CHE 185 PROCESS CONTROL AND DYNAMICSPID Control Applied to MIMO ProcessesPID FOR MULTIPLE INPUT/MULTIPLE OUTPUT (MIMO) SYTEMSCOMPARISON BETWEEN CENTRALIZED AND DECENTRALIZED CONTROLDECENTRALIZED (MULTILOOP) CONTROL HAS SEVERAL SINGLE LOOP CONTROLS IN PARALLEL FOR A SINGLE PROCESS. REACTION SYSTEM EXAMPLE:

PID FOR MULTIPLE INPUT/MULTIPLE OUTPUT (MIMO) SYTEMSTHE ALTERNATE TO THIS APPROACH IS CENTRALIZED (COORDINATED) CONTROL AND FOR THE SAME SYSTEM IT WOULD LOOK LIKE:

PID FOR MULTIPLE INPUT/MULTIPLE OUTPUT (MIMO) SYTEMSTHERE ARE SPECIFIC ADVANTAGES TO WORKING WITH SINGLE INPUT SINGLE OUTPUT (SISO) LOOPS BECAUSE THEY CAN BE TUNED AND OPTIMIZED INDEPENDENTLYTHE INTERACTIONS (COUPLING) CAN TAKE PLACE THROUGH THE PROCESSFOR THE example SYSTEM , THE COMPOSITION MIGHT BE AFFECTED BY TEMPERATURE CONTROL BECAUSE THE TEMPERATURE AFFECTS THE REACTION RATESIMILARLY, TEMPERATURE MIGHT AFFECT THE MEDIA DENSITY, WHICH COULD HAVE SOME IMPACT ON THE RESIDENCE TIME IN THE UNIT AND THE LEVEL CONTROLPID FOR MULTIPLE INPUT/MULTIPLE OUTPUT (MIMO) SYTEMSTHERE ARE SPECIFIC ADVANTAGES TO WORKING WITH SINGLE INPUT SINGLE OUTPUT (SISO) LOOPS BECAUSE THEY CAN BE TUNED AND OPTIMIZED INDEPENDENTLYTHE INTERACTIONS (COUPLING) CAN TAKE PLACE THROUGH THE PROCESSFOR THE example SYSTEM , THE COMPOSITION MIGHT BE AFFECTED BY TEMPERATURE CONTROL BECAUSE THE TEMPERATURE AFFECTS THE REACTION RATESIMILARLY, TEMPERATURE MIGHT AFFECT THE MEDIA DENSITY, WHICH COULD HAVE SOME IMPACT ON THE RESIDENCE TIME IN THE UNIT AND THE LEVEL CONTROLPID FOR MULTIPLE INPUT/MULTIPLE OUTPUT (MIMO) SYTEMSMIMO REFERS TO THE GENERAL CONFIGURATION OF THE CONTROL SYSTEM WITH MULTIPLE INPUTS AND OUTPUTSCONSIDER THE SYSTEM SHOWN AS FIGURE 15.1.1

Example of a 22 MIMO ProcessTwo inputs: Setpoints for flow controller on steam and reflux.Two outputs: Composition of products B and D

PID FOR MULTIPLE INPUT/MULTIPLE OUTPUT (MIMO) SYTEMSTHE STEADY STATE TRANSFER FUNCTION FOR THIS COMBINED SYSTEM CAN BE EXPRESS AS:

STEADY STATE COUPLINGTHE RELATIVE GAIN ARRAY (RGA) IS A MATRIX OF THE GAINS AND PROVIDES A MEASURE OF THE STEADY-STATE EFFECTS OF COUPLINGFOR THE 2x2 SYSTEM ABOVE:

PID FOR MULTIPLE INPUT/MULTIPLE OUTPUT (MIMO) SYTEMSTHE TERMS HAVE THE FOLLOWING VALUES AS PARTIAL FUNCTIONS

THE relative gain array (RGA) REPRESENTS THE PROCESS GAIN WITHOUT COUPLING RELATIVE TO THE PROCESS GAIN WITH COUPLING

PID FOR MULTIPLE INPUT/MULTIPLE OUTPUT (MIMO) SYTEMSEVALUATION OF EACH OF THE TERMS IN THE RGA HELPS DETERMINE THE DEGREE OF COUPLINGAS THE VALUE FOR THE TERM 0, THERE IS LESS INTERACTION, COUPLING INCREASES AS THE VALUE INCREASES.EXAMPLES OF INTERACTION are shown in the table on the next slide

PID FOR MULTIPLE INPUT/MULTIPLE OUTPUT (MIMO) SYTEMS

PID FOR MULTIPLE INPUT/MULTIPLE OUTPUT (MIMO) SYTEMSTHE STEADY STATE GAIN MATRIX FOR THE 2x2 SYSTEM IS:

THE TWO CONTROLLERS MUST BE TUNED SIMULTANEOUSLY TO ACHIEVE STABILITY AND PERFORMANCE.THE VALUES OF THE MANIPULATED VARIABLES THAT MEET CONTROL VARIABLE TARGETS MUST BE DETERMINED SIMULTANEOUSLY.AS THE INTERACTION INCREASES, THE SYSTEM BECOMES MORE MULTIVARIANT AND LESS SINGLE VARIABLE

PID FOR MULTIPLE INPUT/MULTIPLE OUTPUT (MIMO) SYTEMSOTHER RGA CHARACTERISTICSVALUES ARE SCALE INDEPENDENT - SO WILL BE CORRECT AS LONG AS UNITS ARE CONSISTENT FOR ALL TERMSAS SHOWN IN EQUATION 13.2, THE VALUES CAN BE DETERMINED FROM THE OPEN LOOP DATA. oTHER TERMS CAN BE EVALUATED BY TAKING ADVANTAGE OF THE FACT THAT THE RGA ROWS AND COLUMNS MUST SUM TO ZERO. RELATIVE GAIN TERMS CAN BE VERY SENSITIVE TO ERRORS IN THE GAIN CALCULATIONPID FOR MULTIPLE INPUT/MULTIPLE OUTPUT (MIMO) SYTEMSDYNAMIC FACTORS IN CONFIGURATION SELECTIONTHE RGA VALUES DISCUSSED ABOVE ARE FOR SYSTEMS WITH THE SAME DYNAMIC BEHAVIORWHEN ONE OF THE LOOPS HAS FASTER OR SLOWER DYNAMICS THAN THE OTHERS, THE SELECTION OF PAIRINGS CAN BE CHANGEDPID FOR MULTIPLE INPUT/MULTIPLE OUTPUT (MIMO) SYTEMSA FAST LOOP COUPLED WITH A SLOW LOOP CAN BE TUNED AS THOUGH IT IS A SINGLE LOOP CONTROLLER WITHOUT INTERACTIONFOR A SLOW LOOP, THE TUNING CAN BE ADJUSTED BY MULTIPLYING THE SINGLE LOOP CONTROLLER GAIN BY THE APPROPRIATE TERM IN THE RGA - THUS PROVIDING A BIAS FOR THE GAINPID FOR MULTIPLE INPUT/MULTIPLE OUTPUT (MIMO) SYTEMSWHEN LOOPS HAVE SIMILAR DYNAMICS, BOTH LOOPS NEED TO BE DETUNED FROM THEIR SINGLE LOOP SETTINGSMANUAL TUNING IS RECOMMENDEDWORKSHOP #14 IN THE CONTROL STATION PACKAGE IS AN EXAMPLE OF THIS SITUATION.PID FOR MULTIPLE INPUT/MULTIPLE OUTPUT (MIMO) SYTEMSSENSITIVITY TO DISTURBANCESPROCESS VARIABLES HAVE DIFFERENT RESPONSES TO VARIOUS TYPES OF DISTURBANCESEXAMPLE 15.3 IN BOOK LOOKS AT DISTILLATION COLUMN DYNAMICS FOR VARIOUS CONFIGURATIONSTHE RESPONSES MAY NOT BE THE SAME FOR ALL TYPES OF DISTURBANCES, COMPOSITION VS. FLOW FOR DISTILLATION COLUMNSPID FOR MULTIPLE INPUT/MULTIPLE OUTPUT (MIMO) SYTEMSDECOUPLERSDECOUPLING IS APPLIED WHEN THERE ARE TWO SIGNIFICANT OUTPUTS THAT HAVE EQUAL IMPORTANCE AND WHICH ARE NEGATIVELY AFFECTED BY COUPLINGMETHODS TO DECOUPLE THE VARIABLES INCLUDEALTERING THE MANIPULATED VARIABLESALTERING THE CONTROLLED VARIABLESALTERING THE FEEDBACK CONTROL CALCULATIONPID FOR MULTIPLE INPUT/MULTIPLE OUTPUT (MIMO) SYTEMSDECOUPLERSA DECOUPLER ACTS LIKE A FEED FORWARD CONTROL AND CAN BE INSERTED IN THE LOOP TO CHANGE THE FEEDBACK SIGNAL