1. CHE 185 – PROCESS CONTROL AND DYNAMICS PID CONTROL APPLIED TO MIMO PROCESSES

2. PID FOR MULTIPLE INPUT/MULTIPLE OUTPUT (MIMO) SYTEMS COMPARISON BETWEEN CENTRALIZED AND DECENTRALIZED CONTROL DECENTRALIZED (MULTILOOP) CONTROL HAS SEVERAL SINGLE LOOP CONTROLS IN PARALLEL FOR A SINGLE PROCESS. REACTION SYSTEM EXAMPLE:

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

4. PID FOR MULTIPLE INPUT/MULTIPLE OUTPUT (MIMO) SYTEMS THERE ARE SPECIFIC ADVANTAGES TO WORKING WITH SINGLE INPUT SINGLE OUTPUT (SISO) LOOPS BECAUSE THEY CAN BE TUNED AND OPTIMIZED INDEPENDENTLY THE INTERACTIONS (COUPLING) CAN TAKE PLACE THROUGH THE PROCESS –FOR THE EXAMPLE SYSTEM, THE COMPOSITION MIGHT BE AFFECTED BY TEMPERATURE CONTROL BECAUSE THE TEMPERATURE AFFECTS THE REACTION RATE –SIMILARLY, TEMPERATURE MIGHT AFFECT THE MEDIA DENSITY, WHICH COULD HAVE SOME IMPACT ON THE RESIDENCE TIME IN THE UNIT AND THE LEVEL CONTROL

5. PID FOR MULTIPLE INPUT/MULTIPLE OUTPUT (MIMO) SYTEMS THERE ARE SPECIFIC ADVANTAGES TO WORKING WITH SINGLE INPUT SINGLE OUTPUT (SISO) LOOPS BECAUSE THEY CAN BE TUNED AND OPTIMIZED INDEPENDENTLY THE INTERACTIONS (COUPLING) CAN TAKE PLACE THROUGH THE PROCESS –FOR THE EXAMPLE SYSTEM, THE COMPOSITION MIGHT BE AFFECTED BY TEMPERATURE CONTROL BECAUSE THE TEMPERATURE AFFECTS THE REACTION RATE –SIMILARLY, TEMPERATURE MIGHT AFFECT THE MEDIA DENSITY, WHICH COULD HAVE SOME IMPACT ON THE RESIDENCE TIME IN THE UNIT AND THE LEVEL CONTROL

6. PID FOR MULTIPLE INPUT/MULTIPLE OUTPUT (MIMO) SYTEMS MIMO REFERS TO THE GENERAL CONFIGURATION OF THE CONTROL SYSTEM WITH MULTIPLE INPUTS AND OUTPUTS CONSIDER THE SYSTEM SHOWN AS FIGURE 15.1.1

7. EXAMPLE OF A 2×2 MIMO PROCESS TWO INPUTS: SETPOINTS FOR FLOW CONTROLLER ON STEAM AND REFLUX. TWO OUTPUTS: COMPOSITION OF PRODUCTS B AND D

8. PID FOR MULTIPLE INPUT/MULTIPLE OUTPUT (MIMO) SYTEMS THE STEADY STATE TRANSFER FUNCTION FOR THIS COMBINED SYSTEM CAN BE EXPRESS AS: STEADY STATE COUPLING –THE RELATIVE GAIN ARRAY (RGA) IS A MATRIX OF THE GAINS AND PROVIDES A MEASURE OF THE STEADY- STATE EFFECTS OF COUPLING –FOR THE 2X2 SYSTEM ABOVE:

9. PID FOR MULTIPLE INPUT/MULTIPLE OUTPUT (MIMO) SYTEMS THE Λ 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

10. PID FOR MULTIPLE INPUT/MULTIPLE OUTPUT (MIMO) SYTEMS EVALUATION OF EACH OF THE TERMS IN THE RGA HELPS DETERMINE THE DEGREE OF COUPLING AS 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

11. PID FOR MULTIPLE INPUT/MULTIPLE OUTPUT (MIMO) SYTEMS

12. THE 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

13. PID FOR MULTIPLE INPUT/MULTIPLE OUTPUT (MIMO) SYTEMS OTHER RGA CHARACTERISTICS VALUES ARE SCALE INDEPENDENT - SO WILL BE CORRECT AS LONG AS UNITS ARE CONSISTENT FOR ALL TERMS AS 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 CALCULATION

14. PID FOR MULTIPLE INPUT/MULTIPLE OUTPUT (MIMO) SYTEMS DYNAMIC FACTORS IN CONFIGURATION SELECTION THE RGA VALUES DISCUSSED ABOVE ARE FOR SYSTEMS WITH THE SAME DYNAMIC BEHAVIOR WHEN ONE OF THE LOOPS HAS FASTER OR SLOWER DYNAMICS THAN THE OTHERS, THE SELECTION OF PAIRINGS CAN BE CHANGED

15. PID FOR MULTIPLE INPUT/MULTIPLE OUTPUT (MIMO) SYTEMS A FAST LOOP COUPLED WITH A SLOW LOOP CAN BE TUNED AS THOUGH IT IS A SINGLE LOOP CONTROLLER WITHOUT INTERACTION FOR A SLOW LOOP, THE TUNING CAN BE ADJUSTED BY MULTIPLYING THE SINGLE LOOP CONTROLLER GAIN BY THE APPROPRIATE λ TERM IN THE RGA - THUS PROVIDING A BIAS FOR THE GAIN

16. PID FOR MULTIPLE INPUT/MULTIPLE OUTPUT (MIMO) SYTEMS WHEN LOOPS HAVE SIMILAR DYNAMICS, BOTH LOOPS NEED TO BE DETUNED FROM THEIR SINGLE LOOP SETTINGS MANUAL TUNING IS RECOMMENDED WORKSHOP #14 IN THE CONTROL STATION PACKAGE IS AN EXAMPLE OF THIS SITUATION.

17. PID FOR MULTIPLE INPUT/MULTIPLE OUTPUT (MIMO) SYTEMS SENSITIVITY TO DISTURBANCES PROCESS VARIABLES HAVE DIFFERENT RESPONSES TO VARIOUS TYPES OF DISTURBANCES –EXAMPLE 15.3 IN BOOK LOOKS AT DISTILLATION COLUMN DYNAMICS FOR VARIOUS CONFIGURATIONS –THE RESPONSES MAY NOT BE THE SAME FOR ALL TYPES OF DISTURBANCES, COMPOSITION VS. FLOW FOR DISTILLATION COLUMNS

18. PID FOR MULTIPLE INPUT/MULTIPLE OUTPUT (MIMO) SYTEMS DECOUPLERS DECOUPLING IS APPLIED WHEN THERE ARE TWO SIGNIFICANT OUTPUTS THAT HAVE EQUAL IMPORTANCE AND WHICH ARE NEGATIVELY AFFECTED BY COUPLING METHODS TO DECOUPLE THE VARIABLES INCLUDE –ALTERING THE MANIPULATED VARIABLES –ALTERING THE CONTROLLED VARIABLES –ALTERING THE FEEDBACK CONTROL CALCULATION

19. PID FOR MULTIPLE INPUT/MULTIPLE OUTPUT (MIMO) SYTEMS DECOUPLERS A DECOUPLER ACTS LIKE A FEED FORWARD CONTROL AND CAN BE INSERTED IN THE LOOP TO CHANGE THE FEEDBACK SIGNAL