CHE 185 – PROCESS CONTROL AND DYNAMICS

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