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

CHE 185 – PROCESS CONTROL AND DYNAMICS

PID CONTROL APPLIED TO MIMO PROCESSES

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:

LC

AC

TC


• THE ALTERNATE TO THIS APPROACH IS CENTRALIZED (COORDINATED) CONTROL AND FOR THE SAME SYSTEM IT WOULD LOOK LIKE:

CONTROLLERA

T L


• 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


• MIMO REFERS TO THE GENERAL CONFIGURATION OF THE CONTROL SYSTEM WITH MULTIPLE INPUTS AND OUTPUTS

• CONSIDER THE SYSTEM SHOWN AS FIGURE 15.1.1

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


• 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:

Y s

Y s

G s G s

G s G s

C s

C s1

2

11 12

21 22

1

2

( )

( )

( ) ( )

( ) ( )

( )

( )

RGA

11 12

21 22


• 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

11

1

1

1

1

12

1

2

1

2

21

2

1

2

1

22

2

2

2

2

2

2

1

2

2

1

1

1

Y

C

YC

Y

C

YC

Y

C

YC

Y

C

YC

C

Y

C

Y

C

Y

C

Y


• 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


• 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

KK K

K K

11 12

21 22


• 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


• 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


• 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


• 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.


• 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


• 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


• DECOUPLERS• A DECOUPLER ACTS LIKE A FEED FORWARD

CONTROL AND CAN BE INSERTED IN THE LOOP TO CHANGE THE FEEDBACK SIGNAL

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

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