CHE 185 – PROCESS CONTROL AND

DYNAMICSTUNING FOR PID CONTROL

LOOPS

CONTROLLER TUNING

• INVOLVES SELECTION OF THE PROPER VALUES OF Kc, τI, AND τD.

• AFFECTS CONTROL PERFORMANCE.• AFFECTS CONTROLLER RELIABILITY• IN MANY CASES CONTROLLER TUNING IS

A COMPROMISE BETWEEN PERFORMANCE AND RELIABILITY.

AVAILABLE TUNING CRITERIA

• SPECIFIC CRITERIA– DECAY RATIO– MINIMIZE SETTLING TIME

• GENERAL CRITERIA– MINIMIZE VARIABILITY– REMAIN STABLE FOR THE WORST

DISTURBANCE UPSET (I.E., RELIABILITY)– AVOID EXCESSIVE VARIATION IN THE

MANIPULATED VARIABLE

CONTROL PERFORMANCE ASSESSMENT

• PERFORMANCE STATISTICS (IAE, ISE, ETC.) WHICH CAN BE USED IN SIMULATION STUDIES.

• STANDARD DEVIATION FROM SETPOINT WHICH IS A MEASURE OF THE VARIABILITY IN THE CONTROLLED VARIABLE.

• SPC CHARTS WHICH PLOT PRODUCT COMPOSITION ANALYSIS ALONG WITH ITS UPPER AND LOWER LIMITS.

EXAMPLE OF AN SPC CHART

• REFERENCE FIGURE 9.2.3

TUNING CRITERIA ERROR

• CONTROLLED VARIABLE PERFORMANCE– AVOID EXCESSIVE VARIATION– MINIMIZE THE INTEGRAL ABSOLUTE ERROR:

– MINIMIZE THE INTEGRAL TIME ERROR:

IAE y t y t d tsp s

( ) ( )0

ITAE t y t y t d tsp s

( ) ( )0

TUNING CRITERIA ERROR• MANIPULATED VARIABLE

– AVOID EXCESSIVE SPIKES IN RESPONSE TO SYSTEM DISTURBANCES OR SETPOINT CHANGES

– MAINTAIN PROCESS STABILITY WITH LARGE CHANGES• MINIMAL INTEGRAL SQUARE ERROR:

• AND INTEGRAL TIME SQUARE ERROR:

– OBTAIN ZERO STEADY-STATE OFFSET– MINIMAL RINGING (EXCESSIVE CYCLING)

ISE y t y t d tsp s

( ) ( )2

0

IT SE t y t y t d tsp s

( ) ( )2

0

SUMMARY OF GOALS FOR TUNING

• DECAY RATIO APPROACHING QUARTER AMPLITUDE DAMPING, QAD

DECAY RATIO FOR NON-SYMMETRIC OSCILLATIONS

• REFERENCE FIGURE 9.2.1 (c)

CLASSICAL TUNING METHODS

• EXAMPLES: COHEN AND COON METHOD, ZIEGLER-NICHOLS TUNING, CIANIONE AND MARLIN TUNING, AND MANY OTHERS.

• USUALLY BASED ON HAVING A MODEL OF THE PROCESS (E.G., A FOPDT MODEL) AND IN MOST CASES IN THE TIME THAT IT TAKES TO DEVELOP THE MODEL, THE CONTROLLER COULD HAVE BEEN TUNED SEVERAL TIMES OVER USING OTHER TECHNIQUES.

• ALSO, THEY ARE BASED ON A PRESET TUNING CRITERION (E.G., QAD)

CLASSICAL TUNING METHODS

• COHEN AND COON METHOD• TARGET THE VALUES SHOWN IN TABLE

9.2• BASED ON MINIMIZING ISE, QAD AND NO

OFFSET

CLASSICAL TUNING METHODS

• CIANCONE AND MARLIN• DIMENSIONLESS CORRELATIONS BASED

ON A TERM CALLED FRACTIONAL DEADTIME:

• RESULTING PARAMETERS ARE PLOTTED IN FIGURE 9.3.2

CLASSICAL TUNING METHODS

• CIANCONE AND MARLIN• THE SEQUENCE OF CALCULATION OF

TUNING CONSTANTS:– CERTIFY THAT PERFORMANCE GOALS AND

ASSUMPTIONS ARE APPROPRIATE– DETERMINE THE DYNAMIC MODEL USING

AND EMPIRICAL METHOD TO OBTAIN Kp, θp AND τp

– CALCULATE THE FRACTION DEADTIME– USE EITHER THE DISTURBANCE (FIGURES

9.3.2 a - c) OR SETPOINT (FIGURES 9.3.2 d - f) FOR SYSTEM PERTURBATIONS.

CLASSICAL TUNING METHODS

• CIANCONE AND MARLIN• THE SEQUENCE OF CALCULATION OF

TUNING CONSTANTS:– DETERMINE THE DIMENSIONLESS TUNING

PARAMETERS FROM THE GRAPHS: GAIN, INTEGRAL TIME AND DERIVATIVE TIME

– CALCULATE THE ACTUAL TUNING VALUES FROM THE DIMENSIONLESS VALUES: (E.G.):

KK K

Kcp c

p

CLASSICAL TUNING METHODS

• STABILTY-BASED METHOD - ZIEGLER-NICHOLS

• USES THE ACTUAL SYSTEM TO MEASURE RESPONSES TO PERTURBATIONS

• AVOIDS THE LIMITS IN MODELING PROCESSES

• TARGET VALUES ARE IN TABLE 9.3

CLASSICAL TUNING METHODS

• BASED ON A QAD TUNED RESPONSE• BASED ON PROPORTIONAL-ONLY

VALUES• ULTIMATE VALUES• GAIN:

• PERIOD

KG j G j G ju

p C a C s C

1

( ) ( ) ( )

Puc

2

CONTROLLER TUNING BY POLE PLACEMENT (DISCUSSED

PREVIOUSLY)• BASED ON MODEL OF THE PROCESS• SELECT THE CLOSED-LOOP DYNAMIC

RESPONSE AND CALCULATE THE CORRESPONDING TUNING PARAMETERS.

• APPLICATION OF POLE PLACEMENT SHOWS THAT THE CLOSED-LOOP DAMPING FACTOR AND TIME CONSTANT ARE NOT INDEPENDENT.

• THEREFORE, THE DECAY RATIO IS A REASONABLE TUNING CRITERION.

• NOTE EQN 9.4.5 SHOULD BE

CONTROLLER DESIGN BY POLE PLACEMENT

• A GENERALIZED CONTROLLER (I.E., NOT PID) CAN BE DERIVED BY USING POLE PLACEMENT.

• GENERALIZED CONTROLLERS ARE NOT GENERALLY USED IN INDUSTRY BECAUSE– PROCESS MODELS ARE NOT USUALLY

AVAILABLE– PID CONTROL IS A STANDARD FUNCTION

BUILT INTO DCSs.

INTERNAL MODEL CONTROL (IMC)-BASED TUNING

• A PROCESS MODEL IS REQUIRED (TABLE 9.4 CONTAIN THE PID SETTINGS FOR SEVERAL TYPES OF MODELS BASED ON IMC TUNING).

• ALTHOUGH A PROCESS MODEL IS REQUIRED, IMC TUNING ALLOWS FOR ADJUSTING THE AGGRESSIVENESS OF THE CONTROLLER ONLINE USING A SINGLE TUNING PARAMETER, τf.

RECOMMENDED TUNING METHODS

• TUNING ACTUAL CONTROL LOOPS DEPENDS ON PROCESS CHARACTERISTICS

• PROCESSES CAN BE CATEGORIZED AS HAVING SLOW OR FAST RESPONSE, RELATED TO PROCESS DEAD TIME AND THE PROCESS TIME CONSTANT

• SEE TABLE 9,4 FOR TYPICAL TUNING PARAMETERS FOR PROCESS TYPES.

LIMITATIONS ON SETTING TUNING CONSTANTS

• FOR ACTUAL SYSTEMS• IT IS VERY DIFFICULT TO DEVELOP A

RIGOROUS MODEL FOR A PROCESS– .THERE MAY BE MANY COMPONENTS THAT

NEED TO BE INCLUDED IN THE MODEL– .NONLINEARITY IS ALSO A FACTOR

• PRESENT IN ALL PROCESSES• CAN RESULT IN CHANGE IN PROCESS GAIN AND

TIME CONSTANT

LIMITATIONS ON SETTING TUNING CONSTANTS

• ACTUAL PROCESSES MAY EXPERIENCE A RANGE OF OPERATIONS, BUT CONTROL IS TYPICALLY OPTIMIZED FOR ONE SET OF CONDITIONS– TABLE 9.5 SHOWS HOW A CONTROL

SYSTEMS CAN BECOME UNSTABLE DUE TO CHANGES IN FEED CONCENTRATIONS TO A REACTOR

– TABLE 9.6 SHOWS THE SYSTEM REMAINS STABLE UNDER THE SAME LEVELS OF CONCENTRATION CHANGES IF A REACTION PARAMETER (ACTIVATION ENERGY) IS CHANGED

LIMITATIONS ON SETTING TUNING CONSTANTS

• CHANGES IN CONTROL CAN ALSO AFFECT DOWNSTREAM PROCESSES– CHANGING RESIDENCE TIME IN A REACTOR CAN

CHANGE THE FEED CONCENTRATIONS TO A DISTILLATION PROCESS

– CHANGING FEED RATES TO DISTILLATION COLUMNS CAN ALSO IMPACT THE HEAT BALANCE AND PRODUCT CONCENTRATIONS IN THE COLUMN

• IT MAY NOT BE PRACTICAL TO ACTUALLY INTRODUCE TRACERS OR PERTURBATIONS INTO OPERATING SYSTEMS IN ORDER TO OBTAIN TUNING DATA