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