CHE 185 – PROCESS
CONTROL AND DYNAMICS
TUNING 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:

IAE   ysp ( t )  ys ( t ) dt
0
– MINIMIZE THE INTEGRAL TIME ERROR:

ITAE   t ysp ( t )  ys ( t ) dt
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:
ISE  

0
y

2
sp
( t )  ys ( t ) dt
• AND INTEGRAL TIME SQUARE ERROR:



ITSE   t ysp (t )  ys (t ) dt
0
2
– OBTAIN ZERO STEADY-STATE OFFSET
– MINIMAL RINGING (EXCESSIVE CYCLING)
SUMMARY OF GOALS FOR TUNING
• DECAY RATIO APPROACHING QUARTER
AMPLITUDE DAMPING, QAD
DECAY RATIO FOR NONSYMMETRIC 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:
𝜃𝑝
𝜃𝑝 +𝜏𝑝
• 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.):
K p Kc
Kc 
Kp
CLASSICAL TUNING METHODS
• STABILTY-BASED METHOD - ZIEGLERNICHOLS
• 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:
1
Ku 
• PERIOD
Pu 
Gp ( jC )Ga ( jC )Gs ( jC )
2
c
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
𝜏𝑝
𝐹 = 2𝜁
−1
𝜏`𝑝
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