1. CHE 185 – PROCESS CONTROL AND DYNAMICS
TUNING FOR PID CONTROL LOOPS

2. 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.

3. 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

4. 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.

5. Example of an SPC Chart
Reference figure 9.2.3

6. TUNING CRITERIA error CONTROLLED VARIABLE PERFORMANCE
AVOID EXCESSIVE VARIATION
MINIMIZE THE INTEGRAL ABSOLUTE ERROR:
MINIMIZE THE INTEGRAL TIME ERROR:

7. 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)

8. SUMMARY OF GOALS FOR TUNING
DECAY RATIO APPROACHING QUARTER AMPLITUDE DAMPING, QAD

9. Decay Ratio for Non-Symmetric Oscillations
Reference figure (c)

10. 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)

11. Classical Tuning Methods
Cohen and Coon method
TARGET THE VALUES SHOWN IN TABLE 9.2
BASED ON MINIMIZING ISE, QAD AND NO OFFSET

12. Classical Tuning Methods
CIANCONE AND MARLIN
DIMENSIONLESS CORRELATIONS BASED ON A TERM CALLED FRACTIONAL DEADTIME: 𝜃 𝑝 𝜃 𝑝 + 𝜏 𝑝
RESULTING PARAMETERS ARE PLOTTED IN FIGURE 9.3.2

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

14. 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.):

15. 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

16. Classical Tuning Methods
BASED ON A QAD TUNED RESPONSE
BASED ON PROPORTIONAL-ONLY VALUES
ULTIMATE VALUES
GAIN:
PERIOD

17. 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 should be
𝐹= 2𝜁 𝜏 𝑝 𝜏` 𝑝 −1

18. 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.

19. 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.

20. 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.

21. 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

22. 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

23. 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