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: MINIMIZE THE INTEGRAL TIME ERROR:

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)

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: 𝜃 𝑝 𝜃 𝑝 + 𝜏 𝑝 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.):

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

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 𝐹= 2𝜁 𝜏 𝑝 𝜏` 𝑝 −1

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