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Greg McMillan and Stan Weiner bring their wits and more than 66 years of process control experience to bear on your questions, comments, and problems. Write to them at email@example.com.
This month we talk more with Mark Congiundi, engineering associate in process control at Sasol, about the creative use of PID controllers for process improvement.
Stan: Analyzers can take optimization to a higher level by providing the knowledge for achieving an optimum composition and quality. How do you help the PID use the discontinuous, stepped response of a nonlinear process analyzer with a large cycle time?
Mark: The conventional approach for creating a linear loop with a nonlinear measurement is to linearize the setpoint and the process variable. For analyzers, I have developed a method to transform just the process variable using a setpoint-based, power-factor model. This model imparts a curve to the raw reading, creating a transformed reading that always coincides with the setpoint when the raw reading equals the setpoint. The transformed reading increases proportionally less above setpoint than below it, thus de-emphasizing elevated readings compared to depressed readings. This is consistent with the behavior of the readings in a relatively high-purity composition control application. The changes from measurement updates also are ramped over a long enough time to prevent spikes in the output due to proportional and, particularly, rate action. The ramping of a new value takes place over a defined time period. Operators only see the raw signal and enter a setpoint in terms of it, avoiding confusion for both operations and maintenance.
Greg: Exactly achieving desired changes critical for product quality requires some anticipation because a command to stop feed does not instantaneously result in the complete stop of the feed into the equipment. The flow continues during the time needed to close the valve and de-inventory the line downstream of the valve including, in some cases, the dip tube.
Mark: The solution is akin to filling a bucket. When you decide to turn off the hose, it takes time to react and close the valve. Additionally, there is some flow into the bucket even after the valve is closed. The total flow after the decision can be classified as leakage. To incorporate intelligence to compensate for leakage, a model is developed for the external reset feedback of a zero-gain PID controller. The PID setpoint and process variable are the desired and actual flow totals. As soon as the setpoint becomes higher than the process variable, the automatic filling process starts. The PID output is 100% multiplied by the "goal remaining" divided by the "ramp horizon" (quantity remaining when the valve begins to close) and finally biased by a "valve shift" (valve opening when goal is achieved). The "goal remaining" is the "quantity goal" (batch charge) minus the "flow total" (current totalized flow) and minus the "goal shift" (leakage) to provide the necessary anticipation. By calculating the "goal remaining," we can use the term as a trip value when it becomes negative. This model effectively trips the valve when the anticipated goal is achieved, regardless of the controller output prior to that time.
Stan: Temperature loops have some of the tightest control requirements. To make sure the sensor accuracy as a percent of span is well within the required control band, a narrow range temperature transmitter is used for normal operation. For the operator and the control loop to see the entire temperature range during start-up, a wide-range temperature transmitter is used until the temperature is within the normal operating range. Often a single PID for normal control released from output tracking when the temperature is within the narrow range for control is used. What do you have as a more integrated general solution for eliminating the discontinuity of switching between transmitters with different ranges?
Mark: A calculation of the PV provides a smooth transition. The calculation is always watching to see if the PV is within the narrow range transmitter, and filters the transition by using a fraction of one transmitter output versus the other. A factor of 0.3 often provides a reasonable transition time. The span of the PID is constant, so a decrease in PID gain is not required when the PID is using the narrow range transmitter.
Greg: A measurement is not always available for a PID. The PV may not be representative of the process due to interferences, start-up conditions and insufficient sensitivity, the PV being internal to the equipment or missing online analyzers. Distillation columns may start up on ratio control until the mixture is boiling, and the temperature is representative of composition. Key internal operating conditions, such as internal reflux in the column, can be regulated by calculations based on external measurements. Also, the calculation and control of heat duty from multiple measurements is a powerful technique for regulating the energy balance and separation for distillation columns. These calculations can be viewed as feed-forward signals. Any feed-forward calculation should use the setpoint and not the actual PV of the secondary loop manipulated to avoid positive feedback and instability. What do you do when a direct measurement for feedback correction is missing in action?
Mark: I employ a zero-gain PID and the inverse of the model of the missing PV as an external reset feedback for the feed-forward signal. A zero gain ensures that there is no feedback from the PID PV, leaving the PID free to follow the external reset feedback signal. The PID reset tuning value decides how quickly the PID output follows this signal. The time constant is the reset setting in time units or the inverse of a reset setting in repeats per minute. Normally, the PID output goes to a secondary flow controller. Flow measurements are used to update the model, which becomes the PV of the zero-gain PID. The operator thus has a PV and a corresponding setpoint to manipulate. The secondary flow is used in the model for the PV, but the setpoint, not the PV, must be used in the model whose inverse is this zero-gain PID output.
Consider flow ratio control with no ratio feedback correction. The PV is the ratio of the secondary flow to independent flow. The zero-gain PID output is the feed-forward for the required secondary flow computed as the ratio setpoint multiplied by the independent flow. This feed-forward-only ratio controller is used when there is no online composition measurement available for feedback correction. The secondary flow measurement is used in the ratio measurement that is the PV for ratio control. The ratio control setpoint is used in the inverse of the model that is the ratio controller output. The responsibility for the secondary flow PID to follow its setpoint is solely the responsibility of the secondary flow PID. The performance of the secondary flow loop is ignored by the PID for ratio control.
A feed-forward-only controller is also used to regulate internal reflux within a distillation column. The model for the internal reflux PID PV is the measured external reflux flow corrected by the heat capacity of this external stream and the latent heat of vaporization of the vapor stream within the column. The tower overhead vapor temperature and the external reflux temperature are used in the calculation. The inverse of the model is used to set the secondary loop for external reflux flow. Again, for stability, the setpoint rather than the PV of this feed-forward-only controller must be used in the model whose inverse is the internal reflux controller output.
The heat transfer to the reboiler can be controlled instead of just the heating stream flow. The model for the heat duty is simply the heating stream flow multiplied by the stream heat capacity and the difference between the inlet and outlet temperatures (hot oil supply and return temperatures).
This powerful concept can be used for any model-based control, no matter how complex, as long as it can be algebraically inverted. I have used it in inferential control where the model came from statistical regression, and I have used it in dynamic model control, such as a Smith predictor, where the inputs are reconciled with the outputs dynamically.