16.1 Single Stage Control
The fundamental building block has been the proportional plus integral plus derivative (PID) controller whereby the proportional term would adjust the manipulated variable to correct for a deviation between measurement and target or setpoint; the integral term would continue the action of the proportional term over time until the measurement reached the setpoint and the derivative term would compensate for lags in the action in the measurement in responding to actions of the manipulated variable. The classic equation is:
Judicious application of this control strategy on essentially linear single variable control systems which don't exhibit a prolonged delay (dead time) between action by the manipulated variable and measured response by the controlled variable has proven quite effective. Fortunately most single loop control systems exhibit this behavior.
In highly nonlinear applications such as pH control, or in situations where the dynamics of the process change over time as occurs in many chemical reactions, adjustments to the tuning coefficients are needed to adequately control the modified process dynamics. Self-tuning controllers employing expert rule sets for dynamic retuning the PID settings are available for this class of problem. These are also used by many users to determine the optimum settings for the linear systems described above. One such rule system is the EXACT controller by Foxboro (Fig. 16), which automatically adjusts the controller tuning parameters based on the pattern of the measurement signal received.
When the process under control exhibits significant dead time, the problem is considerably more difficult. One approach is to use a simple model-based predictor corrector algorithm such as the Smith predictor1101 which is interposed between the manipulated and controlled variable in parallel with a conventional controller and conditions the measurement signal to the controller based on time conditioned changes to the manipulated variable made by the controller. This works exceedingly well if properly tuned, but is sensitive to changes in process dynamics. Another scheme, introduced by Shinsky'111 recently, utilizes a standard PID controller with a dead time function added to the external reset feedback portion of the loop. This appears to be less sensitive to changes in process conditions.
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