Adaptive tuning

We showed in Chapter 2 that process gain K for most processes is inversely proportional to feed rate. To keep the loop gain constant the controller gain K could be scheduled to vary in proportion to feed rate - although we will show in Chapter 6 that there is a more elegant solution to this problem. 

In some cases it is possible to infer the process gain from process measurements. The controller is tuned for a known process gain. This establishes the value for the loop gain. As the process gain varies the controller gain is automatically adjusted to maintain the loop gain constant. 

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During the 1980s, several adaptive controllers were field-tested and commerciahzed in the U.S. and abroad, including products by ASEA (Sweden), Leeds and Northrup, Foxboro, and Sattcontrol. At the present time, some form of adaptive tuning is available on almost all PID controllers. The ASEA adaptive controller, Novatune, was... 

The weights of the RBFI are adaptively tuned online, on the basis of the output estimation error, via the following update law ... 

Fuel quality, boiler loading, heat exchanger surface fouling, ambient condition, and aging of equipment will all cause the process to drift and affect the model accuracy. Adaptive tuning computations can be built in to take care of... 

What is the objective of the adaptation procedure Clearly it is not to keep the controlled variable at the specified set point. This will be accomplished by the control loop, however badly. We need an additional criterion, an objective function that will guide the adaptation mechanism to the best adjustment of the controller parameters. To phrase it differently, we need a criterion to guide the adaptive tuning of the controller. Any of the performance criteria we discussed in Chapters 16 and 18 could be used ... 

From Chapter 2, we know that (Kp)m varies inversely with feed rate. If we were to configure the output of the bias algorithm to manipulate the fuel flow directly, rather than the fuel-to-feed ratio, then we would need to include adaptive tuning to automatically adjust K to keep it in proportion to feed rate. 

Tis a function of feed rate (F). If feed rate is not constant this can be dealt with by adaptive tuning or feeding forward to the D/F (or B/F) ratio implemented for feed rate feedforward. The values of LKd and LA), are the product specifications. 

At present it appears that only controller gain need be adaptively tuned. The work of Wahl and Harriott su ests that column dynamics are relatively insensitive to small changes in reflux and boilup. This means that reset and derivative (if used) need not be changed. Therefore, after the computer has calculated the appropriate column gain for a particular loop, it can easity calculate required controller gain to hold loop gain constant. 

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