Versions of Control Algorithm

Before embarking on tuning the controller it is important that we understand the exact form of the algorithm. Different versions are in common use for two reasons. Firstly, there are a variety of approaches taken by different DCS vendors in converting the equations written in analog form into their discrete version. Secondly vendors have added a range of enhancements to the standard controller. 

Addressing the first of these issues we can write, by combining Equations (3.2), (3.11) and (3.14), the conventional analog version of the algorithm. 

One approach is to rewrite this directly in its discrete form 

An alternative method is to apply the trapezium rule, where the integral is treated as series of trapeziums. 

By subtracting the equation for the previous scan we obtain a slightly different version of the velocity form of the controller. 

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