First-order plus deadtime model

First-Order Plus Deadtime (FOPDT) Model.1179... 

The most accmate way of determining the dynamic constants is by a computer-based curve fitting technique which uses the values of the MV and PV collected frequently throughout the test. If we assume that the process can be modelled as first order plus deadtime, then in principle this involves fitting the following equation to the collected data. 

We should also remember that the tuning has been based on the assumption that the process is first order plus deadtime. It is theoretically possible to implement a second order equivalent of the lead-lag algorithm but this would require the identification of second order models for the DV and MV, and the calculation of additional tuning constants. It is unlikely therefore to be practical. It would be easier to fine tune the dynamic compensation. This also takes account of any abnormalities in the way in which the DCS vendor may have coded the lead-lag algorithm. 

Perform a step test on the three-heated-lank process and fit a first-order lag plus deadtime model to the response curve. Calculate the ultimate gain and the ultimate frequency from the transfer function and compare with the results from Problem 16.1. 

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