FOPDT Modeling

A First-Order Plus Deadtime (FOPDT) model is a simple representation of the dynamic response of a variable to an influence.  It is alternately termed first-order lag plus deadtime (FOLPDT), or “deadtime” is replaced with delay (FOLPD).  This simple model is often a reasonable approximation to process behavior; and has become the basis of many rules for tuning controllers, structuring decouplers and feedforward control algorithms.  It is used to communicate essential process attributes, and as a computationally simple surrogate model in simulations for training and optimization.

The classic textbook method to generate FOPDT models is the reaction curve technique, a pre-computer era technique.  It is simple to understand and implement; however, I believe it does not express best practices in the computer era.

The reaction curve technique asks you to make a step change in the process input, from an initial steady state, and hold the input until the response variable levels to an ending steady state.  Unfortunately, noise and drifting alternate influences confound the response.  And, a single step pushes the process away from a desired set point.  Further, a push to one side of a nominal value will misrepresent nonlinear aspects of the process.  So, for effective reaction curve tests, we often use an up-down-down-up pattern, a sequence of step-and-hold patterns in the influence.  This generates 4 reaction curves.  Their average can temper the influence of noise and disturbances, and the pattern explores both sides of the original MV value and ideally returns the process to the original value.

The steps must be large enough to make a noticeable change in the response.  If the change is small relative to normal noise and drifts, the FOPDT model coefficients will have a large uncertainty.

This approach, however, requires operator attention for an extended time to wait for 4 steady state periods, may create process deviations that impact downstream quality, and requires the human to interpret the signal to provide data for the mathematical analysis.

In the computer era, by contrast, nonlinear least squares regression is simple to implement; and a skyline input function has advantages in operational duration, magnitude of upsets, and number of excitations over classical methods.  Accordingly, this tutorial r3eda site FOPDT & SOPDT Regression User Guide 2016-08-07 describes how to implement tests and use a nonlinear regression code for generating FOPDT models.  The software is here r3eda Generic LF Dynamic Model Regression FOPDT 2017-04-23.