All process control gurus cut their teeth on the first-order-plus-time-delay (FOTD) process.  Let’s take a look at what this means.

A first order process is one that shows an exponential response to a step input.  Let’s take, for example, a pot of warm water on a heater.  If you increase the heat input to a higher level, then the temperature will rise.  The temperature rises quickly at first, then it slows down as it levels off at a new, higher temperature.  The shape of the response curve can be represented by an equation:

DeltaT * [ 1-e(-t/T) ]

where t is time and T is the effective “lag time” of the process.  The longer this lag, the longer it takes the process to fully respond.  99+% of the process response will be seen after 4 lag times have passed.

First Order Plus Time Delay Response to Step Change

First Order Plus Time Delay Response to Step Change

The “time delay” is the part at the beginning, where nothing happens for a little while.

Many, many industrial processes behave similar to this FOTD response.  For example, flow controls, pressure controls, and some simple temperature controls all have FOTD responses.  So we can use this same model to understand the process behavior, tune control loops, and train operators about how the process will behave.

In a future post, we’ll get into the mathematical modeling of this process with 3 parameters: Process Gain, Dead Time, and Time Constant.

(image courtesy of ExperTune, Inc. –