TCLab Graphical FOPDT Fit

A First Order Plus Dead-Time (FOPDT) model can be obtained through a graphical approach, as shown in this video, or through regression with an optimizer.

The first step is to obtain the gain of the process by computing the change in output divided by the change in input. The second step is to approximate the dead-time by selecting the time from the input change until the process begins to rise with an exponential decay to the new steady-state. The final step is to determine the process time constant by evaluating the time to reach 63.2% of the total change in output.