Integral Error Indices (IAE, ISE, ITAE)

… more less An error index scores a test run with one number, so you can compare two tunings fairly. Log the error, setpoint minus PV, at every sample. IAE adds up the size of the error over time. For each sample, take the error without its sign, multiply by the sample time, and add them all. ISE squares each error before adding, so big errors count far more than small ones. It favors a fast first response and lets small errors linger. ITAE multiplies each error by the time since the test began. Errors late in the test cost the most, so it punishes slow settling and long ringing. A lower score is better. Use them with care. Run the same test both times: the same step size, the same load, and the same starting point. A bigger step gives a bigger score with no change in tuning. Look at the output too, since a low score can hide an output that slams between its limits. Pick the index that matches what you care about. Use ISE if big errors are costly, ITAE if lingering error is costly, and IAE as a fair default. After this Concept you can compute IAE from a logged test in a spreadsheet and use it to choose between two sets of gains.