2. Open-loop linear system models

2.1 Model selection criteria

Control by a simplified PID only requires setting two parameters; this does not require very rigorous modeling of the system, but it must be possible to obtain a fast and reliable estimate of the critical pulsation ω _c .

We also want to characterize the system with a minimum of experimental testing and a few simple measurements: the index test is the most suitable. The aim of model identification is to obtain the PID corrector setting.

The number of parameters to be identified must be as small as possible, so that the identification is not too dependent on the inevitable signal noise. The search for small time constants close to or beyond the system's bandwidth...