PID Tuner Forum › Forums › General PID Discussion › Model identification algorithm › Reply To: Model identification algorithm

June 7, 2021 at 3:51 pm
#90

pidtuner

Keymaster

Hi,

Thank you for your interest. The identification algorithm uses this solution:

https://math.stackexchange.com/questions/1428566/fit-sum-of-exponentials/3808325#3808325

Basically consists in integrating the inputs and outputs of the system (according to the desired model order) and then solving a couple of (linear) least squares problems.

The delay in nonlinear, so given that the (linear) least squares problems are “relatively cheap”, the delay is calculated by brute force initially using a grid of values. Then refinement is made using a simple newton method.

Hope this is helpful.