One common approach is to break the estimation into two steps. First, you can pool the data from all experiments to estimate the common dynamics (the two poles, tp1 and tp2). Then, with these poles fixed, you estimate the experiment‐specific parameters (gain Kp, zero tz, and delay td) individually for each experiment.
Alternatively, if you want to do it in one step you can build a custom grey‐box model (using idgrey or idnlgrey) where your parameter vector includes both the common parameters and the experiment‐specific ones. You then set up linear equality constraints (via the model’s ParameterConstraints property) so that the values for tp1 and tp2 are identical across experiments. Unfortunately, the System Identification Toolbox does not offer a direct “elegant” switch for shared versus unique parameters, so you must implement these constraints manually.
For example, you might organize your combined parameter vector as
% For N experiments, define a parameter vector:
% p = [tp1, tp2, Kp1, tz1, td1, Kp2, tz2, td2, ..., KpN, tzN, tdN]
% Then, in your custom model function, enforce that the first two parameters
% (tp1 and tp2) are used for every experiment.
This approach lets you use the multi‐experiment estimation capabilities of the toolbox while ensuring that the poles remain common and the remaining parameters vary per experiment.
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