Identification of linear, multivariable systems operating under linear feedback control

TLDR

The paper investigates whether process parameters can be estimated from closed‑loop input‑output data. The authors introduce systematic concepts and analyze systems controlled by a linear feedback law or switching among such laws. The study demonstrates that a simple identification scheme yields identifiability equivalent to a more complex closed‑loop method, that switching between linear regulators can achieve open‑loop identifiability, and that the necessary number of regulators depends only on the system’s input‑output count, as illustrated numerically.

Abstract

The possibility of estimating process parameters using input-output data collected when the system operates in closed loop is discussed in this paper. Concepts that are useful for a systematic treatment of the problem are introduced. The results refer to the case where the regulator is a linear feedback law or alternates between several such laws. It is shown that a straightforwardly applied identification scheme has the same identifiability properties as the more complex method in which the parameters of the closed-loop system are estimated first. It is also shown that it is always possible to achieve the same identifiability properties as for open-loop systems by shifting between different linear regulators. The required number of regulators depends only on the number of inputs and outputs. The results obtained are illustrated by a numerical example.