Identification of linear, multivariable systems operating under linear feedback control

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.