Joint input-output identification

There are three different approaches in determining the model structure of a closed-loop system indirect identification, direction identification, and joint input-output identification. 

Joint Input-Output Identification of a Closed-Loop... 

The third and final method for closed-loop process identification is called the joint input-output identification method, which uses all three signals, y and in order to identify a model of the system in a two-step procedure. In the first step, a model between r, and m, is fit to give... 

The identification of plant models has traditionally been done in the open-loop mode. The desire to minimize the production of the off-spec product during an open-loop identification test and to avoid the unstable open-loop dynamics of certain systems has increased the need to develop methodologies suitable for the system identification. Open-loop identification techniques are not directly applicable to closed-loop data due to correlation between process input (i.e., controller output) and unmeasured disturbances. Based on Prediction Error Method (PEM), several closed-loop identification methods have been presented Direct, Indirect, Joint Input-Output, and Two-Step Methods. 

Shah, S. L., Fisher, D. G. and Karim, N. M., "Hyperstability Adaptive Control-A Direct Input-Output Approach without Explicit Model Identification," Proc. Joint Automatic Control Conference, 1979, 481. 

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