Direct Identification (System Identification Toolkit)
If the stimulus and response signals of a closed-loop system are available but you do not have any other information about the system, you can use only the techniques developed for open-loop models to estimate the closed-loop system. However, you cannot apply all open-loop identification methods to estimate the model of a plant in a closed-loop system. Some open-loop model identification methods assume zero correlation between the stimulus signal and output noise. In closed-loop systems, this correlation is nonzero. Thus, if you use certain open-loop model estimation methods, such as the instrument variable (IV) method and the correlation analysis methods, with closed-loop data, you might estimate a model incorrectly. You can use the prediction error method to identify the plant in a closed-loop system.
The direct identification approach is used commonly in real-world applications. This approach is convenient because you do not need to have additional information about a closed-loop system, such as the reference signal or the controller. However, the estimation might not be accurate if the model type you select for a plant does not describe the output noise of the system accurately. For example, if the output noise of a plant is color noise and you select an output-error (OE) model, which assumes the output noise is white noise, the estimation for the OE model might be biased when you use direct identification. The bias might be small, though, if the signal-to-noise ratio (SNR) of the system is high.