Indirect Identification of a Closed-Loop Process

The first method for closed-loop identification is called indirect identification, where Eq. (6.56) is first fit as 

given the controller transfer function, the process transfer function can be calculated as 

Since most processes have low-order dynamics and the overall transfer function, M, is likely to have a large order, plenty of cancellations must occur between Gy and M. However, many of these cancellations will not occur if the model estimates are even slightly off. Thus, there is a potential of creating a very large order model, even if it is not warranted. Furthermore, this method can only be used for identifying data obtained when the process has external excitation. 

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