Design of Experiments in Process Identification

Theoretically, the main concerns lie with identifiability of a process, that is, given a data set and model structure (order of polynomials), what are the conditions for there to be a unique solution to the parameter estimates. For open-loop experiments, the identifiability constraint for a prediction error model can be simply written as 

The matrix, PJ n), is positive definite, or for a symmetric matrix this is equivalent to saying that the matrix is invertible. The n-hy-n matrix T (n) is defined as 

Finally, the bandwidth needs to be selected. The bandwidth represents how much of the frequency domain is excited (or examined) by the given signal. Most chemical processes can be treated as low-pass filters, that is, only low frequencies are important for describing the process. Therefore, there is only a need to excite the process between [0,fuppeA, whereis some upper-bound frequency. For a first-order process, the bandwidth of a process is defined as the inverse of the time constant. For higher-order processes, the bandwidth of a process can be defined as 

6 Modelling Dynamic Processes Using System Identification Methods 

The procedure for running a step test can be summarised as follows  

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