Advanced process control critically relies on a multivariable model of the controlled process. Identifying such a model from input-output data requires an estimate for the dimension of the model order (dimension of state space) and estimation of the related parameters. The accuracy of a model order estimate depends strongly on the kind of input-output data available. It has long been demonstrated (P. Misra & Nikolaou, 2003
) that standard identification experiments with PRBS inputs may not generate data suitable for estimation of system order. In fact, for ill-conditioned systems it was demonstrated that such experiments may yield data that may produce model order estimates ranging from completely wrong (unsuitable for use in controller design) to indeterminate. Experiments using appropriately proportioned rotated
pseudo random binary sequence (PRBS) inputs were demonstrated to produce accurate model order estimates. However, such inputs depend on the very process to be identified. Therefore, some sort of an adaptive procedure is needed, through which an initial experiment is conducted and model identified, which in turn is used to design and conduct the next experiment from which an updated model is identified, and so on.
In this presentation we develop such a procedure. In addition, we generalize the preceding ideas and put them in a more rigorous framework that allows further development (S. Misra & Nikolaou, 2017).
We test the proposed procedure on two case studies namely a high-purity distillation column, and a fluidized catalytic cracking (FCC) reactor-regenerator system. For the latter, the true order of the system, equal to 15, is captured accurately with the proposed procedure, whereas standard approaches completely fail to produce any reasonable number.
Misra, P., & Nikolaou, M. (2003). Input design for model order determination in subspace identification. Aiche Journal, 49, 2124-2132.
Misra, S., & Nikolaou, M. (2017). Adaptive design of experiments for model order estimation in subspace identification. Computers and Chemical Engineering, 100, 119-138.