On adaptive optimal input design: A bioreactor case study

The problem of optimal input design (OID) for a fed‐batch bioreactor case study is solved recursively. Here an adaptive receding horizon optimal control problem, involving the so‐called E‐criterion, is solved “on‐line,” using the current estimate of the parameter vector θ at each sample instant {tk, k = 0, …, N − h}, where N marks the end of the experiment and h is the control horizon for which the input design problem is solved. The optimal feed rate F in*(tk) thus obtained is applied and the observation y(tk+1) that becomes available is subsequently used in a recursive prediction error algorithm to find an improved estimate of the actual parameter estimate θˆ(tk). The case study involves an identification experiment with a Rapid Oxygen Demand TOXicity device (RODTOX) for estimation of the biokinetic parameters μmax and KS in a Monod type of growth model. It is assumed that the dissolved oxygen probe is the only instrument available, which is an important limitation. Satisfactory results are presented and compared to a “naïve” input design in which the system is driven by an independent binary random sequence. This comparison shows that the OID approach yields improved confidence intervals on the parameter estimates. © 2006 American Institute of Chemical Engineers AIChE J, 2006