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 theta at each sample instant [t(k), 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(t(k+1)) that becomes in available is subsequently used in a recursive prediction error algorithm to find an improved estimate of the actual parameter estimate theta(tk). The case study involves an identification experiment with a Rapid Oxygen Demand TOXicity device (RODTOX) for estimation of the biokinetic parameters mu(max) and K-S 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 naive 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. (c) 2006 American Institute of Chemical Engineers.