Robust operation of fed batch fermenters

Abstract

Optimisation of fed batch fermenters can substantially increase the pro®tability of these processes. Optimal control of a fed batch fermenter is usually based on a nominal process model. Parameter uncertainties are not taken into account. Simulation studies show that results obtained with ®xed nominal model parameters can be quite sensitive to the uncertainty in parameter values. This paper presents a method for obtaining robust optimal control pro®les in the presence of uncertainty in the model parameters. The proposed approach is illustrated with a case study. It is also shown that feedback controllers can reduce the effect of the uncertainties. IntroductionThe outcome of a fed batch fermentation depends on variables like fermentation time, feed rate pro®le, substrate concentration in the feed, oxygen concentration and pH in the broth amongst many others variables. Process engineers aim to operate a fermenter at optimum pro®t-ability subject to certain constraints. If a model of the process is available, it can be used to determine the optimal values or trajectories of the process variables. Since some of the optimisation variables are functions of time, the optimisation problem is essentially an optimal control problem. The solution to this problem identi®es the optimal time course of the process variables. However these pro®les can be quite sensitive to model uncertainties and the expected results cannot be achieved in practice. It can be shown through computer simulations that small changes in the parameters can yield results signi®cantly different from the expected performance. It is possible that a non-optimal control strategy performs better under real conditions than the optimal strategy. The optimisation should take model uncertainties into account in order to avoid bad performance under real conditions. This paper is divided into six parts including this Introduction and the Conclusion. In the second part we review several approaches to optimise fed batch processes, including those approaches which take model uncertainty into account. In the third part a general optimal control problem is formulated and the model uncertainty is introduced into the formulation. Solution methods to solve the optimal control problem are then reviewed. In the fourth part we propose a procedure to compute optimal control pro®les for fed batch fermenters taking the effects of model uncertainty into account. In the ®fth part, we apply the procedure to optimise a cell producing fed batch fermenter. Optimal control of fed batch fermentersOptimal control of fed batch fermentation has been widely studied and different approaches for the solution of these problems have been proposed. In [1] the feed rate was used as a control variable and an analytic expression for the switching times between bang-bang control intervals and singular arcs was derived. For the singular arcs, a feedback law for the feed rate was obtained. General characteristics for the optimal feed rate pro®les for different classes of fed batch fermentations were p...

Productivity improvement of recombinant Escherichia coli fermentation via robust optimization

“…Kuhlmann et al [7] found that the implementation of an optimal profile for a fermentation can be quite sensitive to errors in the nominal model used. Inclusion of uncertainty considerations in the optimization procedure and the use of feed back control should together reduce the effects of such uncertainty.…”

Quasi-Polynomial System Representation for the Analysis and Control of Nonlinear Systems

“…The variables and parameters of the model together with their units and parameter values are given in Table 1. The parameter values are taken from (Kuhlmann et al, 1998).…”

Analysis and Control of Nonlinear Process Systems

“…Under the above assumptions the nonlinear state-space model of the fermentation process can be written in the following input-affine form [44]: …”

“…Various difficulties are reported in the literature, which include instability and controllability problems for both continuous and fed-batch fermenters ( [44], [43]). Various difficulties are reported in the literature, which include instability and controllability problems for both continuous and fed-batch fermenters ( [44], [43]).…”

“…The simplest dynamic model of a fed-batch fermenter has been developed in Subsection 4.5.2, which can be written in the following input-affine form [44]:…”