We present a strict Lyapunov function for hyperbolic systems of conservation laws that can be diagonalised with Riemann invariants. The time derivative of this Lyapunov function can be made strictly definite negative by an appropriate choice of the boundary conditions. It is shown that the derived boundary control allows to guarantee the local convergence of the state towards a desired set point. Furthermore, the control can be implemented as a feedback of the state only measured at the boundaries. The control design method is illustrated with an hydraulic application, namely the level and flow regulation in an horizontal open channel.

Abstmct -We consider the optimization of fed-batch fermentation processes involving one limiting substrate for biomass growth and product synthesis, with respect to the volumetric feed rate of this substrate. Until now dassification of these processes -and thus also the determination of the corresponding optimal feed rate strategy-has been based only on the qualitative behavior of the spedfic rates for growth and production as functions of substrate concentration. In this paper we illustrate that the optimal control sequence largely depends on other model characteristics as well, such as the value of the product degradation constant. A detailed optimization study for all possible combinations of the spe&c rates for growth and production reveals that the typical biphasic behavior of processes with growth/production decoupling disappears if product degradation is not modeled.In this sense numerical optimization can prove very useful in solving the model structure discrimination problem. FED-BATCH FERMENTATION PROCESSES WITH PRODUCT FORMATION Mathematical modelConsider a biotechnological process in a stirred tank reactor operated in fed-batch described by the following set of equations:the amount of substrate, X [g D the amount of biomass, P [g] the amount of product, V a the volume of the liquid phase, Csj, [g/L] the substrate concentration in the volumetric feed rate U [L/h], U [g/g DW h] the specific substrate consumption rate, p [I/h] the specific growth rate, T [g/g DW h] the specific production rate, and k [l/h] the product degradation constant. There is no dynamic equation for dissolved oxygen, as dissolved oxygen is considered 'Corresponding author, senior research assistant with the Belgian National Fund for Saentsc Research. This paper presents research results of the Belgian Programme on Interuniversity Attraction Poles initiated by the Belgian State, Prime Ministers Office, Saence Policy Programming. The scientific responsibility rests with its authors.1947 non-limiting by maintaining a sufliciently high aeration level. The three specific rates u, I(, and x are interrelated by the following linear law: with YXIS [g DW/d the biomass on substrate yield coefiaent, Ypls [g/g] the product on substrate yield coefficient, and m [g/g DW h] the s p d c maintenance demand. N e tice that the mathematical model (1)-(2) can describe any metabolism for maintenance of living biomass.Fed-batch fermentation processes have been found to be most effective in overcoming such effects as substrate inhibition, catabolite repression, and glucose effects. In other words, whenever the specific rates of growth ( p ) and/or pr* duction (T) are non-monotonic fnnctions of the limiting substrate concentration, a fed-batch operation may be superior and it is then necessary to determine the optimal feed mte of substmte. Optimization of P ( t j )The optimization problem we consider in this paper can be stated as follows. Determine the optimal volumetric feed rate ~' ( t )which " i z e s the following performance index:ie., maximizes the ...

No abstract

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.