On-line estimation of microbial specific growth rates

-Continuous time algorithms for the on-line estimation of microbial specific growth rates of fermentation processes are proposed. An important feature of the proposed algorithm is that they do not require any kind of analytical description of the specific growth rate which is simply considered as an unknown bounded time varying parameter. Four different input-output configurations are considered. In each case, the stability and convergence properties of the algorithms are described and their feasibility is illustrated by real life experiments. 1. In troduct ion CONTINUOUS microbial growth in a completely stirred bioreactor is commonly described by the following state-space representation: dX(t) dt = lit(t) O(t)]X(t) (1) dS(t) dt = k~ i t ( t )X ( t ) + D(t)[Si .( t ) S(t)] (2) with X(t) the biomass concentration S(t) the limiting substrate concentration Sin(t) the inlet substrate concentration D(t) the dilution rate It(t) the specific growth rate kl the yield coetficient. The growth of microorganisms in bioreactors is often accompanied by the formation of synthesis products, either soluble in the culture or given off in gaseous form. When the formation of products is "growth-associated" (Bailey and Ollis, 1977), the production rate per unit of volume is written as Q(t) = kz#(t)X(t) , (3) where k 2 is a yield coefficient. A typical example is the anaerobic fermentation process where Q(t) is a methane gas flow rate (e.g. Andrews, 1969). In the case of a liquid reaction product, the mass balance in the bioreactor leads to the dynamical equation: * Received 25 February 1985; revised 16 September 1985; revised 29 April 1986; revised 10 June 1986. The original version of this paper was presented at the 7th IFAC/IFORS Symposium on Identification and System Parameter Estimation, York, U.K., 3-7 July 1985. This paper was recommended for publication in revised form by Associate Editor G. C. Goodwin under the direction of Editor P. C. Parks. f Laboratoire d'Automatique, Dynamique at Analyse des Systrmes, Universit6 Catholique de Louvain, Bhtiment Maxwell, B-1348 Louvain-La-Neuve, Belgium. :~ Member of GRECO-SARTA (CNRS, France). 705 dP(tt) = Q(t) D(t)P(t) (4)