Parameter Estimation Using Sliding Mode Observers: Application to the Monod Kinetic Model

Abstract

In this paper a technique borrowed from modern control theory, called sliding mode observers, is used as the vehicle for nonlinear parameter estimation. The observer is a dynamic system derived from the original state equations that guides, in real time, parameter values from initial estimates to optimal ones. This is done by driving errors between the estimated and "data" states to zero. Observers are developed and demonstrated for the Monod model for biokinetics, which has been used widely in bioprocess design for both aerobic and anaerobic bio-processes under both toxic and non-toxic conditions. The Monod model has four parameters; often, two of the parameters (y, yield and b, decay coefficient) are assumed or calculated from other sources such as from thermodynamic considerations. The other two parameters (k, maximum specific uptake rate of the substrate and ks, the half saturation constant for growth) are determined from experimental data. The determination of these parameters is often performed using nonlinear regression or related methods and it has been demonstrated that these are particularly difficult parameter estimation problems. Examples are presented where only k is unknown and when both k and ks are to be determined. One case where the data are corrupted with noise is considered.The primary objective of the paper is to introduce the methodology of sliding mode observers for nonlinear parameter estimation to the chemical and process engineering communities.