Stable adaptive algorithm for simultaneous estimation of time-varying parameters and state variables in aerobic bioprocesses

The application of modern model based control algorithms in the bioprocesses is hampered by the lack of accurate and cheap on-line sensors, capable of providing on-line measurements of the main process variables and parameters. In this paper, a new approach for estimation of immeasurable time-varying parameters and state variable is presented for a class of aerobic bioprocesses using only on-line measurements of the oxygen uptake rate. The approach consists in the design of a new parameter estimator of biomass growth rate and yield coefficient for oxygen consumption on the basis of the theory of adaptive estimation. The dynamical equation of the measurable reaction rate, oxygen uptake rate, is presented as a linear one with respect to the biomass growth rate and the yield coefficient for oxygen consumption. In this way, the structure of the proposed estimator becomes linear time-varying one. After some mathematical transformations, that structure is presented in a form, allowing to be derived the stability conditions using some theoretical results concerning the stability of adaptive observers. The estimates of the yield coefficient for oxygen consumption, the biomass concentration and specific growth rate are obtained then on the basis of the generated estimates using well known kinetic models of bioprocesses. With respect to previous similar approaches, the new estimation algorithm gives stable estimates not only of immeasurable state variable and reaction rates but likewise of an yield coefficient. The behavior of the proposed estimator is studied under inexact initial conditions, step changes of dilution rate and in the presence of measurement noise by simulations using a process model, which belongs to the investigated class of bioprocesses.