An approach for parameter estimation of biotechnological processes

An approach for parameter estimators design of biotechnological processes (BTP) is presented in case of lack of real time information about state variables. It is based on general reaction rate models and measurements of at least one reaction rate. A general parameter estimator of BTP is designed with the help of which specific rate estimators are synthesized. Stability and convergence of an estimator of specific growth rate for a class of aerobic batch processes are proved. Its effectiveness is illustrated by simulation results. The proposed on-line parameter estimation approach can be used for design of BTP on-line variable estimation algorithms (variable observers of BTP).List of Symbols X, S, P g/l biomass, substrate and product concentrations - C g/l oxygen concentration in the culture broth - C _sg/l saturation concentration of oxygen in the culture broth - C _in, C_outg/l oxygen concentrations in the input air flow and in the outlet gasphase - F _in, F_outl/h the input air flow in the fermenter and output air flow - OUR g/(lh) oxygen consumption rate - OUR _mg/(lh) measured values of OUR - V l volume - , , l/h specific growth, consumption and synthesis rates - K _La(o) l/h specific volumetric mass transfer coefficient - D l/h dilution rate - R _X, R_S, R_Pg/(lh) biomass growth, substrate consumption and product synthesis rates - K _b matrix of yield coefficients - H_b(), H() matrices of known functions of - H(R) matrix of known functions of R - and gain matrices - a vector of the state variables - () a reactions rates vector, describing qualitative relations among the components - R() a reactions rates vector, describing qualitative and quantitative relations among the components - F a feed rates vector - Q a gaseous outflow rates vector - _b () a vector of unknown functions of - ₁() a vector of functions - (t) a vector of unknown time-varying parameters - ₂(, ) an auxiliary vector-function of and - Y _X/S, Y_X/C, Y_X/P substrate, oxygen and product yield coefficients - b maintenence coefficient - k _i(i=1...6) kinetic coefficients - C _i(i=1,2) design parameters estimate