Nonlinear adaptive optimization of biomass productivity in continuous bioreactors

A novel on-line adaptive optimization algorithm is developed and applied to continuous biological reactors. The algorithm makes use of a simple nonlinear estimation model that relates either the cell-mass productivity or the cell-mass concentration to the dilution rate. On-line estimation is used to recursively identify the parameters in the nonlinear process model and to periodically calculate and steer the bioreactor to the dilution rate that yields optimum cell-mass productivity. Thus, the algorithm does not require an accurate process model, locates the optimum dilution rate online, and maintains the bioreactors at this optimum condition at all times. The features of the proposed new algorithm are compared with those of other adaptive optimization techniques presented in the literature [1–5]. A detailed simulation study using three different microbial system models [3, 6–7] was conducted to illustrate the performance of the optimization algorithm.List of Symbols A(q^–1) polynomial in q^–1 - b bias term - c_F nutrient cost term - B(q^–1) polynomial in q^–1 - C(q^–1) polynomial in q^–1 - CMPR kg/(m³ · h) cell mass productivity - D 1/h dilution rate - D_opt 1/h optimum dilution rate - E(q^–1) polynomial in q^–1 - h exponential filter constant - J objective function - k time index - K_m Monod's constant - n optimization interval - P covariance matrix - q^–1 backward shift operator - r defined by equation (28) - S kg/m³ substrate concentration - S_Fkg/m³ feed substrate concentration - T_sh sampling period - u vector containing previous input values - V dm³ fermenter volume - X kg/dm³ cell mass concentration - Y output variable - Y vector containing previous output values - Y_x/sg/g yield coefficient - optimization tuning constant - vector linear or nonlinear combination of u and Y - denominator covariance matrix update equation - forgetting factor - parameter vector - 1/h specific growth rate - _m1/h maximum specific grow rate