A control problem arising in typical fermentation process studies is solved here. Fermentation, i.e., microbial growth and substrate consumption, is described by a nonlinear differential system including a set of unknown parameters that may vary in time. The control objective is to get the state of the system to track the state of a given reference model despite the disturbances and system parameter uncertainties. The concentration of microbes is almost always impossible to determine on-line. The evolution of the main substrate is, however, measurable on-line. The system studied is controlled by varying the dilution rate of the concentrated substrate liquid feed. The fixed parameter control law that serves as a basis for the adaptive method uses the calculated references of the specific growth rate and the dilution rate of the reference model. Adaptive state estimation is based on obtaining a stable estimator for the joint system of states and parameters via a Lyapunov technique. The structure of the adaptive controller is determined by the requirement to obtain stable reference model tracking. Application of Lyapunov's method gives a PI-type controller with adaptively adjustable coefficients. Given stability proofs are supported by some realistic simulation results. © 1993.
Zeng, F. Y., Dahhou, B., & Nihtilä, M. T. (1993). Adaptive control of a nonlinear fermentation process via MRAC technique. Applied Mathematical Modelling, 17(2), 58–69. https://doi.org/10.1016/0307-904X(93)90094-W