Nonlinear time-scaling for analysis and controller design of reaction systems

The models that describe the dynamics of reaction systems are usually complex and uncertain. To simplify their description it is useful to identify the states which are dependent/independent of the reactions and flows. This allows us, for instance, to design observers which are independent of the (highly uncertain) reaction functions and, in principle, simplify the controller design. The main contribution of the paper is to show the utility of nonlinear state-dependent time-scaling to carry out these objectives. First, we prove the existence of attractive invariant manifolds, which allows us to reduce the dimension of the system under study. Second, we design reaction-independent observers, which are simpler than the existing ones, and have a guaranteed convergence rate in all operating regimes. As an application we study a fifth order baker´s yeast fed-batch fermentation process model, for which we reduce the essential dynamics to the plane. A simple input-output feedback linearizing controller is designed and its asymptotic stability established