Application of nonlinear time-scaling for robust controller design of reaction systems

Even though the basic mechanisms of operation of reaction systems are relatively simple the dynamical models obtained from first principles are complex and contain highly uncertain terms. To develop reliable model-based controllers it is therefore necessary to simplify the system dynamics preserving the features which are essential for control. Towards this end, co-ordinate transformations identifying the states which are dependent/independent of the reactions and flows have been reported in the literature. This has allowed, for instance, the design of observers which are insensitive to the (usually unknown) reaction functions. The main contribution of this paper is to show the utility of nonlinear state-dependent time-scaling to simplify the system dynamics, and consequently the controller design. In particular, we show that with time-scaling and an input transformation we can reveal the existence of attractive invariant manifolds, which allows us to reduce the dimension of the system. As an application we study the well-known fourth order baker's yeast fed-batch fermentation process model, whose essential dynamics is captured by a planar system perturbed by an exponentially decaying term. We then exploit this particular structure to design, with reduced control authority, a nonlinear asymptotically stabilizing control law which is robust with respect to the reaction function. Copyright (C) 2001 John Wiley Sons, Ltd.