On Bifurcations of the Zero Dynamics - Connecting Steady-State Optimality to Process Dynamics

It is well known that certain properties of the process dynamics can be deduced from steady-state information about a process only. In this paper we consider the dual problem, that of determining steady-state properties from process dynamics. In particular, we are concerned with the problem of determining extremum points in the steady-state input-output map from dynamic response data. This is a highly relevant problem in cases where the aim is to determine steady-state optimal operating conditions using real time process measurements. For this purpose, we first consider the connection between bifurcations of the zero dynamics and the steady-state input-output map. Based on these results, we show that steady-state optimal conditions can be determined from the process dynamics through consideration of local phase-lag properties of the process only. We demonstrate the usefulness of this result by showing that the optimum of a chemical reactor can be located, without any prior knowledge, using sinusoidal perturbations and a phase-lock loop.