Periodic optimization of a chemical reactor system using perturbation methods

Abstract

A perturbation approach is presented to the periodic optimization problem of certain classes of nonlinear dynamical systems, for small-amplitude forcing functions, and within specific frequency ranges derived from Guardabassi'sπ-criterion. The procedure is illustrated by means of a classical example in chemical engineering, involving the optimal periodic operation of a continuous stirred tank reactor, in which two parallel reactions take place. The analysis is performed at cycling frequencies slightly above the minimum frequency, where, according to theπ-criterion, performance improvement by cycling becomes possible. The per cent production gains over the optimal stationary operation are evaluated, as a function of the amplitude and frequency of the oscillations allowed to exist in the system, and as a function of the process parameters. Also the characteristics of the control and state waveforms are analysed. Thus the existence and practical applicability are demonstrated of a mathematical relationship between the optimal periodic control problem, theπ-criterion, and the theory of perturbations.