A Globally Convergent Algorithm for the Run-to-Run Control of Systems with Sector Nonlinearities

作者：Francois Gregory; Srinivasan Bala; Bonvin Dominique^*

来源：Industrial & Engineering Chemistry Research, 2011, 50(3): 1410-1418.

DOI：10.1021/ie100808t

Run-to-run control is a technique that exploits the repetitive nature of processes to iteratively adjust the inputs and drive the run-end outputs to their reference values. It can be used to control both static and finite-time dynamic systems. Although the run-end outputs of dynamic systems result from the integration of process dynamics during the run, the relationship between the input parameters p (fixed at the beginning of the run) and the run-end outputs z (available at the end of the run) can be seen as the static map z(p). Run-to-run control consists in computing the input parameters p* that lead to the reference values z(ref). Although a wide range of techniques have been reported, most of them do not guarantee global convergence, that is, convergence toward p* for all possible initial conditions. This paper presents a new algorithm that guarantees global convergence for the run-to-run control of both static and finite-time dynamic systems. Attention is restricted to sector nonlinearities, for which it is shown that a fixed-gain update can lead to global convergence. Furthermore, since convergence can be very slow, it is proposed to take advantage of the mathematical similarity between run-to-run control and the solution of nonlinear equations, and combine the fixed-gain algorithm with a faster variable-gain quasi-Newton algorithm. Global convergence of this hybrid scheme is proven. The potential of this algorithm in the context of run-to-run optimization of dynamic systems is illustrated via the simulation of an industrial batch polymerization reactor.

• 出版日期2011-2-2