Optimal discrete stochastic control theory for process application

The design of discrete feedback controllers which minimize some linear function of the variances of the output deviations from target subject to possible constraints on the variances of the inputs, for linear systems subject to stochastic disturbances, is treated from two points of view: (1) using transfer function models to characterizing the process dynamics and autoregres-sive-moving-average models to characterize the stochastic disturbances, and then solving the optimal control problem using an approach due to Box and Jenkins and a discrete version of the Wiener-Newton theory; and (2) using state variable models to characterize both the dynamic and stochastic parts of the system, and then solving the optimal control problem using the results of dynamic programming and Kalman filtering. Practical considerations such as model forms, their identification and estimation, and the development of variance relationships that are necessary for the application of these two approaches in the process industries are discussed. The relationship between and a comparison of these two approaches is made. On discute de deux manieres differentes, dans le cas des systemes lineaires qui sont sujets a des perturbations stochastiques, la conception de controleurs de reactions discontinues, lesquels minimisent une fonction lineaire des variations des ecarts du rendement de lobjectif recherche a des contraintes possibles sur les variations de lalimentation fournie. On a procede comme suit: (1) on a employe des modeles de la fonction de transfert pour caracteriser la dynamique du processus et des modeles ordinaires auto-regressifs pour depeindre les perturbations stochastiques, et l'on a resolu le probleme de controle optimal en ayant recours a un mode dapproche de Box et Jenkins et a une version discontinue de la theorie de Wiener et Newton; (2) on a employe des modeles variables de regimes pour caracteriser les parties dynamiques et stochastiques du systeme et lon a resolu le probleme de controle optimal en utilisant les resultats de la programmation dynamique et de la filtration de Kalman. O discute certains points pratiques telles que les formes, lidentification et levaluation des modeles, ainsi que la mise au point de relations entre les variations qui sont necessaires pour appliquer les deux modes dapproche precites aux industries de traitement. On compare les dits modes dapproche en soulignant leur connexite.