The optimal control of a batch reactor often involves that the reaction should be conducted adiabatically at first. By taking observations during the adiabatic part of the reaction information about the kinetics of the reaction can be obtained and later used to program the heat control of the reactor to achieve the desired conversion in the minimum time. In this first part a general perspective of the whole scheme is given and the peculiar problems of determining the unknown kinetics are discussed and illustrated by extensive simulation calculations.
1. Introduction
THE SUBJECT of self-optimizing and adaptive control has attracted the liveliest interest in recent years [l] and continues to provide some of the most stimulating of control problems. The chemical and petroleum industries provide a natural habitat for all species of problem in this genus, for there are many processes of varying complexity constructed and working well on the basis of very sketchy fundamental knowledge, but considerable acumen and sound engineering sense. While the larger problems in this area are only just within sight, there are a number of smaller ones which will repay immediate investigation to give the background experience so necessary if the former are to be successfully attacked.
The word "adaptive", which is so much in use these days and stands in our title, has suffered from its own adaptability. We take it to mean a form of control which recognizes certain gaps in the fundamental knowledge of the plant and which is designed to find the missing information through its experience with the plant and to use this to improve the quality of its control. That this is only one form of adaptive control is acknowledged by the use of the indefinite article. This introductory section will be devoted to a description of the system as a whole and a guide to the rest of the paper where the various parts of the problem are taken up in detail.
The problem of controlling a batch reactor when the ki,netics of the chemical reaction taking place in it are insufficiently known is both of practical importance and suitable for study at this level. For, on the one hand, chemical kinetics are notoriously difficult to determine and, on the other, quite a bit is known about the optimal control of such a reactor. (The literature up to 1960 is summarized in [2], but this has already increased vastly, see e.g. [3]). In particular it is known that the interesting case is that of an exothermic