ELSEVIER J. Proc. Cant. Vol. 8, No.2, pp. 117-138, 1998 © 1998 Elsevier Science Ltd. All rights reserved Printed in Great Britain 0959-1524/98 $19.00 + 0.00 PII: 50959-1524(97)00046-2 Novel developments in process optimisation using predictive control v. M. Becerra."! P. D. Hobertst and G. W. Griffiths- tCity University, Control Engineering Research Centre, Northampton Square, London, UK, ECIV OHB tAspentech (U.K.) Ltd., Waterway House, TheHam, Brentford, UK, TWBBHQ Received 15 May 1996; revised 12 July 1997 In industrial practice, constrained steady state optimisation and predictive control are separate, albeit closely related functions within the control hierarchy. This paper presents a method which integrates pre- dictive control with on-line optimisation with economic objectives. A receding horizon optimal control problem is formulated using linear state space models. This optimal control problem is very similar to the one presented in many predictive control formulations, but the main difference is that it includes in its formulation a general steady state objective depending on the magnitudes of manipulated and measured output variables. This steady state objective may include the standard quadratic regulatory objective, together with economic objectives which are often linear. Assuming that the system settles to a steady state operating point under receding horizon control, conditions are given for the satisfaction of the necessary optimality conditions of the steady-state optimisation problem. The method is based on adaptive linear state space models, which are obtained by using on-line identification techniques. The use of model adaptation is justified from a theoretical standpoint and its beneficial effects are shown in simulations. The method is tested with simulations of an industrial distillation column and a system of chemical reactors. © 1998 Elsevier Science Ltd. All rights reserved Keywords: optimal control; predictive control; process identification The process industry has experienced important changes during the last few decades due to the increased costs of energy and increasingly strict environmental regula- tions. It is believed that emphasis should be on improv- ing efficiency and increasing profitability of existing plants rather than on plant expansion. To achieve such a goal, one of the most important means is optimisa- tion. As computers have become increasingly powerful the size of industrial problems which can be managed by optimisation techniques has increased considerably in the last few decades. Moreover, the decreasing prices of computer hardware have made the industrial imple- mentation of these optimisation techniques feasible from a financial perspective. Optimisation benefits the operation of industrial processes in terms of reduced operating costs and maximised product quality in response to differing feed, market and environmental conditions. The economic optimisation of the operating conditions of a process involves the design of an eco- nomic objective, which should quantify the factors known to have an economic impact in the way the *To whom correspondence should be addressed. Fax: 0171-477 8568 117 plant operates. These factors include, for instance, process yield, energy efficiency, costs of energy and raw materials, product prices, etc. The economic objective, together with the process steady state relations, con- straints associated with physical limits, safety, environ- mental regulations, etc. define the optimal operating conditions of the process. For a continuous flow pro- cess, these optimal operating conditions usually refer to a steady state operating point, called the steady state optimum. Steady state optimisation techniques have also been called optimising control. For batch processes, the optimal operating conditions refer to dynamic trajec- tories. In steady state optimisation, it is often the case that the optimum operating conditions lay at the inter- section of a number of process constraints. Regulating the steady state operation of a multivariable process at such constrained conditions is difficult using conven- tional controllers. Predictive control techniques have been industrially proven to solve effectively this challenging problem. This is why, in industrial practice, the link between pre- dictive control technology and steady state process optimisation has been very close. Predictive control