An approach to dynamic optimizing control of the continuous process

Optimum performance of the multivariable continuous process under transient conditions is considered. A generalized performance criterion is formulated in terms of the cost of operation. Assuming that the essential process behavior is known and that the major disturbance variables may be measured, the necessary conditions for minimum cost of operation are derived by applying calculus of variations in conjunction with the Lagrange multiplers technique. In certain typical cases of process behavior and cost criteria, the resulting necessary conditions reduce to a form which will yield an analytical solution. In particular, by certain approximations of the system behavior in the vicinity of an operating point, the necessary condition for optimum performance is expressed in terms of an inhomogenous Wiener-Hopf integral equation of the second kind and the solution is obtained by spectral factorization. In general, the conditions to be satisfied for minimum cost of operation appear as a set of nonlinear integral equations. A method for handling the general case is suggested.