Flexible operation through optimal tracking in nonlinear processes

In flexible process operation there exist physical variables which are allowed to take a finite number of stationary values. Each of these targets play the role of a typical set-point from the process control point of view. Changes in set-point are handled by industrial regulators. Such controllers, including PIDs, are commonly tuned when put into service, and their parameters remain the same for different set-point values, which is inpractical for linear and nonlinear systems. Here this problem is solved from the tracking - instead of regulation - point of view, and an optimality criteria is introduced. Opposite to the classical approach the formulation of an 'absolute' control cost is emphasized. This means that the energy employed in controlling or tracking should be measured as a whole, and not as a difference with the effort needed to maintain in equilibrium one particular set-point. The main purpose of this article is to deal with the nonlinear dynamics case, where the process is approximated by a general bilinear state equation and the cost is quadratic as usual. This is called the bilinear-quadratic optimal tracking problem. In the paper analytical expressions are found for the solution to this optimal tracking problem under mild simplifying hypothesis, and the traditional optimal control versus the new tracking approaches are compared. Also the effect of nonlinearities over both problems are discussed. In the tracking context the time horizon must necessarily be finite for the optimization problem to be mathematically well posed. Although this finite horizon is dictated by flexibility costraints, once the corresponding optimal tracking strategy is obtained, then it is applied repeatedly without need for further calculations. (C) 2000 Elsevier Science Ltd. All rights reserved.