Self-Optimizing Control Structures with Minimum Number of Process-Dependent Controlled Variables

Abstract

In order to operate continuous processes near the economically optimal steady-state operating point, selfoptimizing control schemes reformulate the optimization problem as a process control problem. The objective is to find controlled variables and constant set points such that the controller leads to optimal adjustments of the inputs in the presence of stable disturbances. In particular, the null space approach consists in selecting the self-optimizing controlled variables as linear combinations of the inactive output variables, based on the first-order variation of the necessary conditions of optimality. In the self-optimizing control structures proposed in the literature, the number of controlled variables required is typically equal to the number of degrees of freedom (inputs) that are available after all the equality and active inequality constrained variables are controlled. In this paper, we propose new self-optimizing control structures based on the null space approach, where depending on the number of disturbances, the number of active constraints, and the number of inputs, it is possible to decrease the number of process-dependent controlled variables by fixing linear combinations of the inputs. The effectiveness of the proposed selfoptimizing control structures with minimum number of process-dependent controlled variables is demonstrated in simulation by means of a continuous stirred tank reactor and an evaporator