Null Space Method for Selecting Optimal Measurement Combinations as Controlled Variables

Abstract

The issue in this paper is to select controlled variables c as combinations of the measurements y. The objective is to obtain self-optimizing control, which is when we can achieve near-optimal steady-state operation with constant setpoints for the controlled variables, without the need to reoptimize when new disturbances perturb the plant. The null space method yields locally optimal controlled variables c = Hy that are linear combinations of measurements y. The requirement is that we at least have as many measurements as there are unconstrained degrees of freedom, including disturbances, and that the implementation error is neglected. The method is surprisingly simple. From a steady-state model of the plant, the first step is to obtain the optimal sensitivity matrix F, with respect to the disturbances. The optimal matrix H satisfies HF = 0; therefore, the next step is to obtain H in the left null space of F. As an illustration, the method is used to obtain temperature combinations for control of a Petlyu...