Local Self-Optimizing Control with Average Loss Minimization

Abstract

Self-optimizing control provides nearly optimal operation of process systems in the face of varying disturbances, where the inputs are adjusted to hold selected controlled variables (c) at constant setpoints. It is possible to have better self-optimizing properties by controlling linear combinations of measurements (c = Hy) than by controlling individual measurements. Previous work focused on selecting combination matrix H to minimize worst-case loss, that arises due to the use of suboptimal self-optimizing control policy. In this paper, we present a method for finding combination matrix H that minimizes average loss for local self-optimizing control. It is further shown that the combination matrix that minimizes average loss is superoptimal in the sense that it also minimizes worst-case loss simultaneously. The usefulness of the results is demonstrated using an evaporator case study.

Equivalence between Neighboring-Extremal Control and Self-Optimizing Control for the Steady-State Optimization of Dynamical Systems

“…Other approaches have also been presented, which use either minimization of an appropriate loss function 17 or measured data directly 18 .…”

An iterative LMI approach to controller design and measurement selection in self-optimizing control

“…What remains is to determine which of unconstrained variables (c) should be kept constant by using the remaining degrees of freedom, in order to minimize loss. To quantify the loss resulting from keeping the selected controlled variables at constant values, methods for calculating the worst case and average loss were derived in [5] and [17].…”

Bidirectional branch and bound for controlled variable selection. Part II: Exact local method for self-optimizing control

“…The MSV rule, however, is approximate and can sometimes lead to non-optimal set of CVs [10]. In general, it is more appropriate to select CVs using the exact local methods [3,9,13]. The objective of this paper is to extend the BAB approach for CV selection using the exact local method with worst-case loss minimization.…”

“…A related problem involves selection of combinations of available measurements as CVs, which provides lower losses than the use of a subset of available measurements as CVs [2,9,12,13]. Halvorsen et al [9] proposed the use of nonlinear optimization based approach to design the combination matrix, which is computationally expensive and may converge to local optima.…”

“…For appropriate selection of CVs using the concept of self-optimizing control, various criteria have been proposed including the minimum singular value (MSV) rule [17] and exact local methods with worst-case [9,12] and average loss minimization [3,13]. Like other control structure selection problems, CV selection is a combinatorial optimization problem; see e.g.…”