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.

Self-optimizing control is a useful method for finding the appropriate set of controlled variables. Recently, some researchersintroduced local methods for finding the locally optimal subset or linear combination of measurements, which can be used as controlled variables. [Halvorsen et al. Ind. Eng. Chem. Res. 2003, 42 (14), 3273−3284.] In this paper, we present a method for finding the optimal combination of measurements for local self-optimizing control for nearly optimal steady-state operation. The proposed method only requires the use of singular value decomposition, followed by the determination of the eigenvectors of a matrix. The proposed results are computationally more efficient and are guaranteed to find the optimal solution, in comparison to the available nonlinear optimization-based and the approximate null space methods.

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The selection of controlled variables (CVs) from available measurements through exhaustive search is computationally forbidding for large-scale processes. We have recently proposed novel bidirectional branch and bound (B 3 ) approaches for CV selection using the minimum singular value (MSV) rule and the local worst-case loss criterion in the framework of self-optimizing control. However, the MSV rule is approximate and worst-case scenario may not occur frequently in practice. Thus, CV selection by minimizing local average loss can be deemed as most reliable. In this work, the B 3 approach is extended to CV selection based on local average loss metric. Lower bounds on local average loss and, fast pruning and branching algorithms are derived for the efficient B 3 algorithm. Random matrices and binary distillation column case study are used to demonstrate the computational efficiency of the proposed method.Index Terms-Branch and bound, combinatorial optimization, control structure design, controlled variables, self-optimizing control. . His current research interests include combinatorial optimization, control structure design, crystallization, decentralized control, process and performance monitoring, and population balance equations.Yi Cao (M'96) received the M.Sc. degree in control engineering from Zhejiang University, Zhejiang, China, in 1985, and the Ph.D. degree in engineering from the University of Exeter, Exeter, U.K., in 1996. He is a Senior Lecturer with the School of Engineering, Cranfield University, Cranfield, U.K. His research interests are in advanced process control, including plant-wide process control, nonlinear system identification, nonlinear model predictive control, and process monitoring.

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