Bidirectional branch and bound for controlled variable selection. Part III: local average loss minimization

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

Branch and bound method for regression-based controlled variable selection

Self-optimizing control is a promising method for selection of controlled variables (CVs) from available measurements. Recently, Ye, Cao, Li, and Song (2012) have proposed a globally optimal method for selection of self-optimizing CVs by converting the CV selection problem into a regression problem. In this approach, the necessary conditions of optimality (NCO) are approximated by linear combinations of available measurements over the entire operation region. In practice, it is desired that a subset of available measurements be combined as CVs to obtain a good trade-off between the economic performance and the complexity of control system. The subset selection problem, however, is combinatorial in nature, which makes the application of the globally optimal CV selection method to large-scale processes difficult. In this work, an efficient branch and bound (BAB) algorithm is developed to handle the computational complexity associated with the selection of globally optimal CVs. The proposed BAB algorithm identifies the best measurement subset such that the regression error in approximating NCO is minimized and is also applicable to the general regression problem. Numerical tests using randomly generated matrices and a binary distillation column case study demonstrate the computational efficiency of the proposed BAB algorithm

Self-optimizing control – A survey

Self-optimizing control is a strategy for selecting controlled variables. It is distinguished by the fact that an economic objective function is adopted as a selection criterion. The aim is to systematically select the controlled variables such that by controlling them at constant setpoints, the impact of uncertain and varying disturbances on the economic optimality is minimized. If a selection leads to an acceptable economic loss compared to perfectly optimal operation then the chosen control structure is referred to as “self-optimizing”. In this comprehensive survey on methods for finding self-optimizing controlled variables we summarize the progress made during the last fifteen years. In particular, we present brute-force methods, local methods based on linearization, data and regression based methods, and methods for finding nonlinear controlled variables for polynomial systems. We also discuss important related topics such as handling changing active constraints. Finally, we point out open problems and directions for future research

Imaging mechanisms analysis of compact digital holographic microscope for microparticles measurement

AbstractConventional optical microscopy suffers from small depth of focus due to its high numerical aperture and magnification of the microscope objective. In comparison, digital in-line holographic microscopy (DIHM) provides information about the entire 3D volume through numerical reconstruction of the single hologram at several depths. This advantage makes DIHM an effective tool for the measurement of microparticles in suspension. Recently, our group has demonstrated the potential of DIHM for accurate measurement of particles with sizes ranging from 40 microns to a few millimetres. In this paper, the applicability of DIHM is extended for measurement of near-micron sized particles. A compact digital holographic microscope with a single microscope objective is presented. The system imaging mechanisms of the microscope is analyzed first and the recording distance of digital hologram is calculated using spatial frequency analysis. Then the system magnification, lateral resolution and depth resolution are analyzed in terms of the hologram recording distance. Finally, the characterization of microparticles with a diameter of 1 micron and 10 microns is demonstrated with the compact setup. The experimental results show the efficiency and accuracy of this method with a measured error less than 1.55% in the diameter of certified particles

Bidirectional branch and bound for controlled variable selection. Part I: principles and minimum singular value criterion.

The minimum singular value (MSV) rule is a useful tool for selecting controlled variables (CVs) from the available measurements. However, the application of the MSV rule to large-scale problems is difficult, as all feasible measurement subsets need to be evaluated to find the optimal solution. In this paper, a new and efficient branch and bound (BAB) method for selection of CVs using the MSV rule is proposed by posing the problem as a subset selection problem. In traditional BAB algorithms for subset selection problems, pruning is performed downwards (gradually decreasing subset size). In this work, the branch pruning is considered in both upward (gradually increasing subset size) and downward directions simultaneously so that the total number of subsets evaluated is reduced dramatically. Furthermore, a novel bidirectional branching strategy to dynamically branch solution trees for subset selection problems is also proposed, which maximizes the number of nodes associated with the branches to be pruned. Finally, by replacing time-consuming MSV calculations with novel determinant based conditions, the efficiency of the bidirectional BAB algorithm is increased further. Numerical examples show that with these new approaches, the CV selection problem can be solved incredibly fast

Branch and bound method for multiobjective pairing selection

Most of the available methods for selection of input-output pairings for decentralized control require evaluation of all alternatives to find the optimal pairings. As the number of alternatives grows rapidly with process dimensions, pairing selection through an exhaustive search can be computationally forbidding for large-scale processes. Furthermore, the different criteria can be conflicting necessitating pairing selection in a multiobjective optimization framework. In this paper, an efficient branch and bound (BAB) method for multiobjective pairing selection is proposed. The proposed BAB method is illustrated through a biobjective pairing problem using selection criteria involving the relative gain array and the mu-interaction measure. The computational efficiency of the proposed method is demonstrated by using randomly generated matrices and the large-scale case study of cross-direction control. (C) 2010 Elsevier Ltd. All rights reserved

Control structure design: New developments and future directions

Control structure design (CSD) deals with the following fundamental question: Given the process flowsheet, where should the controllers be placed, or more specifically, what variables should be measured (sensors) and manipulated (valves) and how should the two sets be interconnected for safe and economic operation? These choices are not obvious for most systems encountered in practice. The problem of CSD is also complicated by the increasing mass, energy and information integration among the different process units, which necessitates consideration of the whole plant together. In comparison with the vast amount of the literature available on controller design, CSD has received only limited attention. Despite the advances made, a systematic method is still lacking, which can be mainly attributed to the lack of proper mathematical formulation of the problem. Process control lore includes tales of multi-million dollar plants that never operated due to lack of sufficient theory for CSD (Luyben et al., 1998)

Limits of Disturbance Rejection for Indirect Control

In many practical problems, the primary controlled variable is not available for feedback and is needed to be controlled indirectly using secondary measurements. We derive bounds on the H2 - and H#-optimal achievable performance for systems under indirect control, which have all scalar signals. These bounds are useful for gaining insights into the factors posing limitations on the achievable performance. It is shown that as compared to direct control, the unstable poles can severely limit the control quality for indirect control. The limiting effect of the unstable poles can be reduced using two degrees of freedom controller, when the disturbance is measurable