Optimal Measurement Combination for Local Self-Optimizing Control

Abstract

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.

Integration of process design and control: A review

“…Two-step approach Joseph (1987) Marlin andHrymak (1997) Two-step approach Joseph (1987) Marlin andHrymak (1997) Identification for optimization Srinivasan and Bonvin (2002) Bias update Forbes and Marline (1994) Constraint adaptation Chachuat , et al (2008) ISOPE Roberts (1979); Tatjewski, P., (2002); Brdys and Tatjewski (2005) Gradient correction Gao andEngell (2005) Marchetti, et al (2009) Self-optimizing Skogestad (2000b); Govatsmark and Skogestad (2005) Extreme seeking Ariyur and Krstic (2003); Guay and Zhang (2003) NCO tracking Francois, et al (2005); Srinivasan, et al(2008) Active constraints tracking Maarleveld and Rijnsdorp (1970 Later, researchers (e.g. Skogestad 2000aSkogestad , 2000bSkogestad , 2004bKariwala 2007) investigated the notion of self-optimizing control. The concept is shown in Fig.…”

“…Therefore, the results are local and must be checked by a nonlinear model. Kariwala (2007) proposed a computationally efficient method using singular value decomposition and Eigen-values for selection of optimal controlled variables. Later, this method was extended ) to use average losses instead of worst-case losses.…”

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

“…The matrix H ∈ R nu×ny defines the measurement combinations, and y ∈ R ny is a subset of the available measurements. Two methods for computing H are the Null-space [7] and Exact local method [5], [6].…”

“…The optimal solution H * in (8) was shown in [4] to be non-unique and for any non-singular matrix D, H = DH * (9) results in the same loss as the solution given by (8). Therefore, both the Null-space and the Exact local method have an infinite number of solutions for H that satisfies (6) or (9) and thus gives the same steady-state operation.…”

“…Besides using single measurements as the controlled variables, selecting linear combinations of measurements will further improve the self-optimizing control performance. Two methods that achieve this are the Exact local method [5], [6] and the Null-space method [7]. Both the Null-space and the Exact local method offers sets, consisting of an infinite number of possibilities for choosing the measurement combinations.…”