Convex formulations for optimal selection of controlled variables and measurements using Mixed Integer Quadratic Programming

Abstract The appropriate selection of controlled variables is important for operating a process optimally in the presence of disturbances. Self-optimizing control provides a mathematical framework for selecting the controlled variables as combinations of measurements, c  =  Hy , with the aim to minimize the steady state loss from optimal operation. In this paper, we present (i) a convex formulation to find the optimal combination matrix H for a given measurement set and (ii) a Mixed-Integer Quadratic Programming (MIQP) methodology to select optimal measurement subsets that result in minimal loss. The methods presented in this paper are exact for quadratic problems with linear measurement relations. The MIQP methods can handle additional structural constraints compared to the branch and bound (BAB) methods reported in literature. The MIQP methods are evaluated on a toy test problem, an evaporator example, a binary distillation column example with 41 stages and a Kaibel column with 71 stages.

[1]  Sigurd Skogestad,et al.  Optimal Selection of Controlled Variables , 2003 .

[2]  Thomas E. Marlin,et al.  Integrating process and controller models for the design of self-optimizing control , 2000 .

[3]  Vladik Kreinovich,et al.  Formulation of the Problem , 2012 .

[4]  Geoff Barton,et al.  Interaction between process design and process control: economic analysis of process dynamics , 1991 .

[5]  R. B. Newell,et al.  Applied Process Control: A Case Study , 1989 .

[6]  Sigurd Skogestad.  Plantwide control: the search for the self-optimizing control structure , 2000 .

[7]  Dominique Bonvin,et al.  Dynamic optimization of batch processes: I. Characterization of the nominal solution , 2003, Comput. Chem. Eng..

[8]  M. Guay,et al.  ADAPTIVE EXTREMUM SEEKING CONTROL OF NONLINEAR DYNAMIC SYSTEMS WITH PARAMETRIC UNCERTAINTIES , 2002 .

[9]  Sebastian Engell.  Feedback control for optimal process operation , 2007 .

[10]  Juan Yianatos,et al.  The long way toward multivariate predictive control of flotation processes , 2011 .

[11]  S. Palanki,et al.  Dynamic Optimization of Batch Processes : II . Handling Uncertainty Using Measurements , 2001 .

[12]  Yi Cao,et al.  Bidirectional branch and bound for controlled variable selection: Part I. Principles and minimum singular value criterion , 2008, Comput. Chem. Eng..

[13]  María Auxilio Osorio Lama,et al.  Mixed Logical-linear Programming , 1999, Discret. Appl. Math..

[14]  Sigurd Skogestad,et al.  NULL SPACE METHOD FOR SELECTING OPTIMAL MEASUREMENT COMBINATIONS AS CONTROLLED VARIABLES , 2007 .

[15]  J. D. Perkins,et al.  Selection of process control structure based on linear dynamic economics , 1993 .

[16]  Sigurd Skogestad,et al.  Application of plantwide control to the HDA process. I-steady-state optimization and self-optimizing control , 2007 .

[17]  Thomas E. Marlin,et al.  Design cost: a systematic approach to technology selection for model-based real-time optimization systems , 1996 .

[18]  Sigurd Skogestad,et al.  STABILIZING OPERATION OF A 4-PRODUCT INTEGRATED KAIBEL COLUMN , 2006 .

[19]  Yi Cao,et al.  Bidirectional Branch and Bound for Controlled Variable Selection Part III: Local Average Loss Minimization , 2010, IEEE Transactions on Industrial Informatics.

[20]  Vinay Kariwala,et al.  Optimal Measurement Combination for Local Self-Optimizing Control , 2007 .

[21]  Manfred Morari,et al.  Studies in the synthesis of control structures for chemical processes: Part I: Formulation of the problem. Process decomposition and the classification of the control tasks. Analysis of the optimizing control structures , 1980 .

[22]  Dominique Bonvin,et al.  Optimal Grade Transition in Industrial Polymerization Processes via NCO Tracking , 2007 .

[23]  Sigurd Skogestad,et al.  Minimum Energy Consumption in Multicomponent Distillation. 3. More Than Three Products and Generalized Petlyuk Arrangements , 2003 .

[24]  George Stephanopoulos,et al.  Studies in the synthesis of control structures for chemical processes: Part IV. Design of steady‐state optimizing control structures for chemical process units , 1980 .

[25]  Alan S. Foss,et al.  Critique of chemical process control theory , 1973 .

[26]  M. Krstić,et al.  Real-Time Optimization by Extremum-Seeking Control , 2003 .

[27]  Johan Löfberg,et al.  YALMIP : a toolbox for modeling and optimization in MATLAB , 2004 .

[28]  Sigurd Skogestad,et al.  Minimum Energy Consumption in Multicomponent Distillation. 1. V min Diagram for a Two , 2003 .

[29]  Wee Hwa Tay,et al.  Application and Evaluation of Three Methodologies for Plantwide Control of the Styrene Monomer Plant , 2009 .

[30]  Marc M. J. van de Wal,et al.  A review of methods for input/output selection , 2001, Autom..

[31]  S. Skogestad.  DYNAMICS AND CONTROL OF DISTILLATION COLUMNS A tutorial introduction , 1997 .

[32]  Ian Postlethwaite,et al.  Multivariable Feedback Control: Analysis and Design , 1996 .

[33]  Sigurd Skogestad,et al.  Economically efficient operation of CO2 capturing process. Part II. Design of control layer , 2012 .

[34]  S. Janardhanan,et al.  OPTIMAL MEASUREMENT COMBINATIONS AS CONTROLLED VARIABLES , 2007 .

[35]  Sigurd Skogestad,et al.  Selection of Controlled Variables: Maximum Gain Rule and Combination of Measurements , 2008 .

[36]  S. Janardhanan,et al.  LOCAL SELF-OPTIMIZING CONTROL WITH AVERAGE LOSS MINIMIZATION , 2008 .

[37]  Steffen Heldt,et al.  Dealing with structural constraints in self-optimizing control engineering , 2010 .

[38]  Dominique Bonvin,et al.  Dynamic optimization of batch processes: II. Role of measurements in handling uncertainty , 2003, Comput. Chem. Eng..

[39]  Yi Cao,et al.  Bidirectional branch and bound for controlled variable selection. Part II: Exact local method for self-optimizing control , 2009, Comput. Chem. Eng..