Lyapunov-based optimizing control of nonlinear blending processes

Blending processes consisting of linear dynamics and a static nonlinearity are considered. We propose a control law that optimizes the equilibrium point of the process and regulates the output to the corresponding equilibrium state. A control Lyapunov function (CLF) is used to derive a stable optimizing update law for the equilibrium point, in combination with a linear quadratic (LQ) feedback law for tracking the optimized equilibrium point. The analysis and design also incorporates the use of an observer for state and bias estimation. Experimental results using a laboratory scale colorant blending process illustrate the efficiency of the method.

[1]  Sigurd Skogestad,et al.  Self-optimizing control: the missing link between steady-state optimization and control , 2000 .

[2]  Jose Alvarez-Ramirez,et al.  Robustness of a Class of Bias Update Controllers for Blending Systems , 2002 .

[3]  E. Allen.  Basic Equations Used in Computer Color Matching , 1966 .

[4]  H. Rhee,et al.  Nonlinear Model Predictive Control Using a Wiener Model of a Continuous Methyl Methacrylate Polymerization Reactor , 2001 .

[5]  R. Abraham,et al.  Manifolds, Tensor Analysis, and Applications , 1983 .

[6]  Costas Kravaris,et al.  Deadtime compensation for nonlinear processes , 1989 .

[7]  Benoit Boulet,et al.  Multivariable control of a paper coloring process: a case study , 2001, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148).

[8]  P ? ? ? ? ? ? ? % ? ? ? ? , 1991 .

[9]  A. Diaz,et al.  Meet changing fuel requirements with online blend optimization , 1996 .

[10]  H. Bloemen,et al.  Wiener Model Identification and Predictive Control for Dual Composition Control of a Distillation Column , 2001 .

[11]  Evanghelos Zafiriou,et al.  Robust process control , 1987 .

[12]  D. Mayne.  Nonlinear and Adaptive Control Design [Book Review] , 1996, IEEE Transactions on Automatic Control.

[13]  D. Sbarbaro-Hofer,et al.  Optimizing control of over-actuated linear systems with nonlinear output maps via control Lyapunov functions , 2003, 2003 European Control Conference (ECC).

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

[15]  P. Bélanger.  Linear-programming approach to color-recipe formulations , 1974 .

[16]  John F. Forbes,et al.  Model-based real-time optimization of automotive gasoline blending operations , 2000 .

[17]  R. Subbarayan,et al.  A color measurement and control system for paper-making processes , 1996, Proceeding of the 1996 IEEE International Conference on Control Applications IEEE International Conference on Control Applications held together with IEEE International Symposium on Intelligent Contro.

[18]  Basil Kouvaritakis,et al.  Efficient Constrained Model Predictive Control with Asymptotic Optimality , 2002, SIAM J. Control. Optim..

[19]  D. Q. Mayne,et al.  Suboptimal model predictive control (feasibility implies stability) , 1999, IEEE Trans. Autom. Control..

[20]  Miroslav Krstic,et al.  Stability of extremum seeking feedback for general nonlinear dynamic systems , 2000, Autom..

[21]  Stephen J. Wright,et al.  Numerical Optimization , 2018, Fundamental Statistical Inference.

[22]  Anthony V. Fiacco,et al.  Nonlinear programming;: Sequential unconstrained minimization techniques , 1968 .

[23]  José A. Romagnoli,et al.  Application of Wiener model predictive control (WMPC) to a pH neutralization experiment , 1999, IEEE Trans. Control. Syst. Technol..

[24]  Aaas News,et al.  Book Reviews , 1893, Buffalo Medical and Surgical Journal.