Online model-based redesign of experiments with erratic models: A disturbance estimation approach

Abstract Model-based design of experiment (MBDoE) techniques are a useful tool to maximise the information content of experimental trials when the purpose is identifying the set of parameters of a deterministic model in a statistically sound way. In a conventional MBDoE procedure, the information gathered during the evolution of an experiment is exploited only at the end of the experiment itself. Conversely, online model-based redesign of experiment (OMBRE) techniques have been recently proposed to exploit the information as soon as it is generated by the running experiment, allowing for the dynamic update of the experimental conditions to yield the most informative data in order to improve the parameter identification task. However, the effectiveness of MBDoE strategies (including OMBRE) may be severely affected by the presence of systematic modelling errors as well as by disturbances acting on the system. In this paper, a novel experiment design approach (DE-OMBRE) is presented, where a model updating policy including disturbance estimation (DE) is embedded within an OMBRE strategy in order to achieve a statistically satisfactory estimation of the model parameters as well as to estimate the possible discrepancy between the real system and the model being identified. The procedure allows reducing (or even avoiding) constraint violations, preserving the optimality of the redesign even in the presence of systematic errors and/or unknown disturbances acting on the system. Two simulated case studies of different levels of complexity are used to illustrate the benefits of the novel approach.

[1]  Håkan Hjalmarsson,et al.  Identification for control: adaptive input design using convex optimization , 2001 .

[2]  K Bernaerts,et al.  Simultaneous versus sequential optimal experiment design for the identification of multi-parameter microbial growth kinetics as a function of temperature. , 2010, Journal of theoretical biology.

[3]  G. Pannocchia,et al.  On the use of Nonlinear Model Predictive Control for pharmacological therapy optimization , 2010, 2010 IEEE Workshop on Health Care Management (WHCM).

[4]  Sandro Macchietto,et al.  The optimal design of dynamic experiments , 1989 .

[5]  Kenneth R. Muske,et al.  Disturbance modeling for offset-free linear model predictive control , 2002 .

[6]  Manfred Morari,et al.  Linear offset-free Model Predictive Control , 2009, Autom..

[7]  Alberto Bemporad,et al.  Combined Design of Disturbance Model and Observer for Offset-Free Model Predictive Control , 2007, IEEE Transactions on Automatic Control.

[8]  Sandro Macchietto,et al.  Model-Based Design of Parallel Experiments , 2007 .

[9]  Jan F. M. Van Impe,et al.  Optimal dynamic experiment design for estimation of microbial growth kinetics at sub-optimal temperatures: Modes of implementation , 2005, Simul. Model. Pract. Theory.

[10]  Federico Galvanin.  Optimal design of clinical tests for the identification of physiological models of type 1 diabetes mellitus in the presence of model uncertainty , 2009 .

[11]  E. Davison,et al.  Pole assignment in linear time-invariant multivariable systems with constant disturbances , 1971 .

[12]  Jan M. Maciejowski,et al.  Predictive control : with constraints , 2002 .

[13]  R. Sargent,et al.  Solution of a Class of Multistage Dynamic Optimization Problems. 2. Problems with Path Constraints , 1994 .

[14]  Luca Costantino Zullo.  Computer aided design of experiments : an engineering approach , 1991 .

[15]  O. Levenspiel.  The monod equation: A revisit and a generalization to product inhibition situations , 1980 .

[16]  Thomas F. Edgar,et al.  PCA Combined Model-Based Design of Experiments (DOE) Criteria for Differential and Algebraic System Parameter Estimation , 2008 .

[17]  Vinay Prasad,et al.  Multiscale Model and Informatics-Based Optimal Design of Experiments : Application to the Catalytic Decomposition of Ammonia on Ruthenium , 2008 .

[18]  J. D. Stigter,et al.  On adaptive optimal input design: A bioreactor case study , 2006 .

[19]  Sten Bay Jørgensen,et al.  A method for systematic improvement of stochastic grey-box models , 2004, Comput. Chem. Eng..

[20]  L. A. Stone,et al.  Computer Aided Design of Experiments , 1969 .

[21]  Gabriele Pannocchia,et al.  Disturbance models for offset‐free model‐predictive control , 2003 .

[22]  Johannes P. Schlöder,et al.  Numerical methods for optimal control problems in design of robust optimal experiments for nonlinear dynamic processes , 2004, Optim. Methods Softw..

[23]  Harvey Arellano-Garcia,et al.  Handling Uncertainty in Model-Based Optimal Experimental Design , 2010 .

[24]  F. Pukelsheim.  Optimal Design of Experiments , 1993 .

[25]  Eric Walter,et al.  On the identifiability and distinguishability of nonlinear parametric models , 1996 .

[26]  Massimiliano Barolo,et al.  Online Model-Based Redesign of Experiments for Parameter Estimation in Dynamic Systems , 2009 .

[27]  Håkan Hjalmarsson,et al.  Identification of ARX systems with non-stationary inputs - asymptotic analysis with application to adaptive input design , 2009, Autom..

[28]  Sandro Macchietto,et al.  Statistical tools for optimal dynamic model building , 2000 .

[29]  Venkat Venkatasubramanian,et al.  High fidelity mathematical model building with experimental data: A Bayesian approach , 2008, Comput. Chem. Eng..

[30]  Raman K. Mehra,et al.  Optimal input signals for parameter estimation in dynamic systems--Survey and new results , 1974 .

[31]  E D Lehmann,et al.  A physiological model of glucose-insulin interaction in type 1 diabetes mellitus. , 1992, Journal of biomedical engineering.

[32]  T. Brubaker,et al.  Nonlinear Parameter Estimation , 1979 .

[33]  Manfred Morari,et al.  Nonlinear offset-free model predictive control , 2012, Autom..

[34]  Axel Munack,et al.  Design of Optimal Dynamical Experiments for Parameter Estimation , 1989, 1989 American Control Conference.