Algorithms with state estimation in linear and nonlinear model predictive control

Abstract Model predictive control (MPC) algorithms with state-space process modelling, both linear and nonlinear, and state estimation methods for this algorithms are the subject of this paper. The considerations are under realistic assumption that processes are under influence of external disturbances and their models are not precise. This leads in most cases to errors in state estimation and, further, may lead to errors in feedback control. Attention has been paid to this problem in recent years. Two approaches are now available, an earlier one with additional disturbance state modelling and process-and-disturbance state estimation and a more recently proposed approach with different way of disturbance modelling and estimation of the process state only. The main aim of this paper is to provide a comprehensive comparison of the two mentioned approaches, including also discussion of available state estimation algorithms. To the best knowledge of the authors, there is still a lack of clear understanding of the differences between the mentioned approaches, in particular from practical point of view. After short presentation of the two methods and analysis of their theoretical aspects, a comprehensive comparative analysis is provided on a nonlinear example of the polymerization reactor.

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

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

[3]  Prashant Mhaskar,et al.  Model predictive control of uni-axial rotational molding process , 2019, Comput. Chem. Eng..

[4]  Ronald K. Pearson,et al.  Nonlinear model-based control using second-order Volterra models , 1995, Autom..

[5]  Marcello Farina,et al.  Assessment and comparison of distributed model predictive control schemes: Application to a natural gas refrigeration plant , 2016, Comput. Chem. Eng..

[6]  Junmo Koo,et al.  Design of a self-tuning adaptive model predictive controller using recursive model parameter estimation for real-time plasma variable control , 2019, Comput. Chem. Eng..

[7]  C. V. Rao,et al.  Steady states and constraints in model predictive control , 1999 .

[8]  John Anthony Rossiter.  Model-Based Predictive Control , 2003 .

[9]  Piotr Tatjewski.  ADVANCED CONTROL AND ON-LINE PROCESS OPTIMIZATION IN MULTILAYER STRUCTURES , 2007 .

[10]  S. Joe Qin,et al.  A survey of industrial model predictive control technology , 2003 .

[11]  Hugh F. Durrant-Whyte,et al.  A new method for the nonlinear transformation of means and covariances in filters and estimators , 2000, IEEE Trans. Autom. Control..

[12]  Piotr Tatjewski,et al.  Offset-Free Nonlinear Model Predictive Control , 2017, KKA.

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

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

[15]  Keyu Li,et al.  8th International IFAC Symposium on Dynamics and Control of Process Systems CONSTRAINED EXTENDED KALMAN FILTER FOR NONLINEAR STATE ESTIMATION , 2007 .

[16]  Piotr Tatjewski,et al.  Offset-free nonlinear Model Predictive Control with state-space process models , 2017 .

[17]  M. Zeitz,et al.  Extended Luenberger observer for non-linear multivariable systems , 1988 .

[18]  H.F. Durrant-Whyte,et al.  A new approach for filtering nonlinear systems , 1995, Proceedings of 1995 American Control Conference - ACC'95.

[19]  Piotr Tatjewski,et al.  Disturbance modeling and state estimation for offset-free predictive control with state-space process models , 2014, Int. J. Appl. Math. Comput. Sci..

[20]  Rahul Bindlish,et al.  Nonlinear model predictive control of an industrial process with steady-state gain inversion , 2020, Comput. Chem. Eng..

[21]  Alejandro H. González,et al.  Conditions for offset elimination in state space receding horizon controllers: A tutorial analysis , 2008 .

[22]  Maciej Lawrynczuk,et al.  Nonlinear State-Space Predictive Control With On-Line Linearisation And State Estimation , 2015, Int. J. Appl. Math. Comput. Sci..

[23]  V. B. Nguyen,et al.  POD-DEIM model order reduction technique for model predictive control in continuous chemical processing , 2020, Comput. Chem. Eng..

[24]  Maciej Lawrynczuk,et al.  Offset-free state-space nonlinear predictive control for Wiener systems , 2020, Inf. Sci..

[25]  Yiguo Li,et al.  Adaptive disturbance rejection model predictive control and its application in a selective catalytic reduction denitrification system , 2020, Comput. Chem. Eng..

[26]  Manuel Berenguel,et al.  Optimal operation of a Solar Membrane Distillation pilot plant via Nonlinear Model Predictive Control , 2018, Comput. Chem. Eng..

[27]  Astrom.  Computer Controlled Systems , 1990 .

[28]  Liuping Wang,et al.  Model Predictive Control System Design and Implementation Using MATLAB , 2009 .

[29]  Manfred Morari,et al.  Offset-free reference tracking with model predictive control , 2010, Autom..

[30]  Marko Bacic,et al.  Model predictive control , 2003 .

[31]  Piotr Tatjewski,et al.  Supervisory predictive control and on-line set-point optimization , 2010, Int. J. Appl. Math. Comput. Sci..

[32]  Rahul Bindlish,et al.  Nonlinear model predictive control of an industrial polymerization process , 2015, Comput. Chem. Eng..

[33]  Piotr Tatjewski,et al.  Soft computing in modelbased predictive control footnotemark , 2006 .