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Technical Brief

Nonlinear Parameters and State Estimation for Adaptive Nonlinear Model Predictive Control Design

[+] Author and Article Information
Hichem Salhi

Université de Tunis El Manar,
Faculté des Sciences de Tunis,
LR11ES20, Laboratoire Analyse,
Conception et Commande des Systèmes,
BP 37, LE Belvedere 1002 Tunis, Tunisie
e-mail: salhi-hichem85@hotmail.com

Faouzi Bouani

Université de Tunis El Manar,
Ecole Nationale d'Ingénieurs de Tunis,
LR11ES20, Laboratoire Analyse,
Conception et Commande des Systèmes,
BP 37, LE Belvedere 1002 Tunis, Tunisie
e-mail: bouani.faouzi@yahoo.fr

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received June 24, 2015; final manuscript received December 25, 2015; published online February 3, 2016. Assoc. Editor: Dejan Milutinovic.

J. Dyn. Sys., Meas., Control 138(4), 044502 (Feb 03, 2016) (8 pages) Paper No: DS-15-1287; doi: 10.1115/1.4032482 History: Received June 24, 2015; Revised December 25, 2015

This paper deals with an adaptive nonlinear model predictive control (NMPC) based estimator in cases of mismatch modeling, presence of perturbations and/or parameter variations. Thus, we propose an adaptive nonlinear predictive controller based on the second-order divided difference filter (DDF) for multivariable systems. The controller uses a nonlinear state-space model for parameters and state estimation and for the control law synthesis. Two nonlinear optimization layers are included in the proposed algorithm. The first optimization problem is based on the output error (OE) model with a tuning factor, and it is dedicated to minimize the error between the model and the system at each sample time by estimating unknown parameters when assuming that all system states are available. The second optimization layer is used by the centralized nonlinear predictive controller to generate the control law which minimizes the error between future setpoints and future outputs along the prediction horizon. The proposed algorithm leads to a good tracking performance with an offset-free output and an effectiveness in perturbation attenuation. Practical results on a real setup show the reliability of the proposed approach.

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References

Adetola, V. , DeHaan, D. , and Guay, M. , 2009, “ Adaptive Model Predictive Control for Constrained Nonlinear Systems,” Syst. Control Lett., 58(5), pp. 320–326. [CrossRef]
Yang, J. , Xiao, L. , Qian, J. , and Li, H. , 2012, “ Output Tracking of Constrained Nonlinear Processes With Offset-Free Input-to-State Stable Fuzzy Predictive Control,” Int. J. Syst. Sci., 43(3), pp. 475–490. [CrossRef]
Tanaskovic, M. , Fagiano, L. , Smith, R. , and Morari, M. , 2014, “ Adaptive Receding Horizon Control for Constrained MIMO Systems,” Automatica, 50(12), pp. 3019–3029. [CrossRef]
Pan, L. , Shen, J. , and Luh, P. , 2012, “ Adaptive General Predictive Control Using Optimally Scheduled Multiple Models for Parallel-Coursing Utility Units With a Header,” ASME J. Dyn. Syst., Meas. Control, 134(4), p. 041008. [CrossRef]
Limon, D. , Alvarado, I. , Alamo, T. , and Camacho, E. , 2010, “ Robust Tube-Based MPC for Tracking of Constrained Linear Systems With Additive Disturbances,” J. Process Control, 20(3), pp. 248–260. [CrossRef]
Zhang, T. , Feng, G. , and Zeng, X. , 2009, “ Nonlinear Model Predictive Control Using Parameter Varying BP-ARX Combination Model,” Automatica, 45(4), pp. 900–909. [CrossRef]
Sawadogo, S. , Faye, R. , and Mora-Camino, F. , 2001, “ Decentralized Adaptive Predictive Control of Multireach Irrigation Canal,” Int. J. Syst. Sci., 32(10), pp. 1287–1296. [CrossRef]
Maeder, U. , and Morari, M. , 2010, “ Offset-Free Reference Tracking With Model Predictive Control,” Automatica, 46(9), pp. 1469–1476. [CrossRef]
Horváth, K. , Galvis, E. , Valentín, M. , and Rodellar, J. , 2015, “ New Offset-Free Method for Model Predictive Control of Open Channels,” Control Eng. Pract., 41, pp. 567–572. [CrossRef]
Salhi, H. , Bouani, F. , and Ksouri, M. , 2013, “ Constrained MIMO Nonlinear Predictive Control Based Derivate-Free State Estimators,” International Conference on Control, Decision and Information Technologies (CoDIT), Hammamet, Tunisia.
Prakash, J. , Patwardhan, S. , and Shah, S. , 2010, “ State Estimation and Nonlinear Predictive Control of Autonomous Hybrid System Using Derivative Free State Estimators,” Control Eng. Pract., 20(7), pp. 787–799. [CrossRef]
Madonski, R. , and Herman, P. , 2015, “ Survey on Methods of Increasing the Efficiency of Extended State Disturbance Observers,” ISA Trans., 56, pp. 18–27. [CrossRef] [PubMed]
Morari, M. , and Maeder, U. , 2012, “ Nonlinear Offset-Free Model Predictive Control,” Automatica, 48(9), pp. 2059–2067. [CrossRef]
Bavdekar, V. , Deshpande, A. , and Patwardhan, S. , 2011, “ Identification of Process and Measurement Noise Covariance for State and Parameter Estimation Using Extended Kalman Filter,” J. Process Control, 21(4), pp. 585–601. [CrossRef]
Liu, C. , Chen, W. , and Andrews, J. , 2012, “ Tracking Control of Small-Scale Helicopters Using Explicit Nonlinear MPC Augmented With Disturbance Observers,” Control Eng. Pract., 20(3), pp. 258–268. [CrossRef]
Nagy, Z. , Mahn, B. , Franke, R. , and Frank, A. , 2007, “ Evaluation Study of an Efficient Output Feedback Nonlinear Model Predictive Control for Temperature Tracking in an Industrial Batch Reactor,” Control Eng. Pract., 15(7), pp. 839–850. [CrossRef]
Tan, C. , Setiawan, R. , Bao, J. , and Bickert, G. , 2015, “ Studies on Parameter Estimation and Model Predictive Control of Paste Thickeners,” J. Process Control, 28, pp. 1–8. [CrossRef]
Adetola, V. , and Guay, M. , 2010, “ Integration of Real-Time Optimization and Model Predictive Control,” J. Process Control, 20(2), pp. 125–133. [CrossRef]
Biegler, L. , Yang, X. , and Fischer, G. , 2015, “ Advances in Sensitivity-based Nonlinear Model Predictive Control and Dynamic Real-time Optimization,” J. Process Control, 30, pp. 104–116. [CrossRef]
Isaksson, A. , Sjöberg, J. , Törnqvist, D. , Ljung, L. , and Kok, M. , 2015, “ Using Horizon Estimation and Nonlinear Optimization for Grey-Box Identification,” J. Process Control, 30, pp. 69–79. [CrossRef]
Opalka, J. , and Hubka, L. , 2015, “ Nonlinear State and Unmeasured Disturbance Estimation for Use in Power Plant Superheaters Control,” Procedia Eng., 100, pp. 1539–1546. [CrossRef]
Marchetti, A. , Ferramosca, A. , and Gonzalez, A. , 2014, “ Steady-State Target Optimization Designs for Integrating Real-Time Optimization and Model Predictive Control,” J. Process Control, 24(1), pp. 129–145. [CrossRef]
Norgaard, M. , Poulsen, N. , and Ravn, O. , 2000, “ New Developments in State Estimation for Nonlinear Systems,” Automatica, 36(11), pp. 1627–1638. [CrossRef]
Salhi, H. , Bouani, F. , and Ksouri, M. , 2012, “ MIMO Nonlinear Control Based on Divided Difference Filters,” Trans. Syst. Signals Device, 7(1), pp. 67–88.
Salhi, H. , Bouani, F. , and Ksouri, M. , 2011, “ Three Tanks Level Estimation Using Divided Difference Filter,” International Conference on Communications, Computing and Control Applications, Hammamet, Tunisia.
Huang, R. , Patwardhan, S. , and Biegler, L. , 2010, “ Stability of a Class of Discrete-Time Nonlinear Recursive Observers,” J. Process Control, 20(10), pp. 1150–1160. [CrossRef]
Huang, R. , Patwardhan, S. , and Biegler, L. , 2012, “ Robust Stability of Nonlinear Model Predictive Control Based on Extended Kalman Filter,” J. Process Control, 22(1), pp. 82–89. [CrossRef]

Figures

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Fig. 1

NMPC based state estimator architecture

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Fig. 4

Three tank system description

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Fig. 5

Pumps characteristic

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Fig. 2

Adaptive NMPC based state estimator

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Fig. 7

Variation of parameters with γ = 0

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Fig. 8

h3 estimation with γ = 0

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Fig. 9

Outputs and control signals with γ = 0

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Fig. 10

Outputs and control signals

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Fig. 11

Parameter estimation under constraints

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Fig. 12

h3 level estimation

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Fig. 6

Outputs and control signals without parameter estimation

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Fig. 17

h3 estimation in the presence of perturbation

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Fig. 18

Outputs and control signals in the presence of perturbations

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Fig. 13

Variation of parameters with γ = 0.001

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Fig. 14

h3 estimation with γ = 0.001

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Fig. 15

Outputs and control signals with γ = 0.001

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Fig. 16

Variation of parameters in the presence of perturbation

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