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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Fig. 1

NMPC based state estimator architecture

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Fig. 4

Three tank system description

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Fig. 2

Adaptive NMPC based state estimator

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Fig. 5

Pumps characteristic

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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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