Design of a Proportional Observer Based on the
Hassene BEDOUI*, Tarek GARNA,
Kamel BEN OTHMAN, Hassani MESSAOUD
LARATSI, National Engineering School of Monastir,
University of Monastir, Monastir, Tunisia
* Corresponding author
Abstract: A new ARX-Laguerre representation is recently built to model the dynamics of complex processes [1, 2]. The ARX-Laguerre models have proven their ability to accurately suit the behavior of systems. In this work, the model is exploited to diagnose the system by detecting its defaults. In this paper we build a proportional observer based on the ARX-Laguerre model. Therefore, the designed observer exploits the inputs and outputs of the Laguerre-ARX model to reconstruct the Laguerre filter outputs. The observer gain is calculated to ensure a fast asymptotic convergence of the estimation error. A simulation example is achieved to illustrate the ability of the proposed approach to estimate the Laguerre filter outputs.
Keywords: Diagnosis, ARX-Laguerre, proportional observer, SISO system, LMI, FDI.
CITE THIS PAPER AS:
Hassene BEDOUI, Tarek GARNA, Kamel BEN OTHMAN, Hassani MESSAOUD, Design of a Proportional Observer Based on theARX-Laguerre Model, Studies in Informatics and Control, ISSN 1220-1766, vol. 24 (4), pp. 471-476, 2015. https://doi.org/10.24846/v24i4y201511
The dynamics of physical processes are often modeled by mathematical relations.These relations are generally differential equations or state representations dedicated exclusively to theoretical models, transfer functions or regressive representations (ARX, ARMAX, Arimax). Recently, Bouzraraet al [1,2] proposed a new representationable to model the dynamics of complex physical processes. The proposed representation called ARX-Laguerre achieves a significant complexity reduction compared to the linear ARX standard model. The principle of the ARX-Laguerre model is based on filtering the input and the output of theARX standard model by the orthogonal Laguerre functions. This new representation is useful in case of observers based diagnosis for state representation modeled systems. Generally, observers used for linear systems are often Luenberger-ones or with proportional gain . In this work, we propose a proportional observer which can reconstructthe Laguerre filter outputs from the inputs and outputs of the ARX-Laguerre model.The reconstruction is achieved througha comparison between the outputs of the estimated Laguerre filters and the real outputs. The ARX-Laguerre based diagnosis is anew approach since the proposed model is recent [1,2].
This work is presented as follows: A theoretical study on the new ARX-Laguerre linear modeling is presented in Section 1, followed in the second section by developing its recursive representation used in the observer design. In the third section, we present the synthesis of proportional observer exploiting the ARX-Laguerre model.
This step is characterized by the development of the observer structure, the synthesis of gain matrices and Lyapunov ones. In addition, the conditions of existence of the observer are established. A work on improving the performance of the new observer is achieved in the same section. In the last section, the synthesis technique of the proportional observer is applied to an illustrative example showing the effectiveness of the developed method.
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