Model structure simplification of a biological reactor

Nagy, Anca Maria; Mourot, Gilles; Marx, Benoît; Schutz, Georges; Ragot, José

doi:10.3182/20090706-3-fr-2004.00043

Cited by 26 publications

(26 citation statements)

References 14 publications

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“…It can also be obtained by black-box approaches, which allow identifying the parameters of the model from inputoutput data. Finally, a T-S model can be obtained from the well-known nonlinear sector transformations (Tanaka and Wang, 2001;Nagy et al, 2009). These transformations allow obtaining an exact T-S representation of a nonlinear model with no information loss on a compact set of the state space.…”

Section: Takagi-sugeno Structure For Modelingmentioning

confidence: 99%

New fault tolerant control strategies for nonlinear Takagi-Sugeno systems

Ichalal¹,

Marx²,

Ragot³

et al. 2012

International Journal of Applied Mathematics and Computer Science

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New methodologies for Fault Tolerant Control (FTC) are proposed in order to compensate actuator faults in nonlinear systems. These approaches are based on the representation of the nonlinear system by a Takagi-Sugeno model. Two control laws are proposed requiring simultaneous estimation of the system states and of the occurring actuator faults. The first approach concerns the stabilization problem in the presence of actuator faults. In the second, the system state is forced to track a reference trajectory even in faulty situation. The control performance depends on the estimation quality; indeed, it is important to accurately and rapidly estimate the states and the faults. This task is then performed with an Adaptive Fast State and Fault Observer (AFSFO) for the first case, and a Proportional-Integral Observer (PIO) in the second. Stability conditions are established with Lyapunov theory and expressed in a Linear Matrix Inequality (LMI) formulation to ease the design of FTC. Furthermore, relaxed stability conditions are given with the use of Polya's theorem. Some simulation examples are given in order to illustrate the proposed approaches.

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Section: Takagi-sugeno Structure For Modelingmentioning

confidence: 99%

New fault tolerant control strategies for nonlinear Takagi-Sugeno systems

Ichalal¹,

Marx²,

Ragot³

et al. 2012

International Journal of Applied Mathematics and Computer Science

Self Cite

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“…Note that a general sector nonlinearity approach has been recently proposed in [16] allowing an adequate choice of additional parameters in order to ensure the observability of the local models (namely, the pairs (A i ,C i )). In our problem, this result can be used in order to guarantee the observability of the pairs (A i + A,C).…”

Section: New Observer Design Algorithmmentioning

confidence: 99%

Observer for Lipschitz nonlinear systems: Mean Value Theorem and sector nonlinearity transformation

Ichalal

Marx

Mammar

et al. 2012

2012 IEEE International Symposium on Intelligent Control

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To cite this version:Abstract-The problem of observer design for nonlinear Lipschitz systems is dealt with in this work. An emphasis is put on the maximization of the admissible Lipschitz constant for which the observer design is possible. This problem is tackled using a Takagi-Sugeno modeling approach. The idea is to rewrite the state estimation error dynamics as an autonomous Takagi-Sugeno system, using the Mean Value Theorem and the sector nonlinearity transformation. State estimation error dynamics stability is studied with the Lyapunov theory by choosing a non-quadratic Lyapunov function and by computing its variation between m consecutive samples. The interest of these manipulations is to obtain LMI conditions admitting solutions for large values of the Lipschitz constant. Finally, illustrative examples are provided in order to highlight the performances of the proposed approach.

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“…The method used here avoids this particular loss and gives an equivalent multiple model form of the initial nonlinear system. Only a brief description of the important points of this method will be given as follows, the technical details can be found in [9]. Considering a nonlinear system with bounded nonlinearities, it can be written in a quasi linear-parameter-varying form:…”

Section: B the Multiple Model Representationmentioning

confidence: 99%

“…The main drawbacks of this technique are: the loss of information, the choice of the premise variables expressing different nonlinearities of the system is not systematically realized, the choice of different operating points still remains very delicate. The method used here avoids this particular loss and gives an equivalent multiple model form of the initial nonlinear system [9]. In addition to that, the method offers several multiple models with different structures, depending on the choice of premise variables.…”

Section: Introductionmentioning

confidence: 99%

State estimation of the three-tank system using a multiple model

Nagy¹,

Marx²,

Mourot³

et al. 2009

Proceedings of the 48h IEEE Conference on Decision and Control (CDC) Held Jointly With 2009 28th Chinese Control Conference

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Abstract-This paper addresses the exact transformation of nonlinear systems into a multiple model form with unmeasurable premise variables. The multiple model structure serves to treat the observability and the state estimation problem of nonlinear systems. Using a method with no information loss, a nonlinear system is transformed into a multiple model, depending on the choice of premise variables. It is a key point, since it allows to choose, between different multiple model forms, the one that has suitable structure and properties, in order to design an observer. The convergence conditions of the state estimation error are expressed in LMI formulation using the Lyapunov method. These proposals are investigated and applied to the three-tank system.

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Model structure simplification of a biological reactor

Cited by 26 publications

References 14 publications

New fault tolerant control strategies for nonlinear Takagi-Sugeno systems

New fault tolerant control strategies for nonlinear Takagi-Sugeno systems

Observer for Lipschitz nonlinear systems: Mean Value Theorem and sector nonlinearity transformation

State estimation of the three-tank system using a multiple model

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