Sliding mode observer for nonlinear uncertain systems

Xiong, Yi; Saif, Mehrdad

doi:10.1109/9.975511

Cited by 257 publications

(161 citation statements)

References 24 publications

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“…Most of the sliding mode observer designs for (10) are based on a step-bystep procedure using successive filtered values of the so-called equivalent output injections obtained from recursive first order sliding mode observers (see e.g. [1,8,9,19,26,36]). However, the approximation of the equivalent injections by low pass filters at each step will typically introduce some delays that lead to inaccurate estimates or to instability for high order systems.…”

Section: A Sliding Mode Observer For a Triangular Observable Formmentioning

confidence: 99%

On sliding mode observers for systems with unknown inputs

Floquet

Edwards

Spurgeon

2007

Adaptive Control & Signal

233

106

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This paper considers the problem of designing an observer for a linear system subject to unknown inputs. This problem has been extensively studied in the literature with respect to both linear and nonlinear (sliding mode) observers. Necessary and sufficient conditions to enable a linear unknown input observer to be designed have been established for many years. One way to express these conditions is that the transfer function matrix between the unknown input and the measured output must be minimum phase and relative degree one. Identical conditions must be met in order to design a 'classical' sliding mode observer for the same problem. This paper shows how the relative degree condition can be weakened if a classical sliding mode observer is combined with sliding mode exact differentiators to essentially generate additional independent output signals from the available measurements. A practical example dedicated to actuator fault detection and identification of a winding machine demonstrates the efficacy of the approach.

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Section: A Sliding Mode Observer For a Triangular Observable Formmentioning

confidence: 99%

On sliding mode observers for systems with unknown inputs

Floquet

Edwards

Spurgeon

2007

Adaptive Control & Signal

233

106

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“…Using an additive nonlinear discontinuous term, SMO constraints the trajectory of the estimation error to remain on a specific surface after finite time such that error is completely insensitive to the disturbances. This interesting property has been utilized either for state estimation [7], [8], [9] and fault detection and isolation [10].…”

Section: Introductionmentioning

confidence: 99%

Design of sliding mode unknown input observer for uncertain Takagi-Sugeno model

Akhenak

Chadli²,

Ragot

et al. 2007

2007 Mediterranean Conference on Control &Amp; Automation

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To cite this version:Abdelkader Akhenak, Mohammed Chadli, José Ragot, Didier Maquin. Design of sliding mode unknown input observer for uncertain Takagi-Sugeno model. P. Antsaklis K. Valavanis Abstract-This paper addresses the analysis and design of a sliding mode observer on the basis of a Takagi-Sugeno (T-S) model subject both to unknown inputs and uncertainties. The main contribution of the paper is the development of a robust observer with respect to the uncertainties as well as the synthesis of sufficient stability conditions of this observer. The stabilization of the observer is performed by the search of suitable Lyapunov matrices. It is shown how to determine the gains of the local observers, these gains being solutions of a set of linear matrix inequalities (LMI). The validity of the proposed methodology is illustrated by an academic example. I. INTRODUCTIONState estimation of linear time-invariant dynamical system driven by both known and unknown inputs has been the subject of many research works [1], [2], [3]. Indeed, in practice, there are many situations where some of the inputs to the system are inaccessible. The recourse to the use of an unknown input observer is then necessary in order to be able to estimate the state of the considered system. This state estimate can be useful either for designing a control law and/or for supervision task. Indeed, in the context of instrument fault detection and isolation, most actuator failures can be generally modelled as unknown inputs to the system [2].In parallel, sliding mode observers (SMO) have received large attention since it offers robustness properties with regard uncertainties [4], [5], [6]. Using an additive nonlinear discontinuous term, SMO constraints the trajectory of the estimation error to remain on a specific surface after finite time such that error is completely insensitive to the disturbances. This interesting property has been utilized either for state estimation [7], [8], [9] and fault detection and isolation [10].All that relates to the linear models was largely developed in the literature. However, this assumption of linearity is checked only in a limited vicinity of a particular operating point. The T-S model approach can apprehend the nonlinear behaviour of a system, while keeping the simplicity of the linear models.Indeed, the real physical systems are often nonlinear. As it is delicate to synthesize an observer for an unspecified nonlinear system, it is preferable to represent this system with a T-S model. The idea of the T-S model

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“…For nonlinear systems without delays, the observability problem has been exhaustively studied, and is characterized respectively by Hermann and Krener (1977); Sontag (1984); Krener (1985) from a differential point of view, and by Diop and Fliess (1991) from an algebraic point of view. For observable systems, many types of nonlinear observers were proposed, such as high-gain observer in Gauthier et al (1992), algebraic observer in , sliding mode observer in Xiong and Saif (2001); and so on.…”

Section: Introductionmentioning

confidence: 99%