A Canonical Form for the Design of Unknown Input Sliding Mode Observers

Floquet, Thierry; Barbot, Jean–Pierre

doi:10.1007/11612735_13

Cited by 53 publications

(52 citation statements)

References 36 publications

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“…However, it is necessary that the system's unknown inputs and outputs satisfy the so-called matching condition [6]. To overcome this limitation, system coordinates transformation are introduced and the use of sliding mode differentiator (SMD) for the auxiliary output generation is generalized [7], [8]. This allows to use a powerful optimization technique, like linear matrix inequality (LMI), to offer a systematic design procedure of the observer gain [9].…”

Section: Lfridman@servidorunammxmentioning

confidence: 99%

Lean and steering motorcycle dynamics reconstruction: An unknown-input HOSMO approach

Nehaoua

Ichalal

Arioui

et al. 2013

2013 American Control Conference

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Abstract-This paper deals with state estimation of Powered Two Wheeled (PTW) vehicle and robust reconstruction of related unknown inputs. For this purpose, we consider a unknown input high order sliding mode observer (UIHOSMO). First, a motorcycle dynamic model is derived using JourdainŠs principle. In a second time, we consider both the observation of the PTW dynamic states, the reconstruction of the lean dynamics (roll angle φ(t)) and the rider's torque applied on the handlebar. Finlay, several simulation cases are provided to illustrate the efficiency of the proposed observer.

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Section: Lfridman@servidorunammxmentioning

confidence: 99%

Lean and steering motorcycle dynamics reconstruction: An unknown-input HOSMO approach

Nehaoua

Ichalal

Arioui

et al. 2013

2013 American Control Conference

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“…[25]; it is also used in Lyapunov-based designs as in e.g., [27] and [16] or in order to decompose the system, as in [30] and [12]. A notable exception (for linear systems) is [14] where the authors propose a method to transform the system into a new canonical form; however, even though the authors of [14] succeed in avoiding the relative degree one assumption, it is assumed that measurements are noise-free i.e., y = C 0 x * . This work was extended in [6] to the case of nonlinear systems, yet locally transformed into a specific triangular observable form, for which a higher order sliding mode observer was introduced.…”

Section: Problem Statementmentioning

confidence: 99%

“…The method has been successfully used in the design of high-order sliding mode estimators; in this case, one may establish finite-time estimation and unknown input reconstruction recursively (step by step). See for instance [6,14] as well as the works on high-order differentiators by [20,21]. The main and clear disadvantage of this method is that it relies on coordinate transformations which are valid locally.…”

mentioning

confidence: 99%

Continuously-implemented sliding-mode adaptive unknown-input observers under noisy measurements

Dimassi

Lorı́a

Belghith

2012

Systems & Control Letters

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We propose an estimator for nonlinear systems with unmatched unknown inputs and under measurement noise. The estimator design is based on the combination of observer design for descriptor systems, sliding-modes theory and adaptive control. The estimation of the measurement noise is achieved thanks to the transformation of the original system into a singular form where the measurement noise makes part of the augmented state. Two adaptive parameters are updated online, one to compensate for the unknown bounds on the states, the unkown inputs and the measurement noise and a second one to compensate for the effect of the nonlinearities. To join robust state estimation and unknown-inputs reconstruction, our approach borrows inpiration from sliding-mode theory however, all signals are comtinuously implemented. We demonstrate that both state and unknown-inputs estimation are achieved up to arbitrarily small tolerance. The utility of our theoretical results is illustrated through simulation case-studies.

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“…It can be shown (see [18] and [28]) that with a suitable choice of gains λ s and α s , a sliding mode appears in finite time on the manifoldξ 1 = · · · =ξ l = 0, and that the following equivalent output injection is obtained:…”

Section: A Sliding Mode Observer For a Triangular Observable Formmentioning

confidence: 99%

“…In addition, the method given in this paper enables estimation of the unknown inputs. Define (v c ) eq as the equivalent output error injection required to maintain the sliding motion in (18). During the sliding motion, one can write thatṡ…”

Section: First/second Order Sliding Mode Unknown Input Observermentioning

confidence: 99%

On sliding mode observers for systems with unknown inputs

Floquet

Edwards

Spurgeon

2007

Adaptive Control & Signal

231

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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A Canonical Form for the Design of Unknown Input Sliding Mode Observers

Cited by 53 publications

References 36 publications

Lean and steering motorcycle dynamics reconstruction: An unknown-input HOSMO approach

Lean and steering motorcycle dynamics reconstruction: An unknown-input HOSMO approach

Continuously-implemented sliding-mode adaptive unknown-input observers under noisy measurements

On sliding mode observers for systems with unknown inputs

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