Sliding-mode observers for systems with unknown inputs: A high-gain approach

Kalsi, Karanjit; Lian, Jianming; Hui, Stefen; Żak, Stanisław H.

doi:10.1016/j.automatica.2009.10.040

Cited by 178 publications

(142 citation statements)

References 9 publications

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“…Applications of these UIOs require that the observer matching condition be satisfied [156,157], which states that the rank of the product of the output matrix and the unknown input matrix in the state space model of the system must be equal to that of the unknown input matrix [110]. However, existing PEA models, such as the one in [92], do not meet this condition.…”

Section: State Estimationmentioning

confidence: 99%

A Survey of Modeling and Control of Piezoelectric Actuators

Peng¹,

Xiongbiao²

2013

MME

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Piezoelectric actuators (PEAs) have been widely used in micro-and nanopositioning applications due to their fine resolution, fast responses, and large actuating forces. However, the existence of nonlinearities such as hysteresis makes modeling and control of PEAs challenging. This paper reviews the recent achievements in modeling and control of piezoelectric actuators. Specifically, various methods for modeling linear and nonlinear behaviors of PEAs, including vibration dynamics, hysteresis, and creep, are examined; and the issues involved are identified. In the control of PEAs as applied to positioning, a review of various control schemes of both model-based and non-model-based is presented along with their limitations. The challenges associated with the control problem are also discussed. This paper is concluded with the emerging issues identified in modeling and control of PEAs for future research.

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Section: State Estimationmentioning

confidence: 99%

A Survey of Modeling and Control of Piezoelectric Actuators

Peng¹,

Xiongbiao²

2013

MME

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“…In turn, the latter is necessary in most unknown-input observers designs -see e.g. [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 * .…”

Section: Problem Statementmentioning

confidence: 99%

“…To see this, note that using the triangle inequality 2ρρ ≤ ρ 2 +ρ 2 , we haveV ≤ −δ |S| − Corollary 2.1 Let Ω be a compact set and assume that x(t) ∈ Ω for all t. Consider the estimator given by (16), (31) and (17) and letρ ≡ ρ. Then, the sliding mode {S = 0} is reached in finite time.…”

Section: Adaptive Compensation Of Nonlinearitiesmentioning

confidence: 99%

“…Secondly, we show the same property forṠ(t) so that asymptotic practical stability may be concluded, in view of (44). Furthermore, instrumental in the proof (to show convergence ofṠ) is the following technical lemma that follows as a corollary from [16,Theorem 2].…”

Section: Proof Of Theoremmentioning

confidence: 99%

“…The establishment of our main result relies on a fundamental but intuitive lemma on high-gain design which follows from [16], we prove that the estimation errors converge arbitrarily close to the sliding manifold and then, to a neighborhood of the origin. Consequently, the states, the unknown inputs and the additive output noise may be reconstructed with arbitrary accuracy.…”

mentioning

confidence: 96%

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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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State estimation and simultaneous unknown input and measurement noise reconstruction based on associated observers

Yang

Zhu

Sun

2012

Adaptive Control & Signal

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SUMMARYThis paper considers the problems of the state estimation and the simultaneous unknown input and measurement noise reconstruction when the observer matching condition is not satisfied. A new augmented system is constructed by introducing a new augmented state vector. An auxiliary output vector is proposed to deal with the observer matching condition issues, and a high‐order sliding mode observer is considered to get the exact estimates of both the auxiliary outputs and their derivatives in a finite time. A reduced‐order observer is developed to asymptotically estimate the system states, and a kind of reconstruction method of the new system's unknown inputs is proposed to reach the goal of reconstructing the original system's unknown input and measurement noise. Finally, a numerical simulation example is given to illustrate the effectiveness of the proposed methods. Copyright © 2012 John Wiley & Sons, Ltd.

show abstract

Sliding-mode observers for systems with unknown inputs: A high-gain approach

Cited by 178 publications

References 9 publications

A Survey of Modeling and Control of Piezoelectric Actuators

A Survey of Modeling and Control of Piezoelectric Actuators

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

State estimation and simultaneous unknown input and measurement noise reconstruction based on associated observers

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