Robust l<sub>1</sub>estimation using the Popov-Tsypkin multiplier with application to robust fault detection

Collins, Emmanuel G.; Song, Tinglun

doi:10.1080/00207170010006628

Cited by 19 publications

(10 citation statements)

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“…Proof: The proof follows from the lemma in Ref. 18. Remark: Minimization of the upper bound is a more appropriate approach than some conventional methods.…”

Section: Robust 1 Estimationmentioning

confidence: 97%

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Robust Fault Detection and Isolation Using Robust l1 Estimation

Curry

Collins

2005

Journal of Guidance, Control, and Dynamics

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The application of robust 1 estimation to robust fault detection and isolation (FDI) is considered. This is accomplished by developing a series, or bank, of robust estimators (full-order observers), each of which is designed such that the residual will be sensitive to a certain fault (or faults) while insensitive to the remaining faults. Robustness is incorporated by ensuring that the residual remains insensitive to exogenous disturbances as well as modeling uncertainty. Mixed structured singular value and 1 theories are used to develop the appropriate threshold logic to evaluate the outputs of the estimators used for determining the occurrence and location of a fault. A real-coded genetic algorithm is used to obtain the estimator gain matrices. This approach to FDI is successfully demonstrated using a linearized model of a jet engine. Nomenclature= ess sup t ≥ 0 z(t) 2 z(·) (∞,2), [N 0 ,N ] = ess sup t∈[N 0 T,N T ] z(t) 2 0, I = zero matrix, identity matrix

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“…Proof: The proof follows from the lemma in Ref. 18. Remark: Minimization of the upper bound is a more appropriate approach than some conventional methods.…”

Section: Robust 1 Estimationmentioning

confidence: 97%

“…Until recent work, 11,14,18,20 the relatively nonconservative mixed structured singular value (MSSV) techniques 21−24 had not been applied to robust estimation, although more conservative techniques, based on the small-gain theorem or fixed quadratic Lyapunov functions, had been used (see Refs. 15,16,[25][26][27].…”

Section: Introductionmentioning

confidence: 99%

Robust Fault Detection and Isolation Using Robust l1 Estimation

Curry

Collins

2005

Journal of Guidance, Control, and Dynamics

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“…This can be achieved, for instance, by using geometric considerations regarding the plant, as in [9], [14], and [15], or by optimizing a particular norm minimization objective, such as the H ∞ -or l 1 -norm (see [6], [8], and [16]- [18]) The latter approach provides, in general, important robustness properties, as stressed in [5], [7], [16], and [19], by explicitly accounting for model uncertainty. In [20], integral quadratic constraints for uncertain systems are used for model validation.…”

Section: Introductionmentioning

confidence: 99%

A Set-Valued Approach to FDI and FTC of Wind Turbines

Casau

Rosa

Tabatabaeipour

et al. 2015

IEEE Trans. Contr. Syst. Technol.

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A complete methodology to design robust fault detection and isolation (FDI) filters and fault-tolerant control (FTC) schemes for linear parameter varying systems is proposed, with particular focus on its applicability to wind turbines. This paper takes advantage of the recent advances in model falsification using set-valued observers (SVOs) that led to the development of FDI methods for uncertain linear time-varying systems, with promising results in terms of the time required to diagnose faults. An integration of such SVO-based FDI methods with robust control synthesis is described, to deploy new FTC algorithms that are able to stabilize the plant under faulty environments. The FDI and FTC algorithms are assessed by resorting to a publicly available wind turbine benchmark model, using Monte Carlo simulation runs.

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“…The main idea in such architectures stems from the designing of filters that are more reactive to faults than to disturbances and model uncertainty. This can be achieved, for instance, by using geometric considerations regarding the plant (), or by optimizing a particular norm minimization objective, such as the

{scriptH}_{MathClass-rel\infty}

‐norm or ℓ 1 ‐norm (). The latter approach provides, in general, important robustness properties, as stressed in , by explicitly accounting for model uncertainty.…”

Section: Introductionmentioning

confidence: 99%

Model falsification using set-valued observers for a class of discrete-time dynamic systems: a coprime factorization approach

Rosa

Silvestre

Athans³

2013

Int. J. Robust. Nonlinear Control

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SUMMARYThis article introduces a new method for model falsification using set‐valued observers, which can be applied to a class of discrete linear time‐invariant dynamic systems with time‐varying model uncertainties. In comparison with previous results, the main advantages of this approach are as follows: The computation of the convex hull of the set‐valued estimates of the state can be avoided under certain circumstances; to guarantee convergence of the set‐valued estimates of the state, the required number of previous steps is at most as large as the number of states of the nominal plant; and it provides a straightforward nonconservative method to falsify uncertain models of dynamic systems, including open‐loop unstable plants. The results obtained are illustrated in simulation, emphasizing the advantages and shortcomings of the suggested method. Copyright © 2013 John Wiley & Sons, Ltd.

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Robust l₁estimation using the Popov-Tsypkin multiplier with application to robust fault detection

Cited by 19 publications

References 0 publications

Robust Fault Detection and Isolation Using Robust l1 Estimation

Robust Fault Detection and Isolation Using Robust l1 Estimation

A Set-Valued Approach to FDI and FTC of Wind Turbines

Model falsification using set-valued observers for a class of discrete-time dynamic systems: a coprime factorization approach

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Robust l1estimation using the Popov-Tsypkin multiplier with application to robust fault detection

Cited by 19 publications

References 0 publications

Robust Fault Detection and Isolation Using Robust l1 Estimation

Robust Fault Detection and Isolation Using Robust l1 Estimation

A Set-Valued Approach to FDI and FTC of Wind Turbines

Model falsification using set-valued observers for a class of discrete-time dynamic systems: a coprime factorization approach

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Robust l₁estimation using the Popov-Tsypkin multiplier with application to robust fault detection