Optimal Robust Fault Detection for Linear Discrete Time Systems

Liu, Nike; Zhou, Kemin

doi:10.1155/2008/829459

Cited by 51 publications

(29 citation statements)

References 35 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The assumption 5 is the case we shall solve in this paper. The opposite case that n y ≤ n d has been solved in [10].…”

Section: Remarkmentioning

confidence: 99%

“…Since pre-multiplying a unitary matrix on a system does not affect its H ∞ norm, V m F is also an optimal filter for our criteria, which is identical to the solution given by [10] in which G d is of full row rank.…”

Section: Remarkmentioning

confidence: 99%

“…In [9], [10], when G d is assumed to be full row rank, this condition is satisfied automatically, which implies the existence of the upper bound. …”

Section: Decoupling Conditionmentioning

confidence: 99%

“…In [9] and [10], in order to constrain the disturbance effect and maximize the fault sensitivity, several criteria such as H − /H ∞ , H 2 /H ∞ and H ∞ /H ∞ are formulated and the same optimal filter is obtained for all three problems, which actually is of an observer form. In addition, the same solution has also been derived in [3] for some different objective that minimizes the ratio of disturbance sensitivity and fault sensitivity.…”

Section: Introductionmentioning

confidence: 99%

“…Furthermore, [11] and [12] have extended these results to time-varying systems based on some time domain formulations. However, in those papers [9], [10] [3], [11] and [12], it is assumed that G d , the transfer function from disturbance to the measurement output, is a square or wide transfer matrix and D d matrix is of full row rank, which is conservative in some sense.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Fault detection for linear discrete-time invariant systems with decoupling and optimization

Zhou

2009

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

Self Cite

View full text Add to dashboard Cite

This paper discusses the robust fault detection design for the criteria such as H−/H∞, H2/H∞ and H∞/H∞ in which G d , the transfer function from disturbance to the measurement output, is a tall transfer matrix and D d is not full column rank. It is shown that the faults in a subspace can be made arbitrarily sensitive, while the faults in the complementary subspace have bounded sensitivities that are maximized by our filter. We also discuss the decoupling and non-decoupling conditions, and their relations with image spaces of G d and G f (the transfer function from disturbance to the measurement output and the transfer function from fault to the measurement output). Furthermore, based on the optimal filter, a method is given to partially decouple the disturbance from the residual without impacting the rest of the fault sensitivities. An example is given to illustrate our results.

show abstract

“…The assumption 5 is the case we shall solve in this paper. The opposite case that n y ≤ n d has been solved in [10].…”

Section: Remarkmentioning

confidence: 99%

Section: Remarkmentioning

confidence: 99%

“…In [9], [10], when G d is assumed to be full row rank, this condition is satisfied automatically, which implies the existence of the upper bound. …”

Section: Decoupling Conditionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Fault detection for linear discrete-time invariant systems with decoupling and optimization

Zhou

2009

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

Self Cite

View full text Add to dashboard Cite

show abstract

LMI solutions to the mixed ℋ︁₋/ℋ︁_∞ fault detection observer design for linear parameter‐varying systems

Wei

Verhaegen

2011

Adaptive Control & Signal

View full text Add to dashboard Cite

This paper addresses the mixed H − /H ∞ fault detection observer design issue for a class of linear parameter-varying (LPV) systems. Analogous to the definition of the quadratic H ∞ performance for LPV systems and the H − index for linear time invariant (LTI) systems, the quadratic H − index and the affine quadratic H − index for LPV systems are defined in terms of linear matrix inequalities (LMIs). The first algorithm for designing the mixed H − /H ∞ observer is proposed, which aims at minimizing the quadratic H ∞ performance and maximizing the quadratic H − index of the observer error dynamic systems. To reduce the conservativeness of this algorithm, the affine quadratic H ∞ performance and the affine H − index for LPV systems are utilized. The robustness conditions and affine H − index conditions for the underlying observer optimization issue are formulated as parameter-dependent LMIs. The Gridding technique and multi-convexity concept are applied, respectively, for reducing the parameter-dependent LMIs to finite LMI constraints. Correspondingly, two iterative algorithms are proposed. Furthermore, the threshold design and the estimation of the worst undetectable fault size are investigated. An example is studied to demonstrate the effectiveness of the proposed algorithms.

show abstract

A New Residual Evaluation Function Based Fault Diagnosis for a Kind of Nonlinear Systems

Hai

Zhong

Liu

2018

Asian Journal of Control

View full text Add to dashboard Cite

In this paper, a new residual evaluation function (EF) is proposed for the H i ∕H ∞ fault detection filter (FDF). Residuals are projected into the direction of fault, then energy of this projection is adopted as the new EF. Compared with the traditional EF, improvement in FD ability of the new EF is demonstrated rigorously, and a recursive way to calculate it is also proposed under the assumption that fault is slowly time varying. Furthermore, application of this new EF for fault isolation (FI) is discussed, which finally leads to a systematic FDI scheme for a kind of nonlinear systems. Simulations with a nonlinear unmanned aerial vehicle (UAV) model validate the proposed method.new,i and J f new,i , the accumulated terms in J r new,i are not quadric forms and their signs may change from step to step, thus it is reasonable to assume that J r new,i is much smaller than J d new,i and J f new,i . That is, J new,i is roughly approximated asThen, since J f new, ≥ J f new,i holds true, it is expected to isolate the fault correctly by J new, when J d new,i ≈ J d new, ≪ J f new, . That is, J new,i and J new, in the fault free case are roughly equal. Compared with the assumption that residual is dominated by fault (r ≈ Ω f ), this conditional is milder and more realistic.However, undesirable situations still exist, that is, J new,i and J new, differs from each other significantly in the fault free case. Without loss of generality, it is assumed that the direction of r 0 is much closer to Ω i , i ≠ , which result in J new,i ≫ J new, in the fault free case. To deal with this situation, the following normalized EF is proposed.where (J 0 new,i ) is an empirical mean of J new,i obtained from historical normal data. Then we havēSince the direction of r 0 is close to Ω i but far from Ω , directions of Ω i and Ω are not close to each other, thus J f new,i is very small when f occurs. Therefore, it is expected thatJ new,i will not increase obviously after f occurs, whileJ new, increase significantly after f occurs. Finally, it is expected to haveJ new, >J new,i . When J new,i and J new, are close to each other in the fault free case, J new,i ≈ 1 + J f new,i (J 0 new,i ) ≤J new, ≈ 1 + J f new, ance instrument, Beihang University, Beijing, China. His research interests are model-based fault diagnosis and applications.Maiying Zhong received the Ph.D. degree in control theory and control engineering from Northeastern University,

show abstract

Optimal Robust Fault Detection for Linear Discrete Time Systems

Cited by 51 publications

References 35 publications

Fault detection for linear discrete-time invariant systems with decoupling and optimization

Fault detection for linear discrete-time invariant systems with decoupling and optimization

LMI solutions to the mixed ℋ︁₋/ℋ︁_∞ fault detection observer design for linear parameter‐varying systems

A New Residual Evaluation Function Based Fault Diagnosis for a Kind of Nonlinear Systems

Contact Info

Product

Resources

About

Optimal Robust Fault Detection for Linear Discrete Time Systems

Cited by 51 publications

References 35 publications

Fault detection for linear discrete-time invariant systems with decoupling and optimization

Fault detection for linear discrete-time invariant systems with decoupling and optimization

LMI solutions to the mixed ℋ︁−/ℋ︁∞ fault detection observer design for linear parameter‐varying systems

A New Residual Evaluation Function Based Fault Diagnosis for a Kind of Nonlinear Systems

Contact Info

Product

Resources

About

LMI solutions to the mixed ℋ︁₋/ℋ︁_∞ fault detection observer design for linear parameter‐varying systems