Fault detection and identification for a class of nonlinear systems with model uncertainty

Yan, Binbin; Su, Housheng; Wei, Ma

doi:10.1016/j.apm.2016.03.018

Cited by 6 publications

(12 citation statements)

References 26 publications

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“…Figure displays the comparable results of fault estimation errors. It should be pointed out that the maximum iterative learning fault estimation error converges to 0.6 in the work of Yan et al and converges to 0 in this technical note. Namely, the proposed method can obtain a better estimation.…”

Section: Illustrative Simulationsmentioning

confidence: 55%

“…For instance, the speed of elevator when it operates between same floors, the speed of carousel in production when it keep on transporting the product in the process from the starting point to the specified location, the speed of reservoir gate in the case that fixed water emission of large reservoir every day, and the speed of a mechanical arm that is used to move materials to a precise position in factory. However, in the most of the reported results, the operation length is usually unchanged in different iterations and the output integral

\int_{0}^{T_{k}} false| ŷ_{k} false(t false) false| d t

need not to satisfy the specified constraints. Thus, it is hard to ensure the given constraint conditions at the end of each iteration if there exists output error.…”

Section: Fe Using Iterative Learning Scheme Under Specific Constraintsmentioning

confidence: 99%

“…To demonstrate the superiority of the proposed method, a single link flexible joint robot arm is considered in this section, described by the following state‐space model:

({, \begin{matrix} array {\dot{x}}_{1} = x_{2} \\ array x_{2} = Φ (x_{1}, x_{2}) + B u + B_{f} f (t) \\ array y = x_{1} + x_{2}, \end{matrix})

in which the nonlinear terms are described as Φ( x 1 , x 2 ) = [Φ 1 ( x 1 , x 2 ),Φ 2 ( x 1 , x 2 )] T ,

Φ_{1} false(x_{1}, x_{2} false) = \frac{k}{J_{m}} A_{1} x_{1} - \frac{b}{J_{m}} A_{2} x_{2}

Φ_{2} false(x_{1}, x_{2} false) = \frac{k}{J_{m}} A_{3} x_{1} - \frac{m sans-serifg h}{J_{1}} \sin false(A_{4} x_{1} false)

, and the parameter matrices are given as

B = {false[\frac{k_{τ}}{J_{m}}, 0 false]}^{T}

, B f = [0,1] T , A 1 = [1, −1] T , A 2 = [1,0] T , A 3 = [1, −1] T , A 4 = [0,1] T ; furthermore, the parameters are

\frac{k}{J_{m}} = 48.6

\frac{b}{J_{m}} = 1.25

\frac{k_{τ}}{J_{m}} = 21.6

\frac{k}{J_{1}} = 1.95

\frac{m sans-serifg h}{J_{1}} = 0.3334

. To ensure the consistency of simulation results, the fault signal is shown as follows:

…”

Section: Illustrative Simulationsmentioning

confidence: 99%

“…Namely, the proposed method can obtain a better estimation. Besides, varying length has not been considered in the aforementioned work . Visibly, the proposed method has more broader prospects.…”

Section: Illustrative Simulationsmentioning

confidence: 99%

“…It is free of precise model and strictly positive realness assumption. (2)To deal with iterative learning observer‐based FE problem for nonlinear repeated systems with specified conditions, truncation operator is proposed to correct the lack and redundancy in tracking information caused by varying trial length. Inversely, in the works of Shi et al and Yan et al, iterative learning observers are based on unchanged operation length. (3)Utilizing λ ‐ n o r m method and mathematical induction, the solutions of iterative learning matrices and observer gain matrix are obtained to get further improvement of FE results. As a result, the proposed approach is easy and simple to achieve desired results, which broaden the application scenario of iterative learning scheme in engineering practice.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Iterative learning scheme‐based fault estimation design for nonlinear systems with varying trial lengths and specified constraints

Feng

Chai

et al. 2018

Intl J Robust & Nonlinear

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Summary This technical note deals with a fault estimation (FE) problem for nonlinear systems with varying trial lengths subjected to specified constraints. An iterative learning observer is developed to achieve FE and state reconstruction simultaneously, which thus to consider the state error and fault estimating information from previous iteration to improve the FE performance in the current iteration. Compared with conventional observer‐based FE methods, the proposed method only requires the bounds of parameter matrices rather than the precise model of the system. To deal with the missing and redundancy problems caused by varying trial lengths, a truncation operator is presented to design the FE law. Different from existing iterative learning methods, the presented method aims at the nonlinear systems with specified constraints, such as filling systems. Furthermore, the λ‐norm method and mathematical induction are employed to obtain the solutions of iterative learning matrices and observer gain matrix. Finally, illustrative examples are introduced to demonstrate the validity and the effectiveness of the proposed FE approach.

show abstract

Section: Illustrative Simulationsmentioning

confidence: 55%

\int_{0}^{T_{k}} false| ŷ_{k} false(t false) false| d t

need not to satisfy the specified constraints. Thus, it is hard to ensure the given constraint conditions at the end of each iteration if there exists output error.…”

Section: Fe Using Iterative Learning Scheme Under Specific Constraintsmentioning

confidence: 99%

“…To demonstrate the superiority of the proposed method, a single link flexible joint robot arm is considered in this section, described by the following state‐space model:

({, \begin{matrix} array {\dot{x}}_{1} = x_{2} \\ array x_{2} = Φ (x_{1}, x_{2}) + B u + B_{f} f (t) \\ array y = x_{1} + x_{2}, \end{matrix})

in which the nonlinear terms are described as Φ( x 1 , x 2 ) = [Φ 1 ( x 1 , x 2 ),Φ 2 ( x 1 , x 2 )] T ,

Φ_{1} false(x_{1}, x_{2} false) = \frac{k}{J_{m}} A_{1} x_{1} - \frac{b}{J_{m}} A_{2} x_{2}

Φ_{2} false(x_{1}, x_{2} false) = \frac{k}{J_{m}} A_{3} x_{1} - \frac{m sans-serifg h}{J_{1}} \sin false(A_{4} x_{1} false)

, and the parameter matrices are given as

B = {false[\frac{k_{τ}}{J_{m}}, 0 false]}^{T}

, B f = [0,1] T , A 1 = [1, −1] T , A 2 = [1,0] T , A 3 = [1, −1] T , A 4 = [0,1] T ; furthermore, the parameters are

\frac{k}{J_{m}} = 48.6

\frac{b}{J_{m}} = 1.25

\frac{k_{τ}}{J_{m}} = 21.6

\frac{k}{J_{1}} = 1.95

\frac{m sans-serifg h}{J_{1}} = 0.3334

. To ensure the consistency of simulation results, the fault signal is shown as follows:

…”

Section: Illustrative Simulationsmentioning

confidence: 99%

Section: Illustrative Simulationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Iterative learning scheme‐based fault estimation design for nonlinear systems with varying trial lengths and specified constraints

Feng

Chai

et al. 2018

Intl J Robust & Nonlinear

View full text Add to dashboard Cite

show abstract

Observer‐based fault estimators using iterative learning scheme for nonlinear time‐delay systems with intermittent faults

Feng

Chai

et al. 2017

Intl J Robust & Nonlinear

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Summary This paper deals with the intermittent fault estimation problem for a class of nonlinear time‐delay systems with measurement noise. The time delays are assumed to occur in state vector, nonlinear term as well as output vector, thus reflecting the time delays influence in reality more closely. The aim of the problem is to estimate the intermittent fault by using iterative learning scheme, with the property of H∞ index, hence attenuating the influence from measurement noise. Different from existing fault estimating schemes, the state error information and fault estimating information in the previous iteration are used in the current iteration to improve the estimating results. The stability and convergence of iterative learning observer and uniform boundedness of dynamic error system are achieved by using Lyapunov function and optimal function design. Simultaneously, an improved sufficient condition for the existence of such an estimator is established in terms of the linear matrix inequality by the Schur complements and Young relations. Furthermore, the results are both suited for the systems with time‐varying delay and the systems with constant delay. Finally, two numerical examples are proposed to illustrate the effectiveness of the proposed method, and a comparability example is presented to demonstrate its superiority. Copyright © 2017 John Wiley & Sons, Ltd.

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An iterative learning scheme-based fault estimator design for nonlinear systems with quantised measurements

Liu

Wei

Chai

2020

Journal of the Franklin Institute

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Fault detection and identification for a class of nonlinear systems with model uncertainty

Cited by 6 publications

References 26 publications

Iterative learning scheme‐based fault estimation design for nonlinear systems with varying trial lengths and specified constraints

Iterative learning scheme‐based fault estimation design for nonlinear systems with varying trial lengths and specified constraints

Observer‐based fault estimators using iterative learning scheme for nonlinear time‐delay systems with intermittent faults

An iterative learning scheme-based fault estimator design for nonlinear systems with quantised measurements

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