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Robust Fault Detection for Observer-Based Feedback Control Systems

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Abstract

This paper is devoted to the issues of robust fault detection for a class of observer-based feedback control systems with model uncertainties, disturbances and faults. As the observer-based feedback controller structure allows a direct access to the residual signal, a robust post-filter is designed such that the modified residual satisfies the optimized robustness against disturbances under a desired sensitivity to faults. Moreover, the detection performance of the designed fault detection system is analyzed. Simulation results are given at the end of the paper to demonstrate the effectiveness of the proposed schemes.

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References

  1. D.U. Campos-Delgado, S. Martinez-Martinez, K. Zhou, Integrated fault-tolerant scheme for a DC speed drive. IEEE/ASME Trans. Mechatron. 10(4), 419–427 (2005)

    Article  Google Scholar 

  2. M. Chadli, A. Abdo, S.X. Ding, \(H_-/H_\infty \) fault detection filter design for discrete-time Takagi–Sugeno fuzzy system. Automatica 49(7), 1996–2005 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  3. M. Chilali, P. Gahinet, P. Apkarian, Robust pole placement in LMI regions. IEEE Trans. Autom. Control 44(12), 2257–2270 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  4. S.X. Ding, Model-Based Fault Diagnosis Techniques: Design Schemes, Algorithms, and Tools (Springer, Berlin, 2013)

    Book  MATH  Google Scholar 

  5. S.X. Ding, Integrated design of feedback controllers and fault detectors. Annu. Rev. Control 33(2), 124–135 (2009)

    Article  Google Scholar 

  6. S.X. Ding, Data-Driven Design of Fault Diagnosis and Fault-Tolerant Control Systems (Springer, Berlin, 2014)

    Book  Google Scholar 

  7. S.X. Ding, G. Yang, P. Zhang, E.L. Ding, T. Jeinsch, N. Weinhold, M. Schultalbers, Feedback control structures, embedded residual signals, and feedback control schemes with an integrated residual access. IEEE Trans. Control Syst. Technol. 18(2), 352–367 (2010)

    Article  Google Scholar 

  8. H. Dong, Z. Wang, H. Gao, Distributed \(H_\infty \) filtering for a class of Markovian jump nonlinear time-delay systems over lossy sensor networks. IEEE Trans. Ind. Electron. 60(10), 4665–4672 (2013)

    Article  Google Scholar 

  9. P. Gahinet, P. Apkarian, A linear matrix inequality approach to \(H_\infty \) control. Int. J. Robust Nonlinear Control 4(4), 421–448 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  10. D. Henry, A. Zolghadri, Design and analysis of robust residual generators for systems under feedback control. Automatica 41(2), 251–264 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  11. Z. Hu, G. Zhao, L. Zhang, D. Zhou, Fault estimation for nonlinear dynamic system based on the second-order sliding mode observer. Circuits Syst. Signal Process. 35(1), 101–115 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  12. I. Hwang, S. Kim, Y. Kim, C.E. Seah, A survey of fault detection, isolation, and reconfiguration methods. IEEE Trans. Control Syst. Technol. 18(3), 636–653 (2010)

    Article  Google Scholar 

  13. C. Jacobson, C. Nett, An integrated approach to controls and diagnostics using the four parameter controller. IEEE Trans. Control Syst. Technol. 11(6), 22–29 (1991)

    Article  Google Scholar 

  14. M.J. Khosrowjerdi, R. Nikoukhah, N. Safari-Shad, A mixed \(H_2/H_\infty \) approach to simultaneous fault detection and control. Automatica 40(2), 261–267 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  15. J. Lan, R.J. Patton, A new strategy for integration of fault estimation within fault-tolerant control. Automatica 69, 48–59 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  16. A. Marcos, G.J. Balas, A robust integrated controller/diagnosis aircraft application. Int. J. Robust Nonlinear Control 15(12), 531–551 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  17. H. Pan, X. Jing, W. Sun, H. Gao, A bioinspired dynamics-based adaptive tracking control for nonlinear suspension systems. IEEE Trans. Control Syst. Technol. (2017). https://doi.org/10.1109/TCST.2017.2699158

    Google Scholar 

  18. R.J. Patton, P.M. Frank, R.N. Clark, Issues of Fault Diagnosis for Dynamic Systems (Springer, London, 2000)

    Book  Google Scholar 

  19. K. Peng, K. Zhang, B. You, J. Dong, Z. Wang, A quality-based nonlinear fault diagnosis framework focusing on industrial multimode batch processes. IEEE Trans. Ind. Electron. 63(4), 2615–2624 (2016)

    Google Scholar 

  20. B. Shen, S.X. Ding, Z. Wang, Finite-horizon \(H_\infty \) fault estimation for linear discrete time-varying systems with delayed measurements. Automatica 49(1), 293–296 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  21. B. Shen, S.X. Ding, Z. Wang, Finite-horizon \(H_\infty \) fault estimation for uncertain linear discrete time-varying systems with known inputs. IEEE Trans. Circuits Syst. II Express Briefs 60(12), 902–906 (2013)

    Article  Google Scholar 

  22. J. Stoustrup, M. Grimble, H. Niemann, Design of integrated systems for the control and detection of actuator/sensor faults. Sens. Rev. 17(2), 138–149 (1997)

    Article  Google Scholar 

  23. W. Sun, H. Pan, H. Gao, Filter-based adaptive vibration control for active vehicle suspensions with electrohydraulic actuators. IEEE Trans. Veh. Technol. 65(6), 4619–4626 (2016)

    Article  Google Scholar 

  24. H.D. Tuan, P. Apkarian, T.Q. Nguyen, Robust filtering for uncertain nonlinearly parameterized plants. IEEE Trans. Signal Process. 51(7), 1806–1815 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  25. Y. Wang, S.X. Ding, D. Xu, B. Shen, An \(H_\infty \) fault estimation scheme of wireless networked control systems for industrial real-time applications. IEEE Trans. Control Syst. Technol. 22(6), 2073–2086 (2014)

    Article  Google Scholar 

  26. Y. Wei, J. Qiu, X. Peng, H.K. Lam, T-S fuzzy-affine-model-based reliable output feedback control of nonlinear systems with actuator faults. Circuits Syst. Signal Process (2017). https://doi.org/10.1007/s00034-017-0547-0

    Google Scholar 

  27. N.E. Wu, Robust feedback design with optimized diagnostic performance. IEEE Trans. Autom. Control 42(9), 1264–1268 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  28. G.H. Yang, H. Wang, Fault detection for a class of uncertain state-feedback control systems. IEEE Trans. Control Syst. Technol. 18(1), 201–212 (2010)

    Article  Google Scholar 

  29. Y. Yang, S.X. Ding, L. Li, Parameterization of nonlinear observer-based fault detection systems. IEEE Trans. Autom. Control 61(11), 3687–3692 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  30. Y. Yang, Y. Zhang, S.X. Ding, L. Li, Design and implementation of lifecycle management for industrial control applications. IEEE Trans. Control Syst. Technol. 23(4), 1399–1410 (2015)

    Article  Google Scholar 

  31. S. Yin, S.X. Ding, A. Haghani, H. Hao, P. Zhang, A comparison study of basic data-driven fault diagnosis and process monitoring methods on the benchmark Tennessee eastman process. J. Process Control 22(9), 1567–1581 (2012)

    Article  Google Scholar 

  32. S. Yin, H. Luo, S.X. Ding, Real-time implementation of fault-tolerant control systems with performance optimization. IEEE Trans. Ind. Electron. 61(5), 2402–2411 (2014)

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. State Key Lab for Turbulence and Complex Systems, Department of Mechanics and Engineering Science, College of Engineering, Peking University, Beijing, 100871, People’s Republic of China

    Zhengen Zhao & Ying Yang

  2. Institute for Automatic Control and Complex Systems, University of Duisburg-Essen, 47057, Duisburg, Germany

    Zhengen Zhao & Steven X. Ding

  3. School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing, 100083, People’s Republic of China

    Linlin Li

Authors
  1. Zhengen Zhao
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  2. Ying Yang
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  3. Steven X. Ding
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  4. Linlin Li
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Corresponding author

Correspondence to Ying Yang.

Additional information

This work has been supported by the National Natural Science Foundation of China under Grants 61633001, 61473004, and 61603033, Beijing Natural Science Foundation under Grant 4174096, and the Fundamental Research Funds for the Central Universities under Grant FRF-TP-16-084A1.

Appendices

Appendix

Appendix 1: The Observer-Based Controller Design

Lemma 2

Given \(\gamma _d>0\),  the observer-based feedback control systems (3) are stable and satisfy the \(H_\infty \) performance \(\Vert z(t)\Vert _2\le \gamma _d\Vert d(t)\Vert _2\), if there exist positive definite matrices \(P_1,~P_{10},~P_2\in {\mathcal {R}}^{n\times n}\), matrices \(F,~F_{0}\in {\mathcal {R}}^{n_u\times n},~\hat{L}\in {\mathcal {R}}^{n\times p}\), and a positive constant \(\varepsilon \) such that

$$\begin{aligned} \begin{bmatrix} \bar{N}_1&0&P_1B_d&\bar{N}_{2}&P_1A_1&P_1&\bar{N}_{3}\\ *&\bar{N}_{4}&\bar{N}_{5}&\bar{N}_{6}&P_2A_1&0&0\\ *&*&-\,\gamma _d I&0&0&0&0\\ *&*&*&-\,\gamma _d I&0&0&0\\ *&*&*&0&-\varepsilon I&0&0\\ *&*&*&0&0&-\,I&0\\ *&*&*&0&0&0&-\,I \end{bmatrix}<0 \end{aligned}$$

where

$$\begin{aligned} \begin{aligned} \bar{N}_{1}&=He\left( P_1A-2P_1P_{10}-F^\mathrm{T}B^TBF_0\right) \\&\quad +2P_{10}P_{10}+F_0^\mathrm{T}B^TBF_0+\varepsilon A_2^\mathrm{T}A_2\\ \bar{N}_{2}&=C_z^\mathrm{T}+F^\mathrm{T}D_z^\mathrm{T},~\bar{N}_{3}=P_1+F^\mathrm{T}B^T\\ \bar{N}_{4}&=He\left( P_2A+\hat{L}C-F^\mathrm{T}B^TBF_0\right) +F_0^\mathrm{T}B^TBF_0\\ \bar{N}_{5}&=P_2B_d+\hat{L}D_d,~\bar{N}_{6}=-\,F^\mathrm{T}D_z^\mathrm{T}. \end{aligned} \end{aligned}$$

Furthermore, the observer gain is given by \(L=P_2^{-1}\hat{L}\) and the feedback control gain F is computed by an iterative LMI algorithm.

Proof

Let the Lyapunov function candidate \(P=\hbox {diag}\{P_1,~P_2\}\). Using the bounded real lemma and the matrix inequalities

$$\begin{aligned} \begin{aligned} -\,P_1P_1&\le -\,P_1P_{10}-P_{10}P_1+P_{10}P_{10}\\ -\,F^\mathrm{T}B^TBF&\le -\,F^\mathrm{T}B^TBF_0-F_0^\mathrm{T}B^TBF+F_0^\mathrm{T}B^TBF_0, \end{aligned} \end{aligned}$$

the conclusion is evident. \(\square \)

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Zhao, Z., Yang, Y., Ding, S.X. et al. Robust Fault Detection for Observer-Based Feedback Control Systems. Circuits Syst Signal Process 37, 3364–3382 (2018). https://doi.org/10.1007/s00034-017-0726-z

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