Detection Filter Method in Diagnostic Problems for Linear Dynamic Systems
DOI:
https://doi.org/10.20535/RADAP.2021.84.30-39Keywords:
model-oriented methods of fault detection, fail-safe control, discrete linear dynamic system, separate state estimationAbstract
In a presented research paper the problem of synthesis of the fault detection unit and failure occurrence locating in linear discrete dynamic time-invariant systems is considered. The result of synthesis is presented in the form of parallel type structure consisting of two independently functioning Kalman filter. The first of them calculates a system state vector estimation without taking note of faults, and the second - a degenerate type, creates a fault estimations. Linear combination of their exits forms the resulting state vector estimation. Both filters have dimensions smaller dimensions of the tested system and use the split procedure of an error differential signal. Splitting of the error signal is carried out before estimation process unlike Kitanidis filter. It allows to get a certain economy in computing costs, due to introduced restrictions and losses in accuracy. In general the obtained structure is suboptimal. Questions of stability and state vector estimation convergence of a dynamic system are briefly considered. Using of the computing resource of MatLab environment results of a functional methodcheck results are given.The article structure is constructed as follows. At first problem definition is executed and its resolvability from the mathematical point of view is analyzed. The following step is synthesis of the detection unit and localization of multiple faults then the convergence and stability of errors of estimation are analyzed. In final sections results of method operability check are given in the form of illustrative numerical example and the results of the performed research are summed up. In the conceptual plan research makes a generalization the known results for the continuous time systems.
References
Blanke M., Kinnaert M., Lunze J., Staroswiecki M. (2016). Diagnosis and Fault-Tolerant Control. Springer-Verlag Berlin, 695 p. DOI:10.1007/978-3-662-47943-8.
Chow E., Willsky A. (1984). Analytical redundancy and the design of robust failure detection systems. IEEE Transactions on Automatic Control, Vol. 29, No. 7, pp. 603-614. DOI:10.1109/TAC.1984.1103593.
Willsky A. S. (1985). Detection of abrupt changes in dynamic systems. In: Basseville M., Benveniste A. (eds) Detection of Abrupt Changes in Signals and Dynamical Systems. Lecture Notes in Control and Information Sciences, Springer, Berlin, Heidelberg, Vol. 77, pp. 27-49. DOI:10.1007/BFb0006388.
Gertler J. J. (1988). Survey of model-based failure detection and isolation in complex plants. IEEE Control Systems Magazine, Vol. 8, No. 6, pp. 3-11. DOI:10.1109/37.9163.
Frank P. M. (1990). Fault diagnosis in dynamic systems using analytical and knowledge base redundancy: A survey and some new results. Automatica, Vol. 26, Iss. 3 pp. 459-474. DOI:10.1016/0005-1098(90)90018-D.
Patton R. J., Uppal F. J., Lopez-Toribio C. J. (2000). Soft Computing Approaches to Fault Diagnosis for Dynamic Systems: A survey. IFAC Proceedings Volumes, Vol. 33, Iss. 11, pp. 303-315. DOI:10.1016/S1474-6670(17)37377-9.
Hwang I., Kim S., Kim Y., Seah C. A (2010). A Survey of Fault Detection, Isolation, and Reconfiguration Methods. IEEE Transactions on Control Systems Technology, Vol. 18, Iss. 3, pp. 636-653. DOI:10.1109/TCST.2009.2026285.
Escobet T., Bregon A., Pulido B., Puig V. (2019). Fault Diagnosis of Dynamic Systems, Quantitative and Qualitative Approaches. Springer-Verlag Berlin, 462 p. DOI:10.1007/978-3-030-17728-7.
Zolghadri A., Henry D., Cieslak J., Efimov D., Goupil P. (2014). Fault Diagnosis and Fault-Tolerant Control and Guidance for Aerospace Vehicles, From Theory to Application. Springer-Verlag Berlin, 216 p. DOI:10.1007/978-1-4471-5313-9.
Volovyk A., Kychak V., Kudriavtsev D., Havrilov D., Yarovyi A., Krylik L. (2020). Simultaneous Estimation in Linear Dynamic Systems with the Indeterminate Structure Disturbances. 2020 IEEE 40th International Conference on Electronics and Nanotechnology (ELNANO), pp. 651-655. DOI:10.1109/ELNANO50318.2020.9088884.
Varga A., Ossmann D. (2013). LPV model-based robust diagnosis of flight actuator faults. Control Engineering Practice, Vol. 31, pp. 135–147. DOI:10.1016/j.conengprac.2013.11.004.
Volovik A. Y., Krylik L. I., Kobylyanska I. M., Kotyra A., Amirgaliyeva S. (2018) Methods of stochastic diagnostic type observers. Proceedings Volume 10808, Photonics Applications in Astronomy, Communications, Industry, and High-Energy Physics Experiments 2018. DOI:10.1117/12.2501693.
Ossmann D., Varga A. (2015). Detection and Identification of Loss of Efficiency Faults of Flight Actuators. International Journal of Applied Mathematics and Computer Science, Vol. 25, Iss. 1, pp. 53-63. DOI:10.1515/amcs-2015-0004.
Gertler J. (1998). Fault Detection and Diagnosis in Engineering Systems. CRC Press/ Marcel Dekker, New York, 504 p.
Isermann R. (2006). Fault-Diagnosis Systems, An Introduction from Fault Detection to Fault Tolerance. Springer-Verlag Berlin, 475 p. DOI: 10.1007/3-540-30368-5.
Ding S. X. (2013). Model-based Fault Diagnosis Techniques, Design Schemes, Algorithms, and Tools, 2nd Edition. Springer-Verlag Berlin, 473 p. DOI:10.1007/978-3-540-76304-8.
Varga A. (2017). Solving Fault Diagnosis Problems. Linear Synthesis Techniques. Studies in Systems, Decision and Control. Springer International Publishing, Vol. 84. 394 p. DOI:10.1007/978-3-319-51559-5.
Friedland B. (1969). Treatment of bias in recursive filtering, IEEE Transactions on Automatic Control, Vol. 14, Iss. 4, pp. 359–367. DOI:10.1109/TAC.1969.1099223.
Chen J., Patton R. J. (1996). Optimal filtering and robust fault diagnosis of stochastic systems with unknown disturbances. IEE Proceedings - Control Theory and Applications, Vol. 143, Iss. 1, pp. 31–36. DOI:10.1049/ip-cta:19960059.
Alouani A. T., Rice T. R., Blair W. D. (1992). Two-Stage Filter for State Estimation in the Presence of Dynamical Stochastic Bias. 1992 American Control Conference, pp. 1784–1788. DOI:10.23919/ACC.1992.4792418.
Ignagni M. (2000). Optimal and suboptimal separate-bias Kalman estimators for a stochastic bias. IEEE Transactions on Automatic Control, Vol. 45, Iss. 3, pp. 547–551. DOI:10.1109/9.847741.
Kim K. H., Lee J. G., Park C. G. (2006). Adaptive two-stage Kalman filter in the presence of unknown random bias. International Journal of Adaptive Control and Signal Processing, Vol. 20, Iss. 7, pp. 305–319. DOI:10.1002/acs.900.
Kim K. H., Lee J. G., Park C. G. (2007). The stability analysis of the adaptive two-stage Kalman filter. International Journal of Adaptive Control and Signal Processing, Vol. 21, Iss. 10, pp. 856–870. DOI:10.1002/acs.950.
Kitanidis P. K. (1987). Unbiased minimum-variance linear state estimation. Automatica, Vol. 23, Iss. 6, pp. 775–778. DOI:10.1016/0005-1098(87)90037-9.
Darouach M., Zasadzinski M. (1997). Unbiased minimum variance estimation for systems with unknown exogenous inputs. Automatica, Vol. 33, Iss. 4, pp. 717–719. DOI:10.1016/S0005-1098(96)00217-8.
Hsieh C. S. (2007). On the optimality of the two-stage Kalman filtering for systems with unknown inputs. Proceedings of CACS International Automatic Control Conference. DOI:10.1002/asjc.205.
Massoumnia M. (1986). A geometric approach to the synthesis of failure detection filters. IEEE Transactions on Automatic Control, Vol. 31, Iss. 9, pp. 839–846. DOI:10.1109/TAC.1986.1104419.
White J., Speyer J. (1987). Detection filter design: Spectral theory and algorithms. IEEE Transactions on Automatic Control, Vol. 32, Iss. 7, pp. 593–603. DOI:10.1109/TAC.1987.1104682.
Gertler J., Monajemy R. (1995). Generating directional residuals with dynamic parity relations. Automatica, Vol. 31, Iss 4, pp. 627–635. DOI:10.1016/0005-1098(95)98494-Q.
Liu N., Zhou K. (2008). Optimal Robust Fault Detection for Linear Discrete Time Systems. Journal of Control Science and Engineering, Article ID 829459, 16 p. DOI:10.1155/2008/829459.
Luenberger D. G. (1971). An introduction to observers. IEEE Transactions on Automatic Control, Vol. 16, Iss. 6, pp. 596–602. DOI:10.1109/TAC.1971.1099826.
De Souza C., Geevers M., Goodwin G. (1986). Riccati equations in optimal filtering of nonstabilizable systems having singular state transition matrices. IEEE Transactions on Automatic Control, Vol. 31, Iss. 9, pp. 831–838. DOI:10.1109/TAC.1986.1104415.
Ellert F. J., Merriam C. W. (1963). Synthesis of Feedback Control Using Optimization Theory: An Example. IEEE Transactions on Automatic Control, Vol. 8, Iss. 2, pp. 89–103. DOI:10.1109/TAC.1963.1105534.
Topcheev Yu. Y. (1989). Atlas dlia proektyrovanyia system avtomatycheskoho rehulyrovanyia: Uchebnoe posobye dlia vtuzov [The atlas for design of automatic control systems. Manual]. Moscow: Mashynostroenye, 752 p. [In Russian].
Bekhtyr V. P., Rzhevskyi V. M., Tsypenko V. H. (1997). Praktycheskaia aэrodynamyka samoleta Tu-154M [Practical aerodynamics of the Tu-154M airplane]. Moscow: Vozdushnsnii transport, 288 p. [In Russian].
Biushhens H.S., Studnev R.V. (1979). Aerodynamyka samoleta: Dynamyka prodolnoho y bokovoho dvyzhenyia [Airplane aerodynamics: Dynamics of longitudinal and lateral motion]. Moscow: Mashynostroenye, 352 p. [In Russian].
Miele A., Wang T., Wang H., Melvin W. W. (1988) Optimal Penetration Landing Trajectories in the Presence of Windshear. Journal of Optimization Theory and Applictions, Vol. 57, No. 1. DOI:10.2514/6.1988-580.
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