In this
paper, an actuator fault diagnosis scheme based on the backstepping method is proposed for a class of nonlinear heat equations.
The fault diagnosis scheme includes fault detection, fault estimation and time
to failure (TTF) prediction. Firstly, we achieve fault detection by comparing
the detection residual with a predetermined threshold, where the detection
residual is defined as the difference between the observer output and the
system measurement output. Then, we estimate the fault function through the
fault parameter update law and calculate the TTF using only limited
measurements. Finally, the numerical simulation is performed on a nonlinear
heat equation to verify the effectiveness of the proposed fault diagnosis
scheme.
References
[1]
Dong, J., Wang, Q., Wang, M. and Peng, K. (2018) Data-Driven Quality Monitoring Techniques for Distributed Parameter Systems with Application to Hot-Rolled Strip Laminar Cooling Process. IEEE Access, 6, 16646-16654. https://doi.org/10.1109/ACCESS.2018.2812919
[2]
Hong, W., Lee, Y.T. and Gong, H. (2004) Thermal Analysis of Layer Formation in a Stepless Rapid Prototyping Process. Applied Thermal Engineering, 24, 255-268. https://doi.org/10.1016/j.applthermaleng.2003.08.015
[3]
Khan, F.A., Imran, M., Abbas, H. and Durad, M.H. (2017) A Detection and Prevention System against Collaborative Attacks in Mobile ad Hoc Networks. Future Generation Computer Systems, 68, 416-427. https://doi.org/10.1016/j.future.2016.07.010
[4]
Song, X., Zhang, Q., Wang, M. and Song, S. (2021) Distributed Estimation for Nonlinear PDE Systems Using Space-Sampling Approach: Applications to High-Speed Aerospace Vehicle. Nonlinear Dynamics, 106, 3183-3198. https://doi.org/10.1007/s11071-021-06725-4
[5]
Song, X., Wang, M., Park, J.H. and Song, S. (2020) Spatial-L∞-Norm-Based Finite-Time Bounded Control for Semilinear Parabolic PDE Systems with Applications to Chemical-Reaction Processes. IEEE Transactions on Cybernetics, 52, 178-191. https://doi.org/10.1109/TCYB.2020.2972634
[6]
Perthame, B. (2004) PDE Models for Chemotactic Movements: Parabolic, Hyperbolic and Kinetic. Applications of Mathematics, 49, 539-564. https://doi.org/10.1007/s10492-004-6431-9
[7]
Ren, Y., Wang, A. and Hong, W. (2017) Fault Diagnosis and Tolerant Control for Discrete Stochastic Distribution Collaborative Control Systems. IEEE Transactions on Systems Man and Cybernetics Systems, 45, 462-471. https://doi.org/10.1109/TSMC.2014.2358635
[8]
Jiang, B., Marcel, S. and Vincent, C. (2006) Fault Accommodation for Nonlinear Dynamic Systems. IEEE Transactions on Automatic Control, 51, 1578-1583. https://doi.org/10.1109/TAC.2006.878732
[9]
Gao, Z., Cecati, C. and Ding, S.X. (2015) A Survey of Fault Diagnosis and Fault-Tolerant Techniques-Part I: Fault Diagnosis with Model-Based and Signal-Based Approaches. IEEE Transactions on Industrial Electronics, 62, 3757-3767. https://doi.org/10.1109/TIE.2015.2417501
[10]
Balogh, A. and Krstic, M. (2002) Infinite Dimensional Backstepping-Style Feedback Transformations for a Heat Equation with an Arbitrary Level of Instability. European Journal of Control, 8, 165-175. https://doi.org/10.3166/ejc.8.165-175
[11]
Cao, F. and Liu, J. (2018) Adaptive Actuator Fault Compensation Control for a Rigid-Flexible Manipulator with ODEs-PDEs Model. International Journal of Systems Science, 49, 1748-1759. https://doi.org/10.1080/00207721.2018.1479002
[12]
Peng, W. and Vachtsevanos, G. (2001) Fault Prognostics Using Dynamic Wavelet Neural Networks. 2001 IEEE Autotestcon Proceedings. IEEE Systems Readiness Technology Conference. (Cat. No.01CH37237), Valley Forge, 20-23 August 2001, 857-870.
[13]
Patan, M. and Uciński, D. (2005) Optimal Activation Strategy of Discrete Scanning Sensors for Fault Detection in Distributed-Parameter Systems. IFAC Proceedings Volumes, 38, 209-214. https://doi.org/10.3182/20050703-6-CZ-1902.01837
[14]
Alonso, A.A. and Ydstie, B.E. (2001) Stabilization of Distributed Systems Using Irreversible Thermodynamics. Automatica, 37, 1739-1755. https://doi.org/10.1016/S0005-1098(01)00140-6
[15]
Demetriou, M.A. and Kazantzis, N. (2004) A New Actuator Activation Policy for Performance Enhancement of Controlled Diffusion Processes. Automatica, 40, 415-421. https://doi.org/10.1016/j.automatica.2003.10.023
[16]
Wang, Z., Zhang, B., Yuan, J. and Che, D. (2018) Robust Adaptive Fault Tolerant Control for a Class of Linearly Parameterized Uncertain Nonlinear Systems: An Integrated Method. Transactions of the Institute of Measurement and Control, 40, 2129-2140. https://doi.org/10.1177/0142331217696142
[17]
Ferdowsi, H., Cai, J. and Sarangapani, J. (2022) Actuator and Sensor Fault Detection and Failure Prediction for Systems with Multi-Dimensional Nonlinear Partial Differential Equations. International Journal of Control, Automation and Systems, 20, 789-802. https://doi.org/10.1007/s12555-019-0622-3
[18]
Baniamerian, A. and Khorasani, K. (2012) Fault Detection and Isolation of Dissipative Parabolic PDEs: Finite-Dimensional Geometric Approach. 2012 American Control Conference, Montreal, 27-29 June 2012, 5894-5899. https://doi.org/10.1109/ACC.2012.6315006
[19]
Demetriou, M.A., Ackleh, A.S. and Reich, S. (1998) Detection and Accommodation of Second Order Distributed Parameter Systems with Abrupt Changes in Input Term: Existence and Approximation. Theory and Practice of Control and Systems, 34, 720-725. https://doi.org/10.1142/9789814447317_0119
[20]
Armaou, A. and Demetriou, M.A. (2008) Robust Detection and Accommodation of Incipient Component and Actuator Faults in Nonlinear Distributed Processes. AIChE Journal, 54, 2651-2662. https://doi.org/10.1002/aic.11539
[21]
Feng, Y., Li, H.X. and Yang, H.D. (2019) Abnormal Source Identification for Parabolic Distributed Parameter Systems. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 51, 5698-5707. https://doi.org/10.1109/TSMC.2019.2956985
[22]
Ghantasala, S. and El-Farra, N.H. (2009) Robust Actuator Fault Isolation and Management in Constrained Uncertain Parabolic PDE Systems. Automatica, 45, 2368-2373. https://doi.org/10.1016/j.automatica.2009.06.024
[23]
Ferdowsi, H. and Jagannathan, S. (2014) Fault Diagnosis of a Class of Distributed Parameter Systems Modeled by Parabolic Partial Differential Equations. 2014 American Control Conference, Portland, 4-6 June 2014, 5434-5439. https://doi.org/10.1109/ACC.2014.6858836
[24]
Du, D.S. (2017) Fault Detection for Discrete-Time Linear Systems Based on Descriptor Observer Approach. Applied Mathematics and Computation, 293, 575-585. https://doi.org/10.1016/j.amc.2016.08.052
[25]
Li, S., Chen, Y. and Zhan, J. (2021) Simultaneous Observer-Based Fault Detection and Event-Triggered Consensus Control for Multi-Agent Systems. Journal of the Franklin Institute, 358, 3276-3301. https://doi.org/10.1016/j.jfranklin.2021.02.009
[26]
Zhao, Z., Yang, Y., Ding, S.X. and Li, L. (2018) Robust Fault Detection for Observer-Based Feedback Control Systems. Circuits, Systems, and Signal Processing, 37, 3364-3382. https://doi.org/10.1007/s00034-017-0726-z
[27]
Dey, S., Perez, H.E. and Moura, S.J. (2019) Robust Fault Detection of a Class of Uncertain Linear Parabolic PDEs. Automatica, 107, 502-510. https://doi.org/10.1016/j.automatica.2019.06.014
[28]
Cai, J., Ferdowsi, H. and Sarangapani, J. (2016) Model-Based Fault Detection, Estimation, and Prediction for a Class of Linear Distributed Parameter Systems. Automatica, 66, 122-131. https://doi.org/10.1016/j.automatica.2015.12.028
[29]
Feng, Y., Wang, Y., Wang, J.W. and Li, H.X. (2022) Backstepping-Based Distributed Abnormality Localization for Linear Parabolic Distributed Parameter Systems. Automatica, 135, Article ID: 109930. https://doi.org/10.1016/j.automatica.2021.109930
[30]
Smyshlyaev, A. and Krstic, M. (2004) Closed-Form Boundary State Feedbacks for a Class of 1-D Partial Integro-Differential Equations. IEEE Transactions on Automatic Control, 49, 2185-2202. https://doi.org/10.1109/TAC.2004.838495
[31]
Smyshlyaev, A. and Krstic, M. (2005) Backstepping Observers for a Class of Parabolic PDEs. Systems and Control Letters, 54, 613-625. https://doi.org/10.1016/j.sysconle.2004.11.001
[32]
Kwan, C., Zhang, X., Xu, R. and Haynes, L. (2003) A Novel Approach to Fault Diagnostics and Prognostics. IEEE International Conference on Robotics and Automation, Taipei, 14-19 September 2003, 604-609. https://doi.org/10.1109/ROBOT.2003.1241660
[33]
Ferdowsi, H., Cai, J. and Jagannathan, S. (2019) Fault Detection and Estimation for a Class of Nonlinear Distributed Parameter Systems. 2019 IEEE International Conference on Prognostics and Health Management, San Francisco, 17-20 June 2019, 1-8. https://doi.org/10.1109/ICPHM.2019.8819432
[34]
Meurer, T. (2013) On the Extended Luenberger-Type Observer for Semilinear Distributed-Parameter Systems. IEEE Transactions on Automatic Control, 58, 1732-1743. https://doi.org/10.1109/TAC.2013.2243312
[35]
Chen, L. (2022) Backstepping-Based Distributed Abnormality Detection for Nolinear Parabolic Distributed Prameter Systems. Engineering, 14, 285-299. https://doi.org/10.4236/eng.2022.147023
[36]
Tarammim, A. and Akter, M. (2022) A Comparative Study of Synchronization Methods of Rucklidge Chaotic Systems with Design of Active Control and Backstepping Methods. International Journal of Modern Nonlinear Theory and Application, 11, 31-51. https://doi.org/10.4236/ijmnta.2022.112003
[37]
Lavretsky, E. and Wise, K.A. (2012) Robust Adaptive Control. In: Lavretsky, E. and Wise, K.A., Eds., Robust and Adaptive Control: With Aerospace Applications, Springer, London, 317-353. https://doi.org/10.1007/978-1-4471-4396-3_11
