×

A backstepping-based fault compensation scheme for a class of Euler-Bernoulli beam-ODE cascade systems. (English) Zbl 1480.93109

Summary: This paper develops a fault compensation scheme for a class of Euler-Bernoulli beam-ODE cascade systems to deal with certain boundary input faults, using a model transform-based backstepping control design. A model transformation is introduced to convert the Euler-Bernoulli beam-ODE cascade system to a Schrödinger-ODE cascade system. The FTC law is designed to compensate boundary input faults for the Schrödinger-ODE cascade system by constructing a normal intermediate system and a new exponentially stable target system. The purposes of the two-step backstepping are to bring in a state feedback and to improve the system performance. The performance of the target system, intermediate system, and Schrödinger-ODE cascade system is analysed in the Riesz basis frame. The stability analysis of the original Euler-Bernoulli beam-ODE cascade system is further provided. Simulation results illustrate the effectiveness of the proposed fault compensation scheme.

MSC:

93B35 Sensitivity (robustness)
93C20 Control/observation systems governed by partial differential equations
93C15 Control/observation systems governed by ordinary differential equations
93B52 Feedback control
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Blanke, M.; Kinnaert, M.; Lunze, J.; Staroswiecki, M., Diagnosis and fault-tolerant control (2015), Berlin: Springer Verlag, Berlin
[2] Cheng, M. B.; Radisavljevic, V.; Su, W. C., Sliding mode boundary control of a parabolic PDE system with parameter variations and bouondary uncertainties, Automatica, 47, 2, 381-387 (2011) · Zbl 1213.35239 · doi:10.1016/j.automatica.2010.10.045
[3] Franze, G.; Tedesco, F.; Famularo, D., Actuator fault tolerant control: A receding horizon set-theoretic approach, IEEE Transactions on Automatic Control, 60, 8, 2225-2230 (2015) · Zbl 1360.93450 · doi:10.1109/TAC.2014.2375731
[4] Gao, S. Q.; Liu, J. K., Adaptive fault-tolerant vibration control of a wind turbine blade with actuator stuck, International Journal of Control, 1-12 (2018)
[5] Gao, Y.; Wu, H. N.; Wang, J. W.; Guo, L., Feedback control design with vibration suppression for flexible air-breathing hypersonic vehicles, Sciece China Information Sciences, 57, 3, 1-14 (2014) · Zbl 1336.93069 · doi:10.1007/s11432-012-4765-6
[6] Ge, S. S.; Zhang, S.; He, W., Vibration control of an Euler-Bernoulli beam under unknown spatiotemporally varying disturbance, International Journal of Control, 84, 5, 947-960 (2011) · Zbl 1245.93065 · doi:10.1080/00207179.2011.584197
[7] Ghantasala, S.; El-Farra, N. H., Robust actuator fault isolation and management in constrained uncertain parabolic PDE systems, Automatica, 45, 10, 2368-2373 (2009) · Zbl 1179.93103 · doi:10.1016/j.automatica.2009.06.024
[8] Guo, B. Z.; Jin, F. F., The active disturbance rejection and sliding mode control approach to the stabilization of Euler-Bernoulli beam equation with boundary input disturbance, Automatica, 49, 9, 2911-2918 (2013) · Zbl 1364.93637 · doi:10.1016/j.automatica.2013.06.018
[9] Guo, B. Z.; Liu, J. J.; Al-Fhaid, A. S.; Younas, A. M. M.; Asiri, A., The active disturbance rejection control approach to stabilisation of coupled heat and ODE system subject to boundary control matched disturbance, International Journal of Control, 88, 8, 1554-1564 (2015) · Zbl 1337.93078 · doi:10.1080/00207179.2015.1010179
[10] Hasan, A.; Aamo, O. M.; Krstic, M., Boundary observer design for hyperbolic PDE-ODE cascade systems, Automatica, 68, 75-86 (2016) · Zbl 1334.93037 · doi:10.1016/j.automatica.2016.01.058
[11] He, W.; Ge, S. S.; How, B. V. E.; Choo, Y. S.; Hong, K. S., Robust adaptive boundary control of a flexible marine riser with vessel dynamics, Automatica, 47, 4, 722-732 (2011) · Zbl 1215.93073 · doi:10.1016/j.automatica.2011.01.064
[12] He, W.; Zhang, S.; Ge, S. S., Adaptive boundary control of a nonlinear flexible string system, IEEE Transactions on Control Systems Technology, 22, 3, 1088-1093 (2014) · doi:10.1109/TCST.2013.2278279
[13] Jiang, B.; Staroswiecki, M.; Cocquempot, V., Fault accommodation for nonlinear dynamic systems, IEEE Transactions on Automatic Control, 51, 9, 1578-1583 (2006) · Zbl 1366.93694 · doi:10.1109/TAC.2006.878732
[14] Kang, W.; Fridman, E., Sliding mode control of Schrödinger-ODE in the presence of unmatched disturbance, Systems & Control Letters, 98, 65-73 (2016) · Zbl 1351.93036 · doi:10.1016/j.sysconle.2016.10.009
[15] Kang, W.; Fridman, E., Boundary constrained control of delayed nonlinear Schrödinger equation, IEEE Transactions on Automatic Control, 63, 11, 3873-3880 (2018) · Zbl 1423.93303 · doi:10.1109/TAC.2018.2800526
[16] Krstic, M., Delay compensation for nonlinear, adaptive, and PDE systems (2009), Birkhauser: Springer, Birkhauser · Zbl 1181.93003
[17] Krstic, M.; Kanellakopoulos, I.; Kokotovic, P. V., Nonlinear and adaptive control design (1995), New York, NY: Wiley, New York, NY
[18] Krstic, M.; Smyshlyaev, A., Boundary control of PDEs: A course on backstepping designs (2008), Philadelphia: Society for Industrial and Applied Mathematics, Philadelphia · Zbl 1149.93004
[19] Liu, Z. J.; Liu, J. K.; He, W., Robust adaptive fault tolerant control for a linear cascaded ODE-beam system, Automatica, 98, 42-50 (2018) · Zbl 1406.93094 · doi:10.1016/j.automatica.2018.09.021
[20] Ma, H. J.; Yang, G. H., Adaptive fault tolerant control of cooperative heterogeneous systems with actuator faults and unreliable interconnections, IEEE Transactions on Automatic Control, 61, 11, 3240-3255 (2016) · Zbl 1359.93228 · doi:10.1109/TAC.2015.2507864
[21] Mahmoud, M. S.; Memon, A. M.; Shi, P., Observer-based fault-tolerant control for a class of nonlinear network control systems, International Journal of Control, 87, 8, 1707-1715 (2014) · Zbl 1317.93089 · doi:10.1080/00207179.2014.883646
[22] Mallavalli, S.; Fekih, A., A fault tolerant tracking control for a quadrotor UAV subject to simultaneous actuator faults and exogenous disturbances, International Journal of Control, 1-14 (2018) · Zbl 1440.93066 · doi:10.1080/00207179.2018.1484173
[23] Meglio, F.; Argomedo, F.; Hu, L.; Krstic, M., Stabilization of coupled linear heterodirectional hyperbolic PDE-ODE systems, Automatica, 87, 281-289 (2018) · Zbl 1378.93102 · doi:10.1016/j.automatica.2017.09.027
[24] Nwokah, O.; Hurmuzlu, Y., The mechanical systems design handbook: Modeling measurement and control (2002), Boca, Raton: CRC Press, Boca, Raton
[25] Patton, R. J.; Frank, P.; Clark, R., Issues of fault diagnosis for dynamic systems (2013), London: Springer Science & Business Media, London
[26] Ren, B. B.; Wang, J. M.; Krstic, M., Stabilization of an ODE-Schrödinger cascade, Systems & Control Letters, 62, 6, 503-510 (2013) · Zbl 1279.93085 · doi:10.1016/j.sysconle.2013.03.003
[27] Smyshlyaev, A.; Krstic, M., Closed form boundary state feedbacks for a class of 1-D partial integro-differential equations, IEEE Transactions on Automatic Control, 49, 12, 2185-2202 (2004) · Zbl 1365.93193 · doi:10.1109/TAC.2004.838495
[28] Su, X.; Shi, P.; Wu, L. G.; Song, Y. D., Fault detection filtering for nonlinear switched stochatic systems, IEEE Transactions on Automatic Control, 61, 5, 1310-1315 (2016) · Zbl 1359.93497 · doi:10.1109/TAC.2015.2465091
[29] Susto, G. A.; Krstic, M., Control of PDE-ODE cascades with Neumann interconnections, Journal of the Franklin Institute, 347, 1, 284-314 (2010) · Zbl 1298.93279 · doi:10.1016/j.jfranklin.2009.09.005
[30] Tao, G.; Chen, S.; Tang, X. D.; Joshi, S. M., Adaptive control of systems with actuator failures (2004), New York, NY: Springer-Verlag, New York, NY · Zbl 1063.93001
[31] Wang, J. M.; Liu, J. J.; Ren, B. B.; Chen, J. H., Sliding mode control to stabilization of cascaded heat PDE-ODE systems subject to boundary control matched disturbance, Automatica, 52, 23-34 (2015) · Zbl 1309.93124 · doi:10.1016/j.automatica.2014.10.117
[32] Wang, J. W.; Liu, Y. J.; Sun, C. Y., Pointwise exponential stabilization of a linear parabolic PDE system using non-collocated pointwise observation, Automatica, 93, 197-210 (2018) · Zbl 1400.93280 · doi:10.1016/j.automatica.2018.03.015
[33] Wang, Y.; Song, Y. D.; Krstic, M.; Wen, C. Y., Fault-tolerant finite time consensus for multiple uncertain nonlinear mechanical systems under single-way directly communication interactions and actuation failures, Automatica, 63, 374-383 (2016) · Zbl 1329.93016 · doi:10.1016/j.automatica.2015.10.049
[34] Wang, J. W.; Wu, H. N., Exponential pointwise stabilization of semilinear parabolic distributed parameter systems via the Takagi-Sugeno fuzzy PDE model, IEEE Transactions on Fuzzy Systems, 26, 1, 155-173 (2018) · doi:10.1109/TFUZZ.2016.2646745
[35] Wang, J. W.; Wu, H. N., Exponentially stabilizing fuzzy controller design for a nonlinear ODE-beam cascaded system and its application to flexible air-breathing hypersonic vehicle, Fuzzy Sets and Systems, 1-21 (2019)
[36] Wang, J. W.; Wu, H. N.; Li, H. X., Fuzzy control design for nonlinear ODE-hyperbolic PDE cascaded systems: A fuzzy and entropy-like lyapunov function approach, IEEE Transactions on Fuzzy Systems, 22, 5, 1313-1324 (2014) · doi:10.1109/TFUZZ.2013.2291569
[37] Wang, Z. P.; Wu, H. N.; Li, H. X., Sampled-data fuzzy control for nonlinear coupled parabolic PDE-ODE systems, IEEE Transactions on Cybernetics, 47, 9, 2603-2615 (2017) · Zbl 1386.93249 · doi:10.1109/TCYB.2017.2690798
[38] Wu, H. N.; Feng, S., Mixed fuzzy/boundary control design for nonlinear coupled systems of ODE and boundary-disturbed uncertain beam, IEEE Transactions on Fuzzy Systems, 26, 6, 3379-3390 (2018) · doi:10.1109/TFUZZ.2018.2826475
[39] Wu, H. N.; Wang, J. W., Static output feedback control via PDE boundary and ODE measurements in linear cascaded ODE-beam systems, Automatica, 50, 2787-2798 (2014) · Zbl 1300.93081 · doi:10.1016/j.automatica.2014.09.006
[40] Yang, H.; Jiang, B.; Staroswiecki, M.; Zhang, Y. M., Fault recoverability and fault tolerant control for a class of interconnected nonlinear systems, Automatica, 54, 49-55 (2015) · Zbl 1318.93032 · doi:10.1016/j.automatica.2015.01.037
[41] Zhang, Y. M.; Jiang, J., Bibliographical review on reconfigurable fault-tolerant control systems, Annual Reviews in Control, 32, 2, 229-252 (2008) · doi:10.1016/j.arcontrol.2008.03.008
[42] Zhang, X. D.; Polycarpou, M. M.; Parisini, T., Adaptive fault diagnosis and fault-tolerant control of MIMO nonlinear uncertain systems, International Journal of Control, 83, 5, 1054-1080 (2010) · Zbl 1197.93091 · doi:10.1080/00207170903580340
[43] Zhao, D.; Jiang, B.; Yang, H.; Tao, G., Fault-tolerant control of flexible air-breathing hypersonic vehicles in linear ODE-beam systems, International Journal of Control, 1-12 (2018)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.