Abstract
This paper deals with the problem of fault-tolerant control (FTC) for switched systems in continuous-time case. A switched proportional integral observer is designed to estimate the state and the fault simultaneously. According to the fault estimation information, a fault-tolerant control strategy is built to automatically accommodate faults while maintaining system performances such as stability. Delay-dependent conditions are derived using a multiple Lyapunov–Krasovskii functional while respecting the average dwell time constraints in the objective to obtain less conservative results. A switched electrical circuit is studied to illustrate the applicability of the suggested FTC technique.
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References
Du D, Jiang B, Shi P (2011) Fault estimation and accommodation for switched systems with time-varying delay. Int J Control Autom Syst 9(3):442–451
Du D, Jiang B, Shi P (2012) Sensor fault estimation and compensation for time-delay switched systems. Int J Syst Sci 43(4):629–640
Du D, Jiang B, Shi P (2015) Fault tolerant control for switched linear systems. Springer, Berlin, pp 119–134
Ladel AA, Benzaouia A, Outbib R, Ouladsine M (2021) Integrated sensor fault estimation and control for continuous-time switched systems: A new separation principle. ISA Trans 112:224–233
Shen Q, Jiang B, Shi P (2017) Adaptive fault tolerant control against actuator faults. Int J Adapt Control Signal Process 31(2):147–162
Zhang K, Jiang B, Shi P (2009) Fast fault estimation and accommodation for dynamical systems. IET Control Theory Appl 3(2):189–199
Zhang K, Jiang B, Shi P (2009) A new approach to observer-based fault-tolerant controller design for Takagi–Sugeno fuzzy systems with state delay. Circuits Syst Signal Process 28(5):679–697
Gao Z, Jiang B, Shi P, Liu J, Xu Y (2012) Passive fault-tolerant control design for near-space hypersonic vehicle dynamical system. Circuits Syst Signal Process 31(2):565–581
Tabatabaeipour S, Zamanabadi RI, Bak T, Ravn A (2012) Passive fault-tolerant control of discrete time piecewise affine systems against actuator faults. Int J Syst Sci 43(11):1985–1997
Davoodi M, Golabi A, Talebi H, Momeni H (2012) Simultaneous fault detection and control design for switched linear systems: a linear matrix inequality approach. J Dyn Syst Meas Control 134(6):061010–061010
Ke Z, Bin J, Vincent C (2008) Adaptive observer-based fast fault estimation. Int J Control Autom Syst 6(3):320–326
Ke Z, Bin J, Peng S, Vincent C (2018) Observer-based fault estimation techniques. Springer, Berlin
Xianghua W, Pin TC, Donghua Z (2017) A novel sliding mode observer for state and fault estimation in systems not satisfying matching and minimum phase conditions. Automatica 79:290–295
Jian Z, Kumar SA, Kiong NS (2013) Robust sensor fault estimation scheme for satellite attitude control systems. J Franklin Inst 350(9):2581–2604
Jian, H., Xiuhua, L., Xinjiang, W., Xin, H., Huifeng, Z., (2019) Reduced-order observer based fault estimation and fault-tolerant control for switched stochastic systems with actuator and sensor faults. ISA Trans 88:91–101
David AJ, Ixbalank T, Alberto V, Alejandro V, Germán B (2022) Experimental validation of an interval observer-based sensor fault detection strategy applied to a biohydrogen production dark fermenter. J Process Control 114:131–142
Sharifuddin M (2015) Design of unknown input observer for non-linear systems with time-varying delays. Int J Dyn Control 3(4):448–456
Bin X, Zhongke S, Fuchun S, Wei H (2018) Barrier Lyapunov function based learning control of hypersonic flight vehicle with AOA constraint and actuator faults. IEEE Trans Cybern 49(3):1047–1057
Hossein S, Ali A (2019) Active fault tolerant control for switched positive linear systems. Int J Robust Nonlinear Control 29(14):4971–4984
Guzman J, López-Estrada F, Estrada-Manzo V, Valencia-Palomo G (2021) Actuator fault estimation based on a proportional-integral observer with nonquadratic Lyapunov functions. Int J Syst Sci 52(9):1938–1951
Shaoxin S, Yingchun W, Huaguang Z, Jiayue S (2020) Multiple intermittent fault estimation and tolerant control for switched TS fuzzy stochastic systems with multiple time-varying delays. Appl Math Comput 377(125):114
Defoort M, Veluvolu K, Rath J, Djemai M (2016) Adaptive sensor and actuator fault estimation for a class of uncertain Lipschitz nonlinear systems. Int J Adapt Control Signal Process 30(2):271–283
Su X, Liu X, Shi P, Song Y (2018) Sliding mode control of hybrid switched systems via an event-triggered mechanism. Automatica 90:294–303
Zhao X, Shi P, Yin Y, Nguang S (2017) New results on stability of slowly switched systems: a multiple discontinuous Lyapunov function approach. IEEE Trans Autom Control 62(7):147–162
Lin H, Antsaklis P (2009) Stability and stabilizability of switched linear systems: a survey of recent results. IEEE Trans Autom Control 54(2):308–322
Xiang W, Lam J, Li P (2018) On stability and \(h_{\infty }\) control of switched systems with random switching signals. Automatica 95:419–425
Yu Q, Yuan X (2021) Stability analysis of positive switched systems based on a \(\phi \)-dependent average dwell time approach. J Franklin Inst
Liu T, Wu B, Wang Y, Liu L (2017) New stabilization results for discrete-time positive switched systems with forward mode-dependent average dwell time. Trans Inst Meas Control 39(2):224–229
Dongsheng D, Vincent C (2018) Non-fragile actuator fault estimation and accommodation for switched systems. IFAC-PapersOnLine 51(24):110–116
Dong Y, Guangdeng Z, Jun Z (2019) \(h_{\infty }\) fault-tolerant control for switched linear parameter-varying systems: a parameter and state-dependent switching method with dwell time. Proc Inst Mech Eng Part I: J Syst Control Eng 233(1):18–30
Liu Z, Zhang X, Lu X, Hou T (2019) Exponential stability of impulsive positive switched systems with discrete and distributed time-varying delays. Int J Robust Nonlinear Control 29(10):3125–3138
Dongsheng D, Bin J (2016) Actuator fault estimation and accommodation for switched systems with time delay: discrete-time case. ISA Trans 62:137–144
Dongsheng D, Bin J, Peng S (2015) Fault tolerant control for switched linear systems. Springer, Berlin, pp 119–134
Montadher S (2015) A robust adaptive observer-based time varying fault estimation. AUT J Model Simul 47(2):11–19
Du D, Jiang B, Shi P (2011) Fault estimation and accommodation for switched systems with time-varying delay. Int J Control Autom Syst 9(3):442–451
Telbissi K, Benzaouia A (2020) Robust fault-tolerant control for discrete-time switched systems with time delays. Int J Adapt Control Signal Process 34(3):389–406
Telbissi K, Benzaouia A (2019) Actuator fault estimation based on proportional–integral observer for delayed continuous-time switched systems. Circuits Syst Signal Process 1–15
Hespanha J, Morse A, (1999), Stability of switched systems with average dwell-time. In: Proceedings of the 38th IEEE conference on decision and control (Cat. No. 99CH36304), vol 3. IEEE, pp 2655–2660
Tseng C, Chen B (2004) \(l \infty \)-gain fuzzy control for nonlinear dynamic systems with persistent bounded disturbances. In: 2004 IEEE international conference on fuzzy systems, vol 2. IEEE, pp 783–788
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Telbissi, K., Benbraim, A. & Benzaouia, A. A fault estimation and fault accommodation-based PI observer for switched systems with time delay. Int. J. Dynam. Control 11, 748–758 (2023). https://doi.org/10.1007/s40435-022-01018-z
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DOI: https://doi.org/10.1007/s40435-022-01018-z