Interval observer versus set-membership approaches for fault detection in uncertain systems using zonotopes. (English) Zbl 1418.93259
Summary: This paper presents both analysis and comparison of the interval observer-based and set-membership approaches for the state estimation and fault detection (FD) in uncertain linear systems. The considered approaches assume that both state disturbance and measurement noise are modeled in a deterministic context following the unknown but bounded approach. The propagation of uncertainty in the state estimation is bounded through a zonotopic set representation. Both approaches have been mathematically related and compared when used for state estimation and FD. A case study based on a two-tanks system is employed for showing the relationship between both approaches while comparing their performance.
MSC:
| 93E10 | Estimation and detection in stochastic control theory |
| 93C41 | Control/observation systems with incomplete information |
| 93C05 | Linear systems in control theory |
Keywords:
fault detection; interval observer; minimum detectable fault; set membership; state estimation; uncertaintyReferences:
| [1] | BlankeM, KinnaertM, LunzeJ, StaroswieckiM. Diagnosis and Fault‐Tolerant Control. New York, NY: Springer; 2006. · Zbl 1126.93004 |
| [2] | GertlerJ. Fault Detection and Diagnosis in Engineering Systems. New York, NY: Marcel Dekker; 1998. |
| [3] | KalmanRE. A new approach to linear filtering and prediction problems. J Basic Eng. 1960;82(1):35‐45. |
| [4] | EfimovD, RaïssiT, ChebotarevS, ZolghadriA. Interval state observer for nonlinear time varying systems. Automatica. 2013;49(1):200‐205. · Zbl 1258.93032 |
| [5] | MazencF, BernardO. Interval observers for linear time‐invariant systems with disturbances. Automatica. 2011;47(1):140‐147. · Zbl 1209.93024 |
| [6] | PuigV, StancuA, EscobetT, NejjariF, QuevedoJ, PattonRJ. Passive robust fault detection using interval observers: application to the DAMADICS benchmark problem. Control Eng Pract. 2006;14(6):621‐633. |
| [7] | BlesaJ, RotondoD, PuigV, NejjariF. FDI and FTC of wind turbines using the interval observer approach and virtual actuators/sensors. Control Eng Pract. 2014;24:138‐155. |
| [8] | RakaSA, CombastelC. Fault detection based on robust adaptive thresholds: a dynamic interval approach. Annu Rev Control. 2013;37(1):119‐128. |
| [9] | RaïssiT, EfimovD, ZolghadriA. Interval state estimation for a class of nonlinear systems. IEEE Trans Autom Control. 2012;57(1):260‐265. · Zbl 1369.93074 |
| [10] | AlamoT, BravoJM, CamachoEF. Guaranteed state estimation by zonotopes. Automatica. 2005;41(6):1035‐1043. · Zbl 1091.93038 |
| [11] | LeVTH, StoicaC, AlamoT, CamachoEF, DumurD. Zonotope‐based set‐membership estimation for multi‐output uncertain systems. Paper presented at: 2013 IEEE International Symposium on Intelligent Control (ISIC); 2013; Hyderabad, India. |
| [12] | MilaneseM, NortonJ, Piet‐LahanierH, WalterÉ. Bounding Approaches to System Identification. New York, NY: Springer Science & Business Media; 2013. |
| [13] | BrondstedA. An Introduction to Convex Polytopes. New York, NY: Springer Science & Business Media; 2012. |
| [14] | WeiG, LiuS, SongY, LiuY. Probability‐guaranteed set‐membership filtering for systems with incomplete measurements. Automatica. 2015;60:12‐16. · Zbl 1331.93205 |
| [15] | ZhangB, LamJ, XuS. Reachable set estimation and controller design for distributed delay systems with bounded disturbances. J Frankl Inst. 2014;351(6):3068‐3088. · Zbl 1290.93020 |
| [16] | Tornil‐SinS, Ocampo‐MartinezC, PuigV, EscobetT. Robust fault detection of non‐linear systems using set‐membership state estimation based on constraint satisfaction. Eng Appl Artif Intell. 2012;25(1):1‐10. |
| [17] | YangF, LiY. Robust set‐membership filtering for systems with missing measurement: a linear matrix inequality approach. IET Signal Process. 2012;6(4):341‐347. |
| [18] | CombastelC. A state bounding observer for uncertain non‐linear continuous‐time systems based on zonotopes. In: Proceedings of the 44th IEEE Conference on Decision and Control; 2005; Seville, Spain. |
| [19] | XuF, PuigV, Ocampo‐MartinezC, OlaruS, StoicanF. Set‐theoretic methods in robust detection and isolation of sensor faults. Int J Syst Sci. 2015;46(13):2317‐2334. · Zbl 1333.93153 |
| [20] | LeVTH, AlamoT, CamachoEF, StoicaC, DumurD. A new approach for guaranteed state estimation by zonotopes. Paper presented at: 18th World Congress IFAC; 2011; Milan, Italy. |
| [21] | CombastelC. A state bounding observer based on zonotopes. Paper presented at: European Control Conference (ECC); 2003; Cambridge, UK. |
| [22] | ChenJ, PattonRJ. Robust Model‐Based Fault Diagnosis for Dynamic Systems. New York, NY: Springer Science & Business Media; 2012. |
| [23] | DingS. Model‐Based Fault Diagnosis Techniques: Design Schemes, Algorithms, and Tools. Berlin, Germany: Springer Science & Business Media; 2008. |
| [24] | ZhongM, DingSX, LamJ, WangH. An LMI approach to design robust fault detection filter for uncertain LTI systems. Automatica. 2003;39(3):543‐550. · Zbl 1036.93061 |
| [25] | SadrniaMA, ChenJ, PattonRJ. Robust fault diagnosis observer design using H_∞ optimisation and μ synthesis. IEE Colloq Model Signal Process Fault Diagn. 1996:1‐9. |
| [26] | LiuN, ZhouK. Optimal solutions to multi‐objective robust fault detection problems. Paper presented at: 46th IEEE Conference on Decision and Control; 2007; New Orleans, LA. |
| [27] | HouM, PattonRJ. An LMI approach to H_−/H_∞ fault detection observers. Paper presented at: UKACC International Conference on Control; 1996; Exeter, UK. |
| [28] | LiX‐J, YangG‐H. Fault detection in finite frequency domain for Takagi‐Sugeno fuzzy systems with sensor faults. IEEE Trans Cybern. 2014;44(8):1446‐1458. |
| [29] | LiuJ, WangJL, YangG‐H. An LMI approach to minimum sensitivity analysis with application to fault detection. Automatica. 2005;41(11):1995‐2004. · Zbl 1087.93019 |
| [30] | HenryD. A norm‐based point of view for fault diagnosis. Application to aerospace missions. Paper presented at: 8th European Workshop on Advanced Control and Diagnosis; 2010; Ferrara, Italy. |
| [31] | JaimoukhaIM, LiZ, PapakosV. A matrix factorization solution to the H_−/H_∞ fault detection problem. Automatica. 2006;42(11):1907‐1912. · Zbl 1261.93040 |
| [32] | WangJL, YangG‐H, LiuJ. An LMI approach to H_− index and mixed H_−/H_∞ fault detection observer design. Automatica. 2007;43(9):1656‐1665. · Zbl 1128.93321 |
| [33] | DingSX, JeinschT, FrankPM, DingEL. A unified approach to the optimization of fault detection systems. Int J Adapt Control Signal Process. 2000;14(7):725‐745. · Zbl 0983.93016 |
| [34] | TabatabaeipourSM, BakT. Robust observer‐based fault estimation and accommodation of discrete‐time piecewise linear systems. J Frankl Inst. 2014;351(1):277‐295. · Zbl 1293.93725 |
| [35] | MeseguerJ, PuigV, EscobetT, SaludesJ. Observer gain effect in linear interval observer‐based fault detection. J Process Control. 2010;20(8):944‐956. |
| [36] | LeVTH, StoicaC, AlamoT, CamachoEF, DumurD. Zonotopes: From Guaranteed State‐Estimation to Control. Hoboken, NJ: John Wiley & Sons; 2013. |
| [37] | CombastelC. Zonotopes and Kalman observers: gain optimality under distinct uncertainty paradigms and robust convergence. Automatica. 2015;55:265‐273. · Zbl 1377.93161 |
| [38] | OgataK. Discrete‐Time Control Systems. Upper Saddle River, NJ: Prentice Hall; 1995. |
| [39] | LeVTH, StoicaC, AlamoT, CamachoEF, DumurD. Zonotopic guaranteed state estimation for uncertain systems. Automatica. 2013;49(11):3418‐3424. · Zbl 1315.93077 |
| [40] | JohanssonKH. The quadruple‐tank process: a multivariable laboratory process with an adjustable zero. IEEE Trans Control Syst Technol. 2000;8(3):456‐465. |
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.
