FAULT ISOLATION IN UNCERTAIN SYSTEMS VIA ROBUST H-infinity FILTERING Internal Control Meeting Zhenhai Li Working with Dr. Imad Jaimoukha, Emmanuel Mazars 18/05/06

Aims and Motivation Project Aims: Design and implement a condition monitoring system to detect and identify sensor, process and actuator faults in a large scale system that is insensitive to disturbances and to system/model mismatch. Military Context: Enhance the reliability of sensor systems, especially in hostile environments, via fault handling or post-fault configuration. Domain of applications: Noisy control and monitoring systems that involve a large number of sensors. Analytical Redundancy: (a)In contrast to hardware redundancy, internal faults are indicated by analysis of input-output relationships. (b)The FDI filter is a condition monitoring system that does not affect the process performance.

Fault and Disturbance Modeling GdGd GfGf Filter F fault residual disturbance ‘small’ gain‘large’ gain Decision threshold (via online/offline testing) post-fault configuration Faults and disturbances affect the system via their corresponding distribution matrices as above. The above figure illustrates different types of faults and disturbances which can be represented in this framework.

Post-fault Configuration Fault handling utilizes integrated fault diagnosis system to carry out self-repairing actions or possible fault-tolerant control. The FDI system also provides information on fault signatures which can facilitate maintenance. And the worst case …

Principles of model-based FDI Analytical redundancy method utilise the following observer to generate residual signals containing fault signatures

Observer-based Isolation Filter Design Problem Formulation: The solution is obtained by minimizing subject to the LMI where P, Z and S are design variables and L 1, L 2 and H 1 depend on T r,f (s). Multiple faults detection and isolation are realized via the design of a stable isolation filter such that the H-infinity norm of the transfer matrix function from disturbances to the residual is minimized (for fault detection) subject to the constraint that the transfer matrix function from faults to residual is equal to a pre--assigned diagonal transfer matrix (for fault isolation). The optimization of disturbance decoupling is accomplished via the help of eigenstructure assignment, Bounded Real Lemma and linear matrix inequalities.

Unfiltered residual signal: faults hard to detect, isolate and distinguish from disturbances. Experimental Testing: 1: Residual for fault indication and identification. 2: Residual for carrying out fault tolerant actions. pitch angle sensor fault (4th sec) pitch rate sensor fault (6th sec) Filtered residual signal: faults easily detected and identified. wind gust (persistent) disturbance (2nd sec) F16XL Model

FDI for Uncertain Systems: Model Matching For robust multi fault detection, we would like to regard the alternative performance index: where is a parameter and S is the set of all transfer matrices with a special structure e.g., diagonal. The problem is solved by quadratic matrix inequalities (QMIs).  Minimizing will improve fault detection  Minimizing will improve fault isolation

Simulation Results GE-21 Jet Engine Example  fault f1 simulated by a positive jump at the 14th second  fault f2 simulated by a negative jump at the 22th second  fault f3 simulated by a soft bias at the 22th second

FDI for Uncertain Systems: Robust Filtering Modeling uncertainties for FDI is far from resolved. We incorporate a reference into a robust H-infinity filtering framework to represent the detection and isolation requirement. Performance Index: zz f w Where z is the estimated residual, z f is the reference residual and w represents extraneous signals. Then, the extended robust H-infinity filtering problem is solved by a non linear matrix inequality (NLMI). Linearization of the NLMI results in a tractable LMI solution.

-A LTI system with uncertainties -Uncertainties are subject to integral quadratic constraints 5 Robust Filtering : System

-Fault isolation filter for uncertainty-free system -Reference residual is constructed as the output of the observer LH -By choosing L and H, we can force the dynamic to be diagonal 5 Robust Filtering : Reference Model

-We incorporate the reference dynamic into our system to form -where -This transform the residual design to be a robust H-infinity filtering problem, namely, finding an optimal estimator 5 Robust Filtering : System Augmentation

P 1 =P 1 T R=R T MNZJ>0 -The robust filtering problem with IQC uncertainties has sufficient solution if there exists P 1 =P 1 T, R=R T, M, N, Z and diagonal J>0 such that 5 Robust Filtering : LMI Formulation

Simulation Results GE-21 Jet Engine Example (with model uncertainty)

Application on Vibration Control: Structured vibration control, is the application of direct velocity feedback control on vibrating structures to provide additional damping and reduce vibration levels, where decentralised controller is deployed. The design of a fault detection system to monitor velocity sensor and electrodynamic inertial actuator is necessary to enhance reliability of the entire system. Difficulties:  Large scale system with n>200  Fault indicating matrix CB f has no full rank Ideas:  Balanced realization to focus on fundamental components.  If CAB f has full rank, design a second order fault transfer matrix T rf.

Technical Outputs Papers  Z. Li, I.M. Jaimoukha and E.F.M. Mazars, “State space solution to the H_/H-infinity fault detection problem”, Int. J. of Robust and Nonlinear Control, 2006, to be submitted  Z. Li, I.M. Jaimoukha, “Observer-based fault detection and isolation filter design”, International Journal of Control, 2006, under review  I.M. Jaimoukha, Z. Li and V. Papakos, “A matrix factorization solution to the H_/H-infinity fault detection problem”, Automatica, 2006, accepted Conferences & Seminar  Z. Li, I.M. Jaimoukha and E. Mazars, “State space solution to the H_/H-infinity fault detection problem”, IEEE Conference on Decision and Control, 2006, submitted  Z. Li, I.M. Jaimoukha and E.F.M. Mazars, “Fault isolation in uncertain systems via robust H-infinity filtering”, International Control Conference 2006, Glasgow, U.K.  I.M Jaimoukha, Z. Li and E. Mazars, “Filter design to the optimal weighted H_/H-infinity fault detection problem”, International Control Conference 2006, Glasgow, U.K.  Z. Li, I.M. Jaimoukha and E.F.M. Mazars, “A reference model based robust H-infinity filtering approach to fault detection in uncertain systems”, IFAC Safeprocess 2006, Beijing, China  E.F.M. Mazars, I.M. Jaimoukha and Z. Li, “A QMI solution to the robust fault detection and isolation problem”, IFAC Safeprocess 2006, Beijing, China  E.F.M. Mazars, I.M. Jaimoukha and Z. Li, “A linear matrix inequality solution to the robust fault detection and isolation problem”, MTNS 2006, Kyoto, Japan  I.M. Jaimoukha, Z. Li and E.F.M. Mazars, “Fault isolation filter with linear matrix inequality solution to optimal decoupling”, IEEE ACC 2006, Minnesota, U.S. Software  Algorithms implemented in MATLAB/SIMULINK and available upon request.

Exploitation Future Direction In addition to robustness, another issue that requires further research is the large scale nature of many sensor systems. Model reduction techniques will be applied to such systems to improve the performance of our schemes. To cope with more practical situations, we can apply the above methods to other classes of system, such as linear parameter-varying systems and descriptor systems, where we have expertise. Our emphasis so far has been on detection and isolation of faults. A natural extension of our work will be in the area of fault tolerant control and post fault reconfiguration.

Thank You