Exact fault and disturbance decoupling by means of direct input reconstruction and estimation of the inverse dynamics ∗ A. EDELMAYER † , J. BOKOR and Z. SZAB ´ O Systems and Control Laboratory, Computer and Automation Research Institute Hungarian Academy of Sciences, Kende u. 13-17, Budapest, H-1111, Hungary. Abstract— The idea of inversion-based direct input recon- struction for robust detection and separation of multiple, possibly simultaneous faults in the presence of external, non-mutually separable disturbances for linear dynamical systems was presented in [1]. In this short paper this concept is pursued further: it is shown how in a specific filtering structure, relying on the inverse representation of the system, a Luenberger state observer can be designed providing esti- mation of the states of the inverse-based residual generator reverting to disturbance decoupled detection residuals with exact fault separation. This result can be considered as a corollary of the approximate disturbance attenuating solution presented in [1]. I. I NTRODUCTION The distinctive term direct input reconstruction is used to identify a relatively new idea that has been proposed and investigated in the methodology of the design of detection filters for detection, separation and estimation of faults in linear as well as in nonlinear systems quite lately. This approach is an application of dynamic inversion to filtering which is dual to the concept of dynamic inver- sion for control. The difference between these inversion approaches is that control uses a right inverse whereas estimation uses a left inverse of the system. The method arrives at detector architectures whose residual outputs consist of the fault signals while their inputs are the standard observables (inputs and outputs) of the system and possible their time derivatives. The approach makes not only the detection and isolation but also the estimation of the fault signals possible as it was rendered in [2] in an algebraic and in [3], [4] in a geometric approach, respectively. The effectiveness and distinctive capabilities of the direct input reconstruction method applied to robust fault detection and isolation was recently demonstrated in [1]. It was shown, how advanced methods of detection filter design, such as inversion-based residual generation and H ∞ optimal filtering, and the novel combination of them, may contribute to the solution of earlier not solvable problems. Namely, direct fault reconstruction combined ∗ This work has been supported by the Hungarian Scientific Research Fund (OTKA) under grant number K 061081, which is gratefully acknowledged by the authors. † Corresponding author. E-mail: edelmayer@sztaki.hu with an H ∞ filter was applied to disturbance attenuated fault decoupling. The idea of inversion-based direct input reconstruction for robust detection, estimation and separation of multiple, possibly simultaneous faults was presented and demon- strated in [1] by considering the linear dynamical system subject to faults and external disturbances ˙ x = Ax + B u u + B d d + L 2 f 2 (1) y 1 = C 1 x + D u,1 u + D d,1 d + Mf 1 , (2) y 2 = C 2 x + D u,2 u + D d,2 d , (3) where M is full rank with x ∈ R n , u ∈ R m and y 1 ∈ R p 1 and y 2 ∈ R p 2 , where the rest of the matrices of the system representation are given in the appropriate dimensions. The unknown, bounded time functions f 1 (t ), f 2 (t ), d (t ) represent the actuator and sensor faults, moreover, the disturbance, respectively. An underlying working assump- tion in [1] was that faults and disturbances in (1)–(3) were non-mutually separable in terms of the separability con- ditions of the traditional filter design techniques such as geometric decoupling or unknown input observer design methods. The objective was to construct a robust residual gen- erator in the state space, that shows up the effects of f (t ) at its output irrespectively of the presence of the disturbance input d (t ) so that the separation between the respective fault transmission levels is maintained making the detection and isolation robustly possible. Because of the presence of the non-separable disturbance in the system, the variety of applicable solution approaches, available in the literature, is traditionally confined to methods providing suppression of the disturbance effects on the filter’s residual. Two approaches of this type were presented and con- trasted to each other in [1]. One of these solutions was obtained with using traditional H ∞ filtering providing optimal disturbance suppression. As it was shown, this solution suffers from a tendency of poor fault separation performance in general. 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