By Andreas Varga
This e-book addresses fault detection and isolation themes from a computational standpoint. in contrast to such a lot present literature, it bridges the distance among the prevailing well-developed theoretical effects and the area of trustworthy computational synthesis procedures.
The model-based method of fault detection and prognosis has been the topic of ongoing study for the prior few many years. whereas the theoretical elements of fault prognosis at the foundation of linear versions are good understood, many of the computational equipment proposed for the synthesis of fault detection and isolation filters aren't passable from a numerical point of view. numerous beneficial properties make this ebook precise within the fault detection literature:
- Solution of normal synthesis difficulties within the such a lot common atmosphere, for either non-stop- and discrete-time structures, whether they're right or now not; as a result, the proposed synthesis tactics can clear up a selected challenge every time an answer exists
- Emphasis at the top numerical algorithms to unravel the synthesis difficulties for linear platforms in generalized state-space shape (also referred to as descriptor systems)
- Development of basic synthesis approaches counting on new computational paradigms, resembling factorization-based layout in line with clear out updating recommendations and nullspace-based synthesis
- Availability of a entire set of unfastened accompanying software program instruments for descriptor structures, which permits readers to simply enforce all synthesis tactics provided within the ebook and guarantees that each one effects are reproducible
This publication is essentially meant for researchers and complicated graduate scholars within the parts of fault analysis and fault-tolerant regulate. it's going to additionally attract mathematicians with an curiosity in control-oriented numerics.
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Extra info for Solving Fault Diagnosis Problems. Linear Synthesis Techniques
N, x (i) (t) ∈ Rn and y(i) (t) ∈ Rp are the state vector and output vector of the i-th system, respectively. For simplicity, we assume that in all models, the dimensions of the state, output and input vectors are the same. 19) describes a family of linearized models for N relevant combinations of plant operating points and plant parameters. In what follows, we describe a simple method to recast such a multiple model into a unique LTI model with additional fictitious noise inputs, which account for the effects of variations in operating points and parameters.
The corresponding TFM is simply G f (λ) := Ss . In the case when f (t) , both actuator and sensor faults are present, then for the fault signal f (t) := a fs (t) the corresponding fault-to-output TFM is G f (λ) := G u (λ)Sa Ss . 4) In general, the matrices Sa and Ss can be chosen to also ensure a certain uniform range of magnitudes of the expected fault signals via appropriate scaling of fault inputs. 2) is obtained with Bf := [ Bu Sa 0 ] and Df := [ Du Sa Ss ]. An important aspect of this approach is that the resulting models with additive faults can simultaneously cover several categories of actuator and sensor faults.
11) S(ρ) = LFTu (M, Δ), M11 M12 is a certain constant matrix with M11 square and Δ = M21 M22 Δ(ρ) is a diagonal matrix depending on the components of ρ such that Δ(ρ0 ) = 0. Straightforward algorithms are available to obtain the above representation. The above LFT-based representation of S(ρ) allows to immediately obtain S (0) = M22 , ΔS = M21 and ΓS (ρ) = Δ(I − ΔM11 )−1 M12 . 5(1 + ρ1 ) C= 011 , 110 Du = 00 . 6 of the nominal value A(0) = A(0, 0). We can recast the effects of uncertain parameters ρ1 and ρ2 as fictitious noise inputs.
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