Solving Fault Diagnosis Problems. Linear Synthesis by Andreas Varga

By Andreas Varga

This publication addresses fault detection and isolation issues from a computational viewpoint. in contrast to such a lot current literature, it bridges the distance among the present well-developed theoretical effects and the world of trustworthy computational synthesis procedures. 

The model-based method of fault detection and prognosis has been the topic of ongoing learn for the prior few many years. whereas the theoretical features of fault prognosis at the foundation of linear types are good understood, lots of the computational equipment proposed for the synthesis of fault detection and isolation filters will not be passable from a numerical point of view. a number of good points make this booklet designated within the fault detection literature:  

  • Solution of normal synthesis difficulties within the so much common atmosphere, for either non-stop- and discrete-time platforms, whether they're right or now not; accordingly, the proposed synthesis approaches can remedy a particular challenge every time an answer exists
  • Emphasis at the top numerical algorithms to resolve the synthesis difficulties for linear platforms in generalized state-space shape (also referred to as descriptor systems)
  • Development of common synthesis methods counting on new computational paradigms, corresponding to factorization-based layout in accordance with filter out updating ideas and nullspace-based synthesis
  • Availability of a entire set of unfastened accompanying software program instruments for descriptor platforms, which permits readers to simply enforce all synthesis systems provided within the ebook and guarantees that every one effects are reproducible 

This booklet is essentially meant for researchers and complex graduate scholars within the components of fault analysis and fault-tolerant regulate. it is going to additionally attract mathematicians with an curiosity in control-oriented numerics.

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Example text

It follows, that all G f j (λ) must have the same set of poles in Ω. To prove sufficiency we show that we can construct a stable filter Q(λ) such that the corresponding R f (λ) is stable and none of its columns R f j (λ), for j = 1, . . , m f , has zeros in Ω. Since all G f j (λ), for j = 1, . . , m f , have the same pole structure for all λ p ∈ Ω, we can express each G f j (λ) in the form G f j (λ) = G f j (λ)/β(λ), where β(λ) is the monic polynomial whose roots are the common poles in Ω of G f j (λ), for j = 1, .

3 In general, the parameter vector ρ can be split in two components, ρ = [ ρ1T ρ2T ]T , where ρ1 includes those model parameters which are susceptible to parametric faults, while ρ2 is the part of parameters which have to be exclusively handled as uncertainties. 15), where, besides the additive fault input terms Bf(0) f (t) and Df(0) f (t), which correspond to the parametric faults in ρ1 , noise input terms Bw(0) w(t) and Dw(0) w(t) have to be added, respectively, which correspond to the parametric uncertainties in ρ2 .

A typical fault evaluation setup used for fault isolation is to define θi (t), the i-th component of θ (t), as a real-time computable approximation of r (i) 2 . The i-th component of ι(t) is set to ιi (t) = 1 if θi (t) > τi (i-th residual fired) or ιi (t) = 0 if θi (t) ≤ τi (i-th residual not fired), where τi is a suitable threshold for the i-th subvector r (i) (t). If a sufficiently large number of measurements are available, then it can be aimed that r (i) is influenced only by the i-th fault signal f i .

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