By Andreas Varga
This publication addresses fault detection and isolation themes from a computational standpoint. not like such a lot current literature, it bridges the distance among the prevailing well-developed theoretical effects and the world of trustworthy computational synthesis techniques.
The model-based method of fault detection and prognosis has been the topic of ongoing examine for the prior few many years. whereas the theoretical facets 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 aren't passable from a numerical viewpoint. numerous positive aspects make this ebook exact within the fault detection literature:
- Solution of ordinary synthesis difficulties within the so much basic atmosphere, for either non-stop- and discrete-time structures, whether they're right or now not; for this reason, the proposed synthesis systems can resolve a particular challenge at any time when an answer exists
- Emphasis at the top numerical algorithms to unravel the synthesis difficulties for linear structures in generalized state-space shape (also often called descriptor systems)
- Development of common synthesis techniques counting on new computational paradigms, equivalent to factorization-based layout in line with filter out updating ideas and nullspace-based synthesis
- Availability of a entire set of loose accompanying software program instruments for descriptor structures, which permits readers to simply enforce all synthesis methods awarded within the booklet and guarantees that each one effects are reproducible
This booklet is basically meant for researchers and complicated graduate scholars within the components of fault prognosis and fault-tolerant keep watch over. it is going to additionally entice mathematicians with an curiosity in control-oriented numerics.
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Example text
Several values for Fa(i) can be employed to cope with different degrees of failures of a single actuator. A complete failure of the i-th actuator can be easily modelled by setting the i-th diagonal element to zero. , bias, drift, frozen value) can be modelled by adding fictive disturbances which act on the respective outputs. For example, for a fault in the i-th output sensor we can define the fault model with (i) G (i) u (λ) = Fs G u (λ), (i) G (i) d (λ) = [ Fs G d (λ), ei ], where Fs(i) is chosen a diagonal matrix (similar to Fa(i) ) to account for the i-th sensor fault and ei is the i-th column of the identity matrix.
22) for i = 1, . . , N can be defined for u(i) = u, d (i) = d and w(i) = w as (i) (i) (i) (i) (i) G (i) u (λ) := G u (λ, ρ ), G d (λ) := G d (λ, ρ ), G w (λ) := G w (λ, ρ ) . 23) for i = 1, . . , N can be defined with E (i) = E ρ (i) , A(i) = A ρ (i) , . . 3 Physical Fault Models 23 and x (i) = x, u(i) = u, d (i) = d and w(i) = w. As an example, consider the modelling of a category of loss of efficiency actuator faults for a system of the form y(λ) = G u (λ)u(λ) + G d (λ)d(λ) , without noise input.
If each individual fault f j has associated a distinct signature s j , the j-th fault can be isolated by simply checking that ι(t) matches the associated signature s j . Similarly to fault detection, besides the decoupling of the control inputs u from the residual r (always possible), the exact decoupling of the disturbance inputs d from r can be strived in the case when w ≡ 0. However, in the general case when w ≡ 0, only approximate decoupling of w can be achieved (at best) and a careful selection of tolerances τi is necessary to perform fault isolation without false alarms and missed detections.