FDI related utilities
fdhinfminus
Evaluation of theH∞-
index of the transfer function matrix of a descriptor system model.fdhinfmax
Evaluation of the maximum of column norm of the transfer function matrix of a descriptor system model.fditspec_
Computation of the weak or strong structure matrix of a descriptor system model.fdisspec_
Computation of the strong structure matrix of a descriptor system model.fdiscond_
Computation of the column-gains sensitivity condition of the transfer function matrix of a descriptor system model.
FaultDetectionTools.fdhinfminus
— Function fdhinfminus(sys,freq) -> (β, ind, fr)
Compute for a stable descriptor system sys = (A-λE,B,C,D)
the H∞-
index β
of its transfer function matrix G(λ)
. If freq = missing
(default), then β
is the minimum H∞-norm
of the columns of G
, ind
is the index of the minimum-norm column and fr
is the frequency where the minimum H∞-norm
of the columns is achieved. If freq
is a real value or a real vector of frequency values, then β
is the minimum of the 2-norms of the columns of the frequency responses of G
evaluated for all values contained in freq
, ind
is the index of column for which the minimum is achieved and fr
is the corresponding frequency.
FaultDetectionTools.fdhinfmax
— Function fdhinfmax(sys,freq) -> (γ, ind, fr)
Compute for a descriptor system sys = (A-λE,B,C,D)
, γ
- the maximum norm of the columns of its transfer function matrix G(λ)
. If freq = missing
(default), then γ
is the maximum H∞-norm
of the columns of G
, ind
is the index of the maximum-norm column and fr
is the frequency where the maximum H∞-norm
of the columns is achieved. If freq
is a real value or a real vector of frequency values, then γ
is the maximum of the 2-norms of the columns of the frequency responses of G
evaluated for all values contained in freq
, ind
is the index of column for which the maximum is achieved and fr
is the corresponding frequency.
FaultDetectionTools.fditspec_
— FunctionS = fditspec_(sysrf::DescriptorStateSpace; FDfreq = missing, block = false, poleshift = false,
FDtol, FDStol, atol = 0, atol1 = atol, atol2 = atol, rtol, fast = true)
Compute the weak or strong binary structure matrix S
of the transfer function matrix of a linear time-invariant system sysrf
(typically representing the transfer channel from the fault inputs to residuals). sysrf
has a descriptor system realization of the form sysrf = (Af-lambda*Ef,Bf,Cf,Df)
with a q x mf
transfer function matrix Rf(λ)
. For the description of keyword parameters see the documentation of fditspec
.
FaultDetectionTools.fdisspec_
— Function fdisspec_(sysrf::DescriptorStateSpace, freq; block = false, stabilize = false, FDGainTol = 0.01,
atol, atol1, atol2, atol3, rtol, fast = true) -> (S, gains)
Compute the strong binary structure matrix S
of the transfer function matrix of a linear time-invariant system sysrf
(typically representing the transfer channel from the fault inputs to residuals). sysrf
has a descriptor system realization of the form sysrf = (Af-lambda*Ef,Bf,Cf,Df)
with a q x mf
transfer function matrix Rf(λ)
. For the description of keyword parameters see the documentation of fdisspec
.
FaultDetectionTools.fdiscond_
— Function fdiscond_(sysrf::DescriptorStateSpace, freq) -> (scond, β, γ)
Compute for a stable descriptor system sysrf = (A-λE,B,C,D)
with the transfer function matrix Rf(λ)
, β
- the H∞- index of Rf(λ)
, γ
- the maximum of the columns norms of Rf(λ)
and scond
- the column-gains sensitivity condition evaluated as scond := β/γ
. If freq
is a vector of real frequency values, then β
and γ
are evaluated over the frequencies contained in freq
.