Building model detection related objects

MDModel <: AbstractFDDObject

Type for component synthesis models employed to solve model detection problems.

If sysc::MDModel is a component synthesis model object, the underlying descriptor system model can be obtained via sysc.sys and the dimensions of the control, disturbance, noise and auxiliary vectors are contained in the integers sysm.mu, sysm.md, sysm.mw and sysm.ma, respectively.

MDModel(sys; mu, md, mw, ma) -> sysc::MDModel

Build for a linear time-invariant descriptor system sys = (A-λE,B,C,D) a component synthesis model object sysm::MDModel to be used in conjunction with the analysis and synthesis functions of model detection filters.

The resulting synthesis model object sysc contains the component model with partitioned inputs, sysc.sys = (A-λE,[Bu Bd Bw Bv],C,[Du Dd Dw Dv]), where Bu, Bd, Bw and Bv are formed from the successive columns of B and are the input matrices from the control inputs u, disturbance inputs d, noise inputs w and auxiliary inputs v, respectively, and Du, Dd, Dw and Dv are formed from the successive columns of D and are the feedthrough matrices from those inputs. The dimensions of control, disturbance, noise and auxiliary input vectors are contained in sysm.mu, sysm.md, sysm.mw and sysm.ma, respectively.

The information on the partition of the input components in control, disturbance, noise and auxiliary inputs can be specified using the following keyword arguments:

mu = nu specifies the dimension nu of the control input vector u (default: nu = 0)

md = nd specifies the dimension nd of the disturbance input vector d (default: nd = 0)

mw = nw specifies the dimension nw of the noise input vector w (default: nw = 0)

ma = na specifies the dimension na of the auxiliary input vector v (default: na = 0)

MDMModel <: AbstractFDDObject

Type for multiple synthesis models employed to solve model detection problems.

If sysm::MDMModel is the multiple synthesis model object, the underlying vector of descriptor system models can be obtained via sysm.sys, the common dimension of the control vectors is contained in the integer sysm.mu, and the dimensions of the disturbance, noise and auxiliary input vectors for the i-th model sysm.sys[i] are contained in the i-th components of the integer vectors sysm.md, sysm.mw and sysm.ma, respectively.

MDMModel(sys; mu, md, mw, ma) -> sysm::MDMModel

Build for a vector of linear time-invariant system models sys, with the i-th component model sys[i] = (Ai-λEi,Bi,Ci,Di), a multiple synthesis model object sysm::MDMModel to be used in conjunction with the analysis and synthesis functions of model detection filters.

The resulting multiple synthesis model object sysm contains the vector sysm.sys of component models with partitioned inputs, with the i-th model sysm.sys[i] = (Ai-λEi,[Bui Bdi Bwi Bvi],Ci,[Dui Ddi Dwi Dvi]), where Bui, Bdi, Bwi and Bvi are formed from the successive columns of Bi and are the input matrices from the control inputs u, disturbance inputs di, noise inputs wi and auxiliary inputs vi, respectively, and Dui, Ddi, Dwi and Dvi are formed from the successive columns of Di and are the feedthrough matrices from those inputs. The dimensions of control, disturbance, noise and auxiliary input vectors are contained in sysm.mu, sysm.md[i], sysm.mw[i] and sysm.ma[i], respectively.

If N is the number of component models, the information on the partition of the input components in control, disturbance, noise and auxiliary inputs can be specified using the following keyword arguments:

mu = nu specifies the dimension nu of control input vector u (default: nu = 0)

md = nd specifies the vector nd containing the N dimensions of disturbance input vectors, such that the i-th disturbance vector di has dimension nd[i] (default: nd = zeros(Int,N))

mw = nw specifies the vector nw containing the N dimensions of noise input vectors, such that the i-th noise vector wi has dimension nw[i] (default: nw = zeros(Int,N))

ma = na specifies the vector na containing the N dimensions of auxiliary input vectors, such that the i-th auxiliary vector vi has dimension na[i] (default: na = zeros(Int,N))

mdmodset(sys; controls, c, disturbances, d, noise, n, aux) -> sysm::MDMModel

Build for a vector of linear time-invariant system models sys, with the i-th component model sys[i] = (Ai-λEi,Bi,Ci,Di), a multiple synthesis model object sysm::MDMModel to be used in conjunction with the analysis and synthesis functions of model detection filters.

The information on the partition of the input components in control, disturbance, noise and auxiliary inputs can be specified using the following keyword arguments:

controls = inpu or c = inpu specifies the indices inpu of the control inputs (default: void)

disturbances = inpd or d = inpd specifies the indices or a vector of indices inpd of the disturbance inputs (default: void)

noise = inpn or noise = inpn specifies the indices or a vector of indices inpn of the noise inputs (default: void)

aux = inpa specifies the indices or a vector of indices inpa of the auxiliary inputs (default: void)

The indices of inputs can be specified as integer vectors, integer scalars or integer UnitRanges. For disturbance, noise and auxiliary inputs, vectors of integer vectors or vectors of integer UnitRanges can be used to specify possibly different set of indices for each component model.

The resulting sysm contains the vector sysm.sys of partitioned systems, with the i-th model sysm.sys[i] = (Ai-λEi,[Bui Bdi Bwi Bvi],Ci,[Dui Ddi Dwi Dvi]), where Bui, Bdi, Bwi and Bvi are the input matrices from the control inputs u, disturbance inputs di, noise inputs wi and auxiliary inputs vi, respectively, and Dui, Ddi, Dwi and Dvi are the feedthrough matrices from those inputs. The dimensions of control, disturbance, noise and auxiliary input vectors are contained in sysm.mu, sysm.md[i], sysm.mw[i] and sysm.ma[i], respectively.

Method: If Gi(λ) is the p x mi transfer function matrix of sys[i], then the resulting component system sysm.sys[i] has an equivalent input output form [Gui(λ) Gdi(λ) Gwi(λ) Gvi(λ)], where the following relations define the component matrices: Gui(λ) = Gi(λ)*Su, Gdi(λ) = Gi(λ)*Sdi, Gwi(λ) = G(λ)*Swi, Gvi(λ) = Gi(λ)*Svi, with the selection matrices Su, Sdi, Swi and Svi formed from the columns of the mi-th order identity matrix (note that Su is the same for all component models).

mdmodset(sysc::Vector{<:MDModel}) -> sysm::MDMModel

Build for a vector of component synthesis models sysc, a multiple synthesis model object sysm::MDMModel to be used in conjunction with the analysis and synthesis functions of model detection filters.

MDFilter <: AbstractFDDObject

Type for model detection filters resulted as solutions of model detection problems.

If filter::MDFilter is the model detection filter object, the underlying i-th descriptor system model can be obtained via filter.sys[i] and the dimensions of the partitioned filter input vectors as measured outputs and control inputs, can be accessed as the integers contained in filter.ny and filter.mu, respectively.

MDFilterIF <: AbstractFDDObject

Type for the internal form of model detection filters resulted as solutions of model detection problems.

If filter::MDFilterIF is the model detection filter internal form object, the underlying (i,j)-th descriptor system model can be obtained via filter.sys[i,j] and the corresponding dimensions of control, disturbance, fault, noise and auxiliary input vectors are contained in sysm.mu, sysm.md[j], sysm.mw[j] and sysm.ma[j], respectively.

mdIFeval(sysQ::MDFilter, sysm::MDMModel; minimal = false, atol, atol1 = atol, atol2 = atol, rtol, fast = true) -> sysR::MDFilterIF

Compute the internal form sysR of the model detection filter sysQ applied to the multiple synthesis model sysm. If the j-th component model sysm.sys[j] has the partitioned transfer function matrix Gj(λ) = [ Guj(λ) Gdj(λ) Gwj(λ) Gvj(λ) ] in accordance with the partitioned system inputs as controls, disturbances, noise and auxiliary inputs, respectively, and Qi(λ) = [ Qyi(λ) Qui(λ) ] is the partitioned transfer function matrix of the i-th filter sysQ.sys[i] in accordance with the partitioned filter inputs as outputs and controls, then the transfer function matrix Rij(λ) corresponding to the (i-th filter,j-th model) pair in the resulting internal form sysR.sys[i,j] is given by

 Rij(λ) = | Qyi(λ)  Qui(λ) | * | Guj(λ)  Gdj(λ) Gwj(λ) Gvj(λ) |
                               |  I      0      0      0      |

Minimal descriptor realizations are computed if minimal = true and a (possibly) non-minimal realization is determined if minimal = false (default).

The minimal realization computation relies on pencil manipulation algorithms which employ rank determinations based on either the use of rank revealing QR-decomposition with column pivoting, if fast = true, or the SVD-decomposition. The rank decision based on the SVD-decomposition is generally more reliable, but the involved computational effort is higher.

If (Arij-λErij,Brij,Crij,Drij) is the full order descriptor realization of sysR.sys[i,j], then the keyword arguments atol1, atol2, and rtol, specify, respectively, the absolute tolerance for the nonzero elements of matrices Arij, Brij, Crij, Drij, the absolute tolerance for the nonzero elements of Erij, and the relative tolerance for the nonzero elements of Arij, Brij, Crij, Drij and Eirj. The default relative tolerance is nij*ϵ, where ϵ is the working machine epsilon and nij is the order of the system sysR.sys[i,j]. The keyword argument atol can be used to simultaneously set atol1 = atol and atol2 = atol.