The work discusses the development of a MATLAB/SCILAB toolbox for
systems modeled in the LTI or LPV descriptor framework. The properties of
regularity, solvability, controllability and observability are presented.
Full and reduced order,
proportional and proportional-integral observers are included. Some of these
observers consider unknown inputs.
The main contribution is provide a toolbox than can be
used as auxiliary in state-estimation and fault detection based observers.
These observers have been considered from few papers published recently.
The fault detection and isolation can be achieved by the construction of bank
of observers. These banks of observers can be built by the selection of the
input/output matrices or automatically by using the proposed algorithms.
This functions are showed in the next table.
dss2tf----- Descriptor system state space to transfer function
dcontr----- computes C, R and I controllability
dobsv------ computes C, R and I observability matrices
dstabil-----Computes the stability
qrrse-------Computes the QR restricted system equivalence (r.s.e.)
invrse-------computes the inverse r.s.e form
There contain some observers for state estimation. This observers are based
principally in the works of (Darouach1995s, Darouach1996, Hamdi2009, Hamdi2011)
abcdcoeff---- a,b,c and <d coefficients for Darouach observer
darobsv95---- Full order observer
redobsv95---- Reduced order observer
darobsv96---- Reduced order observer with unknown input
puiobsv------ Proportional unknown input observer (PUIO)
piuiobsv----- Proportional-integral unknown input observer (PIUIO)
For fault detection applications the following commands compute automatically
the gains to generate a bank of observers. This bank of observers
are based in a proportional and a proportional-integral unknown input observer
(PUIO and PIUIO).
gosbank1--- For a generalized observer scheme (GOS) with some of the observers
dosbank2-----For a dedicated observer scheme (DOS) with some of the observers
The put the observer in a stability region the LMI are solved with the
LMITOOL of Scilab.
And finally for analysis, state estimation and fault detection of LPVD system:
lpvpuiobsv---- LPVD Proportional unknown input observer
lpvpiuiobsv--- LPVD Proportional-integral unknown input observer
lpvweig4------ For the construction weighting functions of 4 vertices.
lpvweig3------ For the construction weighting functions of 3 vertices.
lpvweig2------ For the construction weighting functions of 2 vertices.
lpvgosbank1---- For create a bank of oservers using a generalized observer
For more information consult the help files and the attached paper
COMMENTS AND CONTRIBUTIONS ARE WELCOME