This WORK present a descriptor system package for the the analysis of
state-space and linear parameter varying descriptor systems. All the algorithms
were programed by using the free software Scilab even for
solving LMIs. The properties of regularity, solvability, C-controllability
(observability), R-controllability (observability), I-controllability and
stability are analyzed. The Karampetakis method for discretized continuous
systems in descriptor form is presented and an algorithm of solution is
proposed. Unlike the state-space systems, in non-singulars determining these
properties is not always a trivial task, and on occasions can be a difficult
task because there is not a specialized toolbox. Therefore, this work
propose a set of functions that complement those of Scilab. A compilation of
some observers for descriptor systems are include in the package.
This observers can be used for design fault detection method by constructions of
banks of observers. This banks of observers can be building
by the selection of the input/output matrices or automatically by using the
Due to the lack of adequate tools for descriptors system management,
this work presents a set of functions that complement the Scilab package.
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
COMMENTS AND CONTRIBUTIONS ARE WELCOME