FID Fractional-order Transfer Function SISO system identification
Usage: [A,NA,B,NB,L,GID] = FID(FSIM|G,GPARAM,IDD,NPOINTS,TYPE,FIXPOLY,LIMITS,OP)
where A,NA,B,NB, L and GID - identified system coefficients, input/output
delay from delay term exp(-Ls) and FOTF object.
If the algorithm is
FSIM | G - either FSPARAM structure to use approximations for
identification with the initial function or the
initial function as a FOTF object. If the FOTF object
has a set ioDelay value, it will also be identified
in the ensuing optimization. To ignore the delay
parameter set it to [] (i.e. empty matrix) in the initial
model.
GPARAM - a cell array with explicit model parameters: {K, L},
where K is the static gain and L is the input-output
delay in seconds. Specifying this input argument as
[] (or each individual parameter, e.g. {K, []}) will
remove the parameter(s) from the identification problem.
NOTE! The static gain will ONLY be identified in case
of free identification (all parameters of both
polynomials are identified).
IDD - a FIDATA sturcture with collected system samples.
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Optional arguments
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NPOINTS - number of points to use for identification; this
allows to reduce the time it takes to estimate a
model, i.e. for obtaining an initial estimate, at an
expense of accuracy. If the number of points
specified here is larger than half the number of
points in the dataset, all available points will be
used for identification. Specifying 0 or [] will
yield the same effect, that is all points are used,
and it is also the default behavior.
TYPE - identification type: 'n' - free identification,
'c' - fix coefficients, 'e' - fix exponents
(default: 'n')
FIXPOLY - a vector with two values: [BFIX; AFIX], where BFIX
and AFIX can be 1, in which case the corresponding
polynomial is fixed during identification, or 0.
Note that in case BFIX = AFIX = 1 the initial model
will be immediately returned with no identification
conducted. Default: [0; 0]
LIMITS - a cell array with two vectors, which may also be
empty, containing polynomial coefficient and
exponent limits in the form {[CMIN;CMAX],[EMIN;EMAX]}.
Default: [] (i.e. no limits are imposed.)
OP - additional optimization options for lsqnonlin
(use optimset). Note, that you can set the preferred
optimization algorithm here. This is done as follows:
OP.IdentificationAlgorithm = 'trr':
Trust-Region-Reflective algorithm is used;
OP.IdentificationAlgorithm = 'lm':
Levenberg-Marquardt algorithm is used, for the latter
OP.Lambda determines the lambda parameter, 0.01 by
default. NB! The 'lm' algorithm does not handle bound
constraints! The upper/lower limits of search
parameter space will be discarded!
See also: fsparam, fidata, optimset, lsqnonlin