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Purpose
Transformations between the residue res and statespace ss forms.
Syntax
SYS = res2ss(RES) SYS = res2ss(RES,'AllIO') [a,b,c,d] = res2ss(res,po,idopt) RES = ss2res(SYS) [res,po,idopt] = ss2res(a,b,c,d)
Description
The functions res2ss and ss2res provide transformations between the complex / normal mode residue forms res (see section 5.6) and the state space forms (see section 5.4). You can use either high level calls with data structures or low level calls providing each argument
ci=demosdt('demo gartid est') SYS = res2ss(ci.Stack{'IdMain'}); RES = ss2res(SYS); ID=ci.Stack{'IdMain'}; [a,b,c,d] = res2ss(ID.res,ID.po,ID.idopt);
Important properties and limitations of these transformations are
Asymptotic corrections (see idopt.ResidualTerms) other than the constant and s^{−2} are not included.
Theory
For control design or simulation based on identification results, the minimal model resulting from id_rm is usually sufficient (there is no need to refer to the normal modes). The statespace form is then the reference model form.
As shown in section 2.4.1, the residue matrix can be decomposed into a dyad formed of a column vector (the modal output), and a row vector (the modal input). From these two matrices, one derives the [B] and [C] matrices of a real parameter statespace description of the system with a bloc diagonal [A] matrix

where the blocks of matrices B_{1}, B_{2}, C_{1}, C_{2} are given by

Form the state space model thus obtained, FRFs in the xf format can be readily obtained using qbode. If the state space model is not needed, it is faster to use res2xf to generate these FRFs.
See also
demo_fe, res2xf, res2nor, qbode, id_rm, id_rc