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可與隨機減量技術及自然激勵技術結合用于模態參數識別

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function?[ABCD]=era(hnNTsdef);
%?Eigensystem?Realization?Algorithm?(ERA)
%
%?Author:?Samuel?da?Silva?-?UNICAMP
%?e-mail:?samsilva@fem.unicamp.br
%?Date:?2006/10/20
%?
%?[ABCD]=era(hnNTsdef);
%?
%?Inputs:
%????h:?discrete-time?impulse?response
%????n:?order?of?the?system
%????N:?number?of?samples?to?assembly?the?Hankel?matrix
%????Ts:?sample?time
%????def:?if?=?1:?the?output?will?be?the?discrete-time?state-space?model
%?????????if?=?2:?the?output?will?be?the?continuous-time?state-space?model
%??????????
%?Otputs:
%????[ABCD]:?state-space?model
%??
%?Note:?For?now?it?works?to?SISO?systems?and?it?is?necessary?the?control?toolbox
%
%?References:?Juang?J.?N.?and?Phan?M.?Q.?“Identification?and?Control?of
%?Mechanical?Systems“?Cambridge?University?Press?2001
%?Hankel?matrix
H0?=?hankel(h(2:N+1));????????????%?k?=?0
H1?=?hankel(h(3:N+2));????????????%?k?=?1;
%?Factorization?of?the?Hankel?matrix?by?use?of?SVD
[RSigmaS]?=?svd(H0);???
%?R?and?S?are?orthonormal?and?Sigma?is?a?rectangular?matrix
Sigman?=?Sigma(1:n1:n);????????????
Wo?=?R(:1:n)*Sigman^0.5;???????????%?observability?matrix
Co?=?Sigman^.5*S(:1:n)‘;???????????%?controllability?matrix
%?The?identified?system?matrix?are:
A?=?Sigman^-.5*R(:1:n)‘*H1*S(:1:n)*Sigman^-.5;????????????%?dynamic?matrix
B?=?Co(:1);????????????????????%?input?matrix
C?=?Wo(1:);????????????????????%?output?matrix
D?=?h(1);???????????????????????%?direct-transmission?matrix
sysdisc?=?ss(ABCDTs);???????%?discrete-time?system
if?def?==?2????????????????????????????
????syscont?=?d2c(sysdisc‘zoh‘);???????%?Conversion?of?discrete?LTI?models?to?continuous?time
????[ABCD]=ssdata(syscont);??????????%?continuous?system
end
%--------------------------------------------------------------------------
?屬性????????????大小?????日期????時間???名稱
-----------?---------??----------?-----??----
?????文件????????1840??2018-07-11?20:25??era.m
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