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

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?屬性????????????大小?????日期????時間???名稱
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?????文件????????1840??2018-07-11?20:25??era.m