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function [yhat,xi,thpred]=predict(varargin)% h* t. @: C f# ~/ F9 N' d
%PREDICT Computes the k-step ahead prediction.- q V, M$ k/ n4 d, _" x
% YP = PREDICT(MODEL,DATA,K)& F+ ]( u- }9 {: Y& \) G
%
+ f" r0 I9 ]" P- x. E1 G. Z% DATA: The output - input data as an IDDATA object, for which the
% Q- j1 J( V/ p# x% prediction is computed.8 K8 o& |6 e1 b1 Z+ K
%
' t+ i2 W% C2 m# ~. n% MODEL: The model as any IDMODEL object, IDPOLY, IDSS, IDARX or IDGREY.! k3 N- x8 V5 i" X
%
; D2 ^( t, q+ H. H) ~% K: The prediction horizon. Old outputs up to time t-K are used to2 D0 b! G. X- R1 ]+ z3 g
% predict the output at time t. All relevant inputs are used.1 A/ y4 `+ @' T( x* T8 ~/ A
% K = Inf gives a pure simulation of the system.(Default K=1).% @# N1 I7 e0 u, N% i" c' E/ H
% YP: The resulting predicted output as an IDDATA object. If DATA
; i' O: t+ u) f. F' e4 y" w# Q% contains multiple experiments, so will YP.
2 W8 m, s8 D) ?* X# H5 _" {/ A%) V6 V& e* ^- ` y
% YP = PREDICT(MODEL,DATA,K,INIT) or% K* ^- A$ R5 T; Y+ Y; V8 b! R
% YP = PREDICT(MODEL,DATA,K,'InitialState',INIT) allows the choice of! m1 m9 m4 v% v8 A9 T: c) b
% initial state vector:" k+ E8 ]" u2 k" l; m6 L0 q
% INIT: The initialization strategy: one of
6 P8 ?1 K6 S/ x& j% X% 'e': Estimate initial state so that the norm of the" `" I5 V" R* u) A) ~
% prediction errors is minimized.
, R+ P; [& o. h" P% This state is returned as X0e, see below. For multiexperiment
6 q5 R+ c1 i8 k. O% u% DATA, X0e is a matrix whose columns contain the initial states
/ W5 L' _% I0 Y- v. K1 W% for each experiment.
$ a+ W G9 m8 C: @: y% 'z': Take the initial state as zero- |$ G& c; i# O# J
% 'm': Use the model's internal initial state.
2 U, p' i& j6 ^3 C% 'd': Same as 'e', but if Model.InputDelay is non-zero, these delays: S+ p/ e0 ]* f- E
% are first converted to explicit model delays, so that the are
! r/ a8 C5 r4 C6 {# b% contained in X0 for the calculation of YP.! Q% X- e! K( T& m* q) N% c& F0 }. p
% X0: a column vector of appropriate length to be used as initial value.
9 q2 p2 [7 j6 W1 P( k# k. I' ~% For multiexperiment DATA, X0 may be a matrix whose columns give1 ~! Q% k" ~" {! @' C. z
% different initial states for each experiment.8 r x! E5 b- Z) U
% If INIT is not specified, Model.InitialState is used, so that( H9 g- v9 Z5 Z- }8 N4 I) h
% 'Estimate', 'Backcast' and 'Auto' gives an estimated initial state,: u/ k) K y1 J5 s! ?
% while 'Zero' gives 'z' and 'Fixed' gives 'm'. If Model is an IDARX
0 q' l- v* i8 N$ Q7 U, g% model the default initial state is 'z'.% ?: }8 U$ g+ I* s0 j% z
%
3 N t' v u5 @6 t) |6 k% With [YP,X0e,MPRED] = PREDICT(MODEL,DATA,K) the initial state(s) and the& s$ Q% `8 e% p
% predictor MPRED are returned. Note that if MODEL is continuous time, X0e
( ^0 {' S$ ]; Z, h% is returned as the states of this model. These may differ from the initial/ e+ X7 {& [3 ]5 E. ]; c% L s3 K, Z
% states of the discrete time model that has the sampling interval(s) of
+ J1 c2 `! E+ @, ?% DATA. Also when INIT = 'd' only the states of MODEL are returned in6 o( }& f W( M" ~; R- E, E
% X0e. (To obtain the full X0, apply first INPD2NK to a discrete time
- t1 ^0 e- N8 Q7 I% version of the model.)
6 F; n5 C7 P8 I; |9 [% MPRED is a cell array of IDPOLY objects,$ |0 r0 \: F8 u5 z& O* l
% such that MPRED{ky} is the predictor for the ky:th output. The matching& O" |, k K p& s2 c4 c4 E
% the channels of MPRED with data follows from its InputNames.) r& K" o, D, L& ]
% See also COMPARE and IDMODEL/SIM.% D& y1 D, Y& i. l: R
% L. Ljung 10-1-89,9-9-946 q7 j9 ?0 W* w
% Copyright 1986-2008 The MathWorks, Inc.
5 b# p( t- \ a1 Z- A# \% $Revision: 1.1.8.9.2.1 $ $Date: 2008/08/01 15:32:39 $+ q5 c3 f$ y1 g0 K
) |6 ` D( h* d) x1 Y1 \7 s8 [
% First find if there is any pair 'InitialState', init in the argument: Y- n$ B; v; a7 M
% list:3 {/ f+ o* h V+ Q/ X
nr = find(strncmpi(varargin,'in',2));
% _% `! c# p9 }init =[]; xi = [];
$ G4 t% Y3 t- ~- S$ Q2 Fif ~isempty(nr)
: R# n7 I9 f- b: l @0 e3 m if length(varargin)<nr+1
6 t& s# G- F$ g2 o# N$ r% T error('Ident:general:optionsValuePair',...4 U7 D: s* A0 m9 H0 _3 s: s
'The "%s" option of the "%s" command must be specified using a name/value pair. Type "help %s" for more information.',...
8 p; K' D6 v; g* R: ?3 D' n& Q4 b D 'InitialState','predict','predict')* @5 }9 R7 _$ p1 R5 J
end
# u3 Z8 \6 b. M* H: e: W init = varargin{nr+1};/ n: M# O" Z! X8 [' v0 h/ I
if ~isa(init,'char') && ~isa(init,'double')
) D/ I/ Y: P! a( h* c error('Ident:analysis:IniSpec2',...
( i9 N2 b ~% [! P 'The "InitialState" option of the "%s" command must be set to a valid character or a vector/matrix. Type "help %s" for more information.','predict','predict')* t$ t: V, K: B4 @- z
end
+ O# D. s- t- B' W C& P: H! h varargin(nr:nr+1)=[];%$ I4 x* S0 E' {! V
end
4 C5 d) p: p+ I8 `7 _* aif length(varargin)<2
, {0 e8 W8 B$ }6 i- H& z disp('Usage: YP = PREDICT(MODEL,DATA)')
" L2 \# p. [$ H+ ~5 _ disp(' YP = PREDICT(MODEL,DATA,M)')
; _4 x+ Q, `6 c* A! V, O yhat = []; xi=[];
& D# s+ u/ v6 V2 O9 a [8 U return
- o( }$ r/ G7 Z# ^5 C! l a* rend4 n3 H/ }5 Y$ _5 D2 V+ r
data = varargin{1};
0 R' ]- Y6 ^5 Btheta = varargin{2};$ L( q5 a1 [; S: u, `$ m! K
if length(varargin)>2
) o& t" P F4 j; e( ` m = varargin{3};1 ]: D+ `$ H, j* ?+ H( j
if ~isnumeric(m) || ~isscalar(m) || ~isreal(m) || round(m)~=m || m<10 Q$ s# y. L4 \
error('Ident:analysis:predictInvalidHorizon',... F6 x" h" b. t7 p4 W; s: _6 ~+ ^
'In the "predict(MODEL,DATA,K)" command, the prediction horizon K must be a positive integer.')- C n6 d0 D9 {
end
+ z/ ^' L/ a. P* ~, t) J" L. H! ielse
5 C y0 ?% q% w2 E/ x/ {7 Q/ X m = 1;
* Y4 P) C# \" @$ }$ X0 b, h; Hend( K0 ` k. [9 J5 { z5 Y
if length(varargin)>3 && isempty(init)
6 ^- C) g8 E7 P( c# p init = varargin{4};
' d p8 |9 }) t' k& y2 ]7 jend
& H, w% R' ]3 @0 k) `thpred = [];
; C3 B0 n, J0 Lyhat = [];
9 x0 Z, b- t1 l! K8 n& _if isa(data,'idmodel') % Forgive order
$ }0 z( q& U8 F# a! s data1 = theta;
; Z( M) h& |( L4 S* f theta = data;
0 C. h2 F, U8 U; k5 o data = data1;. i) B! Y# L6 i5 y( ^: k% @( I' h
end
# R0 j% J/ G Dnxorig = length(ssdata(theta));
, a* A i6 ^% A" w6 B% A5 X# @: v5 @[nym,num] = size(theta);
m% @( D3 P1 }7 Z4 ^" s# \0 {if isa(data,'frd') || isa(data,'idfrd')
2 _# w; p. @' P6 A+ [ error('Ident:analysis:predictIDFRD',...
\5 s7 f5 q1 ]0 M5 W% g 'The "predict" command is not applicable to frequency response data (IDFRD object).')
5 A) s5 [! z, P: u2 O( F1 s k6 send3 e1 {% p7 C; F: d$ I
if isa(data,'iddata')4 V9 t7 ^$ `0 k
[Ncap,ny,nu] = size(data);: N+ `7 a: U. M$ W& @
if ny~=nym || nu~=num8 [3 I0 N; a2 W8 a9 z: T
error('Ident:general:modelDataDimMismatch',...+ }; ^$ C* g- J/ X6 w) e' C2 t
'The number of inputs and outputs of the model must match that of the data.')
- F) ]" h$ X& p; p end
7 L% g1 S3 e5 Z; m& e' |end7 K) B- ^% t, u Z9 a
if isempty(m), m=1; end8 q6 Y& a, o! q% R6 o
if ~isinf(m),# F- }7 X+ N2 C; U( j+ D
if m<1 || m~=floor(m)$ a b9 T! Z# G$ f: h6 n7 j
error('Ident:analysis:predictInvalidHorizon',...5 o4 D9 P6 c' k+ m
'In the "predict(MODEL,DATA,K)" command, the prediction horizon K must be a positive integer.')
$ y2 _+ x# L8 F0 w4 l6 E" L5 H end
0 `9 y& n" E' v# z, ^9 h# Tend* _) h3 B# h$ F. w& L' Q" B
% First deal with the special case of continuous time data and continuous* b6 K' B8 C( v9 X4 f
% model:, ^; V# N3 N" j# E
if isa(data,'iddata') && any(cell2mat(pvget(data,'Ts'))==0)
8 U: g$ s6 i- `7 k2 U5 y if ~isinf(m)" Z( Q s7 p3 u! U( [8 M3 [' |8 b
error('Ident:analysis:predictCTData',...
; `. ]3 `3 m6 E2 e5 e6 N, S- A7 u& q 'The "predict" command cannot be used with continuous time data.')6 h9 O1 @: L# C: z8 A; d
end
1 W0 U7 q5 ]3 f" B: F) N yhat = sim(data,theta);%没懂, J" {& U8 e# j8 t( s7 e
if nargout == 01 c& }6 M% ?; ~7 a
utidplot(theta,yhat,'Simulated')
+ |4 o q/ x5 s& c( l clear yhat6 e- |( k" A% j
end' e; ?5 c* h9 e+ i
return& E" Z7 ^; s* c2 s$ o1 F3 s9 n
end) ?# r) e( V% P1 f! K/ V
if isempty(init)6 c+ F) { T% ~9 i/ r o& o$ x, H
if isa(theta,'idarx')
$ ?1 S, q4 k5 v- v8 x: o! | init='z';
( D; w0 x' {! ]& T) g6 _7 N else
* t9 E6 p1 H4 y3 s( ~$ O init=pvget(theta,'InitialState');0 D6 }' A1 K6 u" G. r
end
# Q$ t# ?5 X. O9 `2 F0 A, W+ I init=lower(init(1));. p" y! O; |8 X" E0 K+ y$ H9 h
if init=='d'5 c6 q W2 r E& c1 V" d4 b5 Z# D) j
inpd= pvget(theta,'InputDelay');
" t& Q; X; G. O( r% d0 j1 n) U if norm(inpd)==0, L! Q a8 Q5 T! s% _
init = 'e';
3 i$ R# x7 R2 U+ \ end; w- a8 n1 [' b
end' G2 @+ a4 B) V) D
if init=='a' || init=='b'
+ h5 H$ @) V; d! T5 w8 |! |. Y init = 'e';* i' v& O* f+ [* G2 @
elseif init=='f'. A4 u* u M: `
init = 'm';) D4 M" g) P* F! q6 l* k! ^. {+ U( Y( N( N
end- R- n1 v4 v O/ C$ _2 y% v
elseif ischar(init)
. \* {5 `( w+ q. P2 M0 }8 I: N init=lower(init(1));
; X; K9 Z: e' }! ^! o. r if ~any(strcmp(init,{'m','z','e','d'}))0 r' f' V0 ~2 x! N
error('Ident:analysis:predictIni3',..." R$ S* M0 z. J% l4 v' w0 A. B
'The "InitialState" option of the "idmodel/predict" command must be set to ''E(stimate)'', ''Z(ero)'', ''M(odel)'', ''D(elayconvert)'', or a vector.')
$ K% H) h0 o' k* n& N5 [ end' `" W5 A) O% n6 f& ^
if init=='m' && isa(theta,'idpoly')& d& a- l- r2 w. ~" Z1 P
warning('Ident:analysis:predictIni4',...6 j/ W; b: t$ F- X4 V2 V
'Setting the "InitialState" option to ''m'' in the "predict" command is same as setting it to ''zero'' for IDPOLY models.')
0 b: t8 N2 D6 y9 ?+ R; y end8 t4 }. m9 u: A. ^1 F9 P
end5 {9 i7 @& i' ^6 l/ h
%% Now init is either a vector or the values 'e', 'm', 'z' 'd'* ^& Q; M* X. B$ G
if isa(data,'iddata');$ s; S. r. j. E0 F
if strcmp(pvget(data,'Domain'),'Frequency')
# z" l# [$ X1 l) Y. c if m<inf a4 Z; {3 t/ s
error('Ident:analysis:predictFreqDataFiniteK',...! @ g/ w/ y. z' ^! ^
'Prediction with finite horizon is not applicable to frequency domain data.')
6 ^' X! z! H/ G1 N$ z; g3 M end
; G/ \& U& E! J5 P" u+ G- G q( [ end
! z: ]! u% y# \* \5 Kend# k& n8 a$ S4 I: q: T
if isa(data,'iddata')
( o5 }* B+ t* B4 i1 N2 E. l8 p [uni,Tsd,inters] = dunique(data);5 i) e( L( J7 H* d# W* ]# S
iddflag = 1;5 |4 }$ g9 Z- c% `- A' D
else
; B, y9 L7 C/ ]1 a4 M7 ? iddflag = 0;" o0 u* d+ K9 q2 w! w' D
uni = 1;* R8 x$ ~/ t; A7 V
Tsd = 1;
0 @: m9 n5 _1 q- S, [ inters = 'z';
, ]$ G& p$ Z7 H0 @2 v3 Send
( O. a% w5 m6 S%% Do away with continuous time right away:' N0 G6 z, ]1 }+ X; d
Ts = pvget(theta,'Ts');
; K& N2 h6 m; a. d) o: Wif Ts == 03 J7 P2 w, n# C9 v$ ], j2 M
theta = pvset(theta,'CovarianceMatrix',[]); % Less calculations/ o, r+ a+ h# N8 P0 g8 x
ms = idss(theta);
4 E" a, _$ y8 v- Z$ k nc = size(ms,'nx');
" E8 W1 z* J6 m2 ]! l% p5 q- U% ` if ischar(init)
9 m2 q) N3 C+ m% o if init=='m';' Y9 z& z; n6 e
init=pvget(ms,'X0');
0 W* B8 `5 ~; l8 g end. x7 z# u5 M5 z# [* H% j
if init=='z'
# C3 f4 _5 m+ c7 ^- K init=zeros(nc,1);. d Y/ z- Z6 b/ d" c# J* ]8 j
end6 E9 U t9 _# ^6 S. |% V
end
# \* r( c) s0 m2 d, o if ~isa(data,'iddata')+ X# s! l+ _1 D* Q. ~
error('Ident:analysis:predictDataFormat',...
" q( X P( g4 N; Z( G2 I' T* u! ^ ['For a continuous time model, data must be specified using an IDDATA object.',...
; q) a( Q. G L) @8 { 'Type "help iddata" for information on how to create the IDDATA object.'])( i4 s# f' V1 W
end- \: j3 e' Z9 M/ x
Nex = size(data,'Ne');0 x8 }0 u8 q8 S4 d" O$ Z
u = pvget(data,'InputData');, L' M2 b7 x/ u0 B4 q& O
u1 = [];6 K0 X7 ]6 E3 @- i% m
for kexp = 1:length(u);
7 _9 H% c; s s% \1 P* G u1 = [u1,u{kexp}(1,:).'];& X9 L. q! D2 L; b6 G
end
$ Y. y( b; _; u. T% ?9 Q8 [ nu = size(data,'nu');: a. E5 W6 w k) H& b, E
if uni- R. A/ S8 [( P5 E+ V5 a5 s
nc = size(ms,'Nx');/ {. p/ N6 F% F8 s' Z
[md,Gll] = c2d(ms,Tsd,inters);- z/ G3 @- r& U+ G1 g9 @6 B0 P$ X
if init=='d', md = inpd2nk(md); init='e';end( [0 N4 z$ _8 P& d* G* t3 y
% First work on init
1 f8 d+ ]6 }/ ~8 r9 a7 u8 q if isa(init,'double')% @$ S8 o8 D8 [/ s2 B
[nxi,mexp]=size(init);
$ G4 {9 A' i) Y% @9 ` if nxi~=nc4 U9 b- a& D. d+ k% W
error('Ident:analysis:IniRows',...
7 ?: ]) J F5 K& S 'The value of the "InitialState" option should have %d row(s).',nc)+ p" y# n' W5 f) g# g4 k
end
2 `" m% Y( N J; v. Y* {# P if mexp==1 && Nex>1
! ^6 p$ g5 g+ @# y9 l init = init*ones(1,Nex);
4 }. I: n# z; Y6 q mexp = Nex;
+ O' K( I* D3 L1 v. l" N0 {1 j, @9 T end/ Y, |8 d+ e& {: ^4 v' S, a& k
if mexp~=Nex( m) H ]5 @7 m) j1 |" a4 o4 _
error('Ident:analysis:IniSize',...7 y( E8 v* M- O Y4 w7 X
'The "InitialState" option value must have either 1 or Ne columns, where Ne = no. of data experiments.');
* N6 ` V* p- @ end$ X( L( t6 `' c9 b9 o
if ~isempty(Gll)
; t3 N, k- Q& p' N' k" w0 c init = Gll*[init;u1];2 y8 [ R* o% I+ q- Y4 ~
end3 S8 z7 t0 Y0 v
end
3 _1 H' M. T; ~' s if init == 'e'/ o; W p1 k' H3 Q1 E
inite = x0iniest(md,data);
, `8 v' Y1 U4 X$ ?2 j4 x else
+ s4 k @7 g; w inite = init;
# p' A4 G% b ^ end. d8 o. i7 P( z
yhat = predict(md,data,m,inite); %Check XIC!. q1 @6 g7 y1 s8 G6 u3 o: g P0 }
if ~isempty(Gll)% F4 u5 U: U2 K% P1 c8 {
xi = inite(1:nc,:)-Gll(1:nc,nc+1:nc+nu)*u1;$ v d: n- |: R: A
else
7 E( u0 t; R# i7 b( ?- y xi = inite(1:nc,:);, v+ |6 f/ f- @5 G. k
end" u5 o/ E! j+ j0 j8 E4 m w% `+ T
else % Different sampling intervals1 L! [+ \( g. g7 s
Tsd = pvget(data,'Ts');' G% |; q. i+ J2 M
ints = pvget(data,'InterSample');4 ?3 j/ |& f$ Z6 n; f" @1 x2 n% w
%xic=zeros(nc,Nex);$ z; u1 e6 b1 k e# [1 J2 D
for kexp = 1:Nex. J8 J5 q/ O; T- F+ {# g
[md,Gll] = c2d(theta,Tsd{kexp},ints{1,kexp});# j$ s9 R* G+ q; K
if init == 'd', md = inpd2nk(md); init = 'e';end
. f9 P" s, J3 o if isa(init,'double')& y1 u2 Z. @! u; ?7 ~2 U/ l
if ~isempty(Gll): M+ {8 b7 g! i% v$ D; Q; @: i
if size(init,2)==1
& i, u; u' g+ ~: E; r0 M; x4 t0 W8 l initk = Gll*[init;u1(:,kexp)];3 j! I2 y8 ?3 M% c
else; k! j/ Y9 J& M( p5 a3 W, X2 @" u
if size(init,2)~=Nex3 G- R0 S9 w5 O) Z8 \$ E
error('Ident:analysis:IniSize',...3 {9 O0 q# F- Q7 c4 |% k* ~7 ]
'The "InitialState" option value must have either 1 or Ne columns, where Ne = no. of data experiments.');
# w6 V4 Q. ~' o2 i end
3 W# f5 L1 @$ u9 m initk = Gll*[init(:,kexp);u1(:,kexp)];
* b0 V6 H# [7 n5 o0 D! C end, H# c' F8 g4 ?+ c8 {
end
) A; V) M- H5 ^4 P; O8 r else
7 e: F6 d2 k- H# j h initk = init;2 c# i' _. H. s' q* n
end
5 @$ w1 X' p% Q+ y/ | if init == 'e'" r5 l+ d8 ~; @: H5 ^, R8 j- y1 c' s
initk = x0iniest(md,getexp(data,kexp));+ ?0 r) e9 c+ W; a+ [) M$ ?
end
6 ^, ^3 g `1 Y: I if ~isempty(Gll); K2 p4 x- Q, R" d8 u4 _. A
xi(:,kexp) = initk(1:nc)-Gll(1:nc,nc+1:nc+nu)*u1(:,kexp);
# l& c! |# O$ T5 t! Z# i else. X1 B8 F. B/ W8 j
xi(:,kexp) = initk(1:nc);7 x* q+ n {9 R/ ], j- r2 @8 n
end
4 @1 e3 V9 g7 J: `: |" G4 y* I3 S yhatk = predict(md,getexp(data,kexp),m,initk);
& d. W2 T3 W2 X if isempty(yhat)- X' ^3 C4 K( d- W* x, o
yhat = yhatk;
+ F' o$ I8 b& ~2 a2 W else
' z# c$ c" G, I' t7 d- [& X# k yhat=merge(yhat,yhatk); I. I3 c* ^7 I: _1 N
end) U4 `2 ]3 y6 K$ k
end( O( X1 R* S3 `2 G" n" M
end
% ^4 u5 n n& S1 g if nargout == 0" A$ [* @# |( X! r
utidplot(md,yhat,'Predicted'); R) g3 [4 Q6 |. m! `9 Q S9 b
clear yhat" I S0 a6 s( i! x [
end
* u# l1 R4 }$ m8 A return& a7 Z& q4 ~7 y. ~
else %Ts>0
3 a/ n/ T2 B4 S# k) [. R2 F if init=='d'- s# e5 z4 t) ^6 B( c
if any(pvget(theta,'InputDelay')>0). _ A' m1 z% Z* v; S% }( j: z
theta = inpd2nk(theta);) c$ h3 W) ~- M
end
3 y5 H9 Y, X4 O: v9 ~5 e init = 'e';
$ z/ n7 O* T# c1 {8 T ~6 }: @ end9 T0 x2 s% X4 }1 M
end' n5 m }& w* S3 X; T$ W2 `, q4 G
if isinf(m)
# |) V/ n( n% R# q1 y if ischar(init) && init=='e'
1 T7 k y8 o9 J# o X0 = x0iniest(theta,data);4 {) u d/ S7 `* r0 \0 w6 T, {" O, c
init = X0; % Note the difference with COMPARE, which fits* Y$ [$ J6 g [" ~: p# k
% X0 with K = 0;8 i6 D8 L4 K% f/ `) ^! `) \* O! ~
end
- @. r$ V) i1 g. {. U if ~isa(data,'iddata')
- W8 |) I) u! K data = data(:,nym+1:end);
& Y9 o6 |3 ]5 J. g& \' ]7 [ end, ~1 E5 P5 A W
[lw0,id0] = lastwarn; was = warning('off','Ident:analysis:unstableSim');
- K+ B/ x3 r9 J& [, h4 u3 | try/ m4 n6 O! f# _+ H1 y
yhat = sim(theta,data,init);* w# @# g3 T* U% R) d7 F
catch E' W6 k8 I: a; f' b
warning(was)) P& O/ U$ I6 m
lastwarn(lw0,id0);/ m1 g4 [3 P5 o) a; R% X h1 j5 s0 o
throw(E)
6 ? b; W- z% H) ? end# C9 u8 M9 K+ Q
warning(was)8 r! k* k% ~- _$ `; l$ S9 ^
lastwarn(lw0,id0); _( g1 q. y- X
* ^- }* C+ s) I% F thpred = theta;
- E" i3 e+ m" M' s7 B if nargout == 0
1 W3 M; K0 ~- S( G5 _4 x' m- p utidplot(theta,yhat,'Predicted')
. t/ R4 J2 a4 Z9 L clear yhat
6 K2 ^, V) T# o, z elseif nargout>16 S" j- H A h2 s2 r
xi = init;; U h" h; b1 ^, G. T: B
end
5 N8 V" r; D- J0 O return
! Z4 C R: R+ o) H& ?6 I# _1 ]end
, g7 h, G+ w) c. `* ^+ H%Inpd = pvget(theta,'InputDelay');7 U$ e! ?( V/ i4 Z' d1 r- z5 w
nu = size(theta,'nu');
6 N: j& S$ S9 e! ^5 b4 k2 Eif ~uni
4 n: |% N8 \" g' e, p/ j Tsd = pvget(data,'Ts'); Tsd = Tsd{1};
0 @( h# D3 J' [" Q warning('Ident:estimation:nonUniqueDataTs',...
+ I9 |3 t1 j; C ['The data set contains experiments with different sampling intervals.\n',...
% P' X/ X- l# l& ? 'Sampling interval from the first experiment (=%g) will be used.'],Tsd)
3 v: l, U1 M% N: P! Dend! P0 |" U9 b' n u
if iddflag && any(abs(Ts-Tsd)>1e4*eps)
# F% B( v( Q8 y warning('Ident:analysis:dataModelTsMismatch',...
- q9 f& R. v% m' e) S5 D/ m 'The data and model sampling intervals are different. The data sampling interval will be used.')* v) G; q! r9 J9 Z9 f
end: y; l; _5 Q" h: p. O5 y2 }
Inpd = pvget(theta,'InputDelay');- m; f/ o+ D6 X
if init=='d'
1 [* t/ {8 q. D. H8 K! H init = 'e';
' L( w- s9 e5 _# S: n. o theta = inpd2nk(theta);4 d# U5 S: @/ }+ V
Inpd = zeros(size(Inpd));* J- }( k0 y( B3 P5 |" x
end4 h. G9 _; ]& f( M3 l
if isa(data,'iddata')$ i; r! A, l6 E0 K
if isnan(data)- z$ S2 \ T" x: `. |
error('Ident:general:idprepMissingData',...6 A/ z% B6 p) E2 U; `! e1 s
'Data contains NaNs which represent missing values. Use the "misdata" command to fill in the missing values before using.');' Z9 H$ [$ A9 h8 d; Q7 O$ ^
end: c" G C$ T Z) Y3 {$ ^4 n, m" d
data = nkshift(data,Inpd,'append');
% x v# r$ ]2 i# T) K4 ~ theta = pvset(theta,'InputDelay',zeros(nu,1));
2 P' h; G! B; Y1 i6 y [ze,Ne,ny,nu,Ts,Name,Ncaps,errflag] = idprep(data,0,'dummy');
! t! E* I$ F0 |4 r F %if ~isempty(errflag.message), error(errflag), end
+ k2 ]6 ~' ?% ~7 ?9 f s# r2 w. j& V) N if ~isempty(Name), data.Name = Name; end: _) y, a0 ~; d- l7 d+ K
iddatflag = 1;
$ v/ k' z; y5 `3 F6 Melse
( B# S# h, v) U8 T2 p if norm(Inpd)>eps
. d/ P5 ~6 {8 Q3 ^; m3 H if iscell(data)
. P+ U* X Z: r% q# l# ^' Q data = data{1};
7 U8 W6 D' w+ c2 A. A ~0 e9 a end
0 n+ n* T' Z6 v- y4 g% v [Ncap,nudum] = size(data);" l, I" S2 o' O& g/ V
nk1 = Inpd;5 E4 j; Y) u: j7 G5 o8 d9 K
ny = nudum - length(nk1);: g @; J% Y8 |4 K, F* p! `
Ncc = min([Ncap,Ncap+min(nk1)]);. @" m& u1 [. G+ X p5 d
for ku = 1:length(nk1)2 f* x& @; T6 d: n0 z% ?
u1 = data(max([nk1(:);0])-nk1(ku)+1:Ncc-nk1(ku),ny+ku);) C( H: }; O7 r2 _) Z7 [4 F3 {6 {
newsamp = Ncap-length(u1);
& R @/ n1 {3 z6 n, p3 | if nk1(ku)>0
- I. ?+ e8 A8 ] u1= [zeros(newsamp,1);u1];
+ {" z: t* r1 [8 ?" z else
& R6 H( H; G, ~ u1 = [u1;zeros(newsamp,1)];
m; {) B* k5 }9 U9 U6 y M& p1 x F9 V end
0 a# i+ f' l9 [% v/ X7 a data(:,ny+ku) = u1;; N+ ~" j3 U+ c' }$ N$ ?
end1 m* F3 S# m3 h: E+ m' l3 p+ p
end
: F( d) p: w& q1 ` iddatflag= 0;
1 e* f% I- J- S V4 V) X4 x if ~iscell(data), ze ={data};else ze = data;end
) Y! v |* S) u1 M C Ne = length(ze);4 L' G, V- W B$ \* w# B; [
nz = size(ze{1},2);/ K C- N( C2 {' ?$ @$ @. k C$ y
for kexp = 1:Ne" N c! k7 W# n- {4 c' b# Z( P
Ncaps(kexp) = size(ze{kexp},1);
4 @) x. w1 F! X0 q3 o end; i) C( |2 L) x. d0 [0 u' ~7 C2 F
%Ts =[];
- H, q, ^% \/ y" a( gend
! v/ J' q( ^3 H) d' rif m>=min(Ncaps)
( h) T9 y* P7 P' k- T" `/ B error('Ident:analysis:predictLargeK',...+ f( _, A2 g7 ^) ]. t/ a
'Prediction horizon must be smaller than the number of data samples.')
# X0 Y2 C" S0 {) Y+ Send. q4 H/ \4 o$ y3 j' ^$ I( \
[A,B,C,D,K,X0]=ssdata(theta);7 B& B9 e2 ] o* [: l& t( [* ?
[nyt,nx]=size(C);nut=size(B,2);( q- I* ^, u+ F- [$ R
if iddatflag
5 L) y0 G% h/ | if ny~=nyt || nu~=nut
* l7 @3 B4 Q9 W: a5 {" |3 W9 N1 m error('Ident:general:modelDataDimMismatch',...
d8 l4 H4 w( V. @& |' A- z 'The number of inputs and outputs of the model must match that of the data.')$ K4 q, l# }& K: h5 y
end" J: o u0 S C9 u( c- q0 ]
else% Q3 y! g( K7 U1 G, O; {
if nz~=nyt+nut! {; R' T b! C2 \# F
error('Ident:general:modelDataDimMismatch',...& ]* f9 `0 A3 g5 l" t o( A
'The number of inputs and outputs of the model must match that of the data.')
! p; ?- F1 B$ O end
# @. [3 @7 ?4 c& }1 C! {! }5 r ny = nyt; nu = nut;
4 C0 ~* H" j) u j+ Z* p4 k2 Mend7 u( m. A* y5 g) E: S: L& F
if strcmp(init,'e')5 M- ]4 O! a4 H& X2 ?
X0 = x0iniest(theta,ze);( D3 p/ G9 X3 T1 s
elseif strcmp(init,'z'), T+ s) u9 d& O) n4 b
X0 = zeros(size(X0));5 }+ I: r3 _ N, F
end
d0 {* I4 B! w; Gif ~ischar(init)" w7 t5 }- C" p6 ]& X9 o+ w
X0 = init;1 G7 d+ k) }5 u! B' |* ?
end, v- @: l, q( u
if nargout>1
" \: i% H, l! Y7 h3 H xi = X0;
% v" G; z. i" y: w @end
! c% d, Q6 p' m" u% ~5 _[xnr,xnc]= size(X0);
7 v1 o5 D3 i1 @: n' bif xnc~=1 && xnc~=Ne4 R$ u' R# x) M) d5 h( R
error('Ident:analysis:IniSize',...
$ t' x$ Q f! F8 V& q 'The "InitialState" option value must have either 1 or Ne columns, where Ne = no. of data experiments.');' {4 L4 `! ^1 h$ J
end# p$ m) c- v6 R }) b& o
if xnr~=nx( W4 @2 V; a+ c% H: v; ~1 B
error('Ident:analysis:IniRows',...: u7 L& G; j7 d/ I& X& {
'The value of the "InitialState" option should have %d row(s).',nx)
' ~9 v: M* u' h, ^end
j$ _2 [4 N. u1 K1 d. {- G8 q* Kif xnc==1 && Ne>1
! t% ~- x/ J9 f: V" ?/ ?0 L- z X0= X0*ones(1,Ne);! W7 J; T$ |& [2 R/ A/ o) u0 U: t
end& y2 q* ^8 p) v) B
for kexp = 1:Ne
# K3 l: N! R. T) p z = ze{kexp};
8 h/ a# A! [" B' F ]/ Q: R& Q5 i u = z(:,1+ny:end);5 b: F! k6 H8 G2 z' U
Ncap = Ncaps(kexp);, [8 U+ U8 r7 B+ o. x
if m==inf,
) ?$ ^6 T* T* j4 F- `/ w+ P" o yhat=sim(theta,u,X0(:,kexp));
/ P( u8 T1 ~$ R+ a8 o6 h else
/ t+ G' z* ~& x1 E2 X' w x=ltitr(A-K*C,[K B-K*D], z, X0(:,kexp));+ B- ]6 R% u4 h. G
if m==1,
* L7 Q' t1 p- ?* u% V& x7 v yhat=(C*x.').';( O/ U, @( C8 l9 z( z" g( W
if ~isempty(D),yhat=yhat + (D*u.').';end9 B; E/ G- ?5 h" Q
else' J' p; O7 w2 z T
F=D;Mm=eye(length(A));
5 v8 E) s& F: T, k$ ` for km=1:m-1, X3 M- L3 X x/ Q
F=[F C*Mm*B];
. q6 W# S7 }0 m Mm=A*Mm;3 Y H& W7 i" Z! x% H3 l3 I4 I6 \
end2 y. C: I* X$ b# F/ b
yhat=zeros(Ncap,ny);%corr 911111
" o8 X) C' B0 Q; ? G8 X& t2 y for ky=1:ny- w1 A4 {/ O% t$ f0 L0 ^* O
for ku=1:nu, Y! Q) v3 F% ?% ^% \
yhat(:,ky)=yhat(:,ky)+filter(F(ky,ku:nu:m*nu),1,u(:,ku));
6 Z8 H6 H7 s+ E9 \ end
! L4 }, ^" _# ?. F& J, ] end% `, T9 x8 P& j& _2 I$ k
if isempty(yhat),yhat=zeros(Ncap,ny);end/ a1 R: S+ c- T* q4 P. P3 u8 h% W( j
yhat(m:Ncap,:)=yhat(m:Ncap,:)+(C*Mm*x(1:Ncap-m+1,:).').';
$ A6 N6 W! n# c* g; q if nu>0
T5 |& g2 t3 b( `) s# v. x6 Z x=ltitr(A,B,u(1:m,:),X0(:,kexp));9 }* E. U! a7 W+ g: X, i4 g; h
yhat(1:m,:)=(C*x.').';( ~( R1 C. t! f5 F6 y0 d# }6 }
end
4 A9 q: Z0 \0 Q; Z7 d! j! E8 W4 ]5 _ if ~isempty(D),yhat(1:m,:)=yhat(1:m,:) + (D*u(1:m,:).').';end/ U& {2 L: I! V6 H5 h: |5 ]
end, Q! ?! J# ^7 |9 T+ p Q1 |8 F, ^
end- I; I4 I | Y5 t# P" E
yhatc{kexp} = yhat;7 g( d% n( W* e+ S9 f" c2 P; w
end# Q* U. [. h' P& x+ C3 j
if iddatflag
* M, ^* ~9 m7 f5 H8 Z& e( [% ? yhat = data;
: [; h# w2 T; K! `& I# D yhat = pvset(yhat,'OutputData',yhatc,'InputData',[]);% q' M5 j% s2 c9 I; L' \6 D/ l- P
else
; Q0 V$ d1 |" I- ?' U yhat = yhatc;
A8 y8 P7 n! x! n T3 cend
6 v; f- f4 r7 {: G# V& _# t% Sif nargout >2
/ E* }1 Z" Q/ C/ h5 h thpred = polypred(theta,m);
: ]$ \1 N+ `- W r+ t$ V- _3 lend6 P" s* }; q3 Z9 R' D( Z
if nargout > 1
! }+ U) U4 h( m# s. @' ?8 n try( X9 j/ {4 h' e5 k q7 |4 K+ n9 y
xi = xi(1:nxorig,:);
, w) Y* W1 w4 b3 z, k9 K end
$ s, o: v, H8 R' vend/ b9 W0 o ]3 a' ]$ o; ?
if (nargout == 0)3 X8 t2 E$ e6 \2 B6 J: e7 e P
% Plot y and yhat.
- C7 k/ ~3 T" t( a. x utidplot(theta,yhat,'Predicted');/ s; `% n% B$ L1 Q
clear yhat x0;
% l7 d! y9 l" J( N9 \# B3 ]7 r8 ]end! R0 \5 Z K+ y
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
/ [( V3 S0 b) Z%%%%% LOCAL FUNCTIONS
1 [+ _3 l8 F2 [7 e# ]%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1 u, o/ g! Z( R+ Qfunction xi = x0iniest(m,data)
0 W2 c6 y: o+ a/ t' s# [& kif isa(data,'iddata') && strcmpi(pvget(data,'Domain'),'frequency')+ q" b9 e* v0 ~# h {; F
[dum,xi] = pe_f(m,data);
" t* ^. `$ P6 o, G- B( x return
( B6 l( V# e, K/ f! A: f$ C) S/ cend
+ j7 o. g& [: L* PInpd = pvget(m,'InputDelay');
; b) J3 ~( A' o, X4 Mif isa(data,'iddata')( }0 x% x/ B9 V4 S# X/ A% P* o
data = nkshift(data,Inpd,'append'); t7 Z+ Y' R% t3 G$ O
[ze,Ne,ny,nu,Ts,Name,Ncaps,errflag] = idprep(data,0,'dummy');- g4 }* [7 c4 Q7 W8 S1 |
%if ~isempty(errflag.message), error(errflag), end
; H O# P6 z( C if ~isempty(Name)
) E% b4 I! \) G/ e data.Name = Name;
* T9 a/ y% f1 M( y. {. E end
% r9 R9 R# k; [+ jelse
% T: z' @) ~- g, J7 L if iscell(data)
/ j) i/ ~ n& A% U1 P4 m- D ze = data;3 y2 O! ~3 m5 q( p( g# I( z
else# c8 W3 E8 J) z5 K+ k' r
ze = {data};
7 ]+ j/ g3 Q1 y7 P- R( [5 d1 z4 u end2 Y1 L3 @" ^$ _* v- {
end- g6 K+ ^2 q. u6 @ P( Y
alg=pvget(m,'Algorithm'); l0 N8 B" M5 R, Y
maxsize=alg.MaxSize;
1 n( h# Z& p. M( h# E" E[A,B,C,D,K,X0]=ssdata(m);
( c7 Q) T& Z7 K6 knx=length(A);& t4 S8 Z) L. n5 p- v. N; T! P
if ischar(maxsize)
& v9 T4 N% f! D" m1 y maxsize = idmsize(length(ze{1}),nx);! k9 T" Y% U7 P: g, R) ]; ^7 F
end+ w% F9 m& e. g$ i/ Q8 Q( v
AKC=A-K*C;
, @. v" l. y% A9 z' X: d[ny,nx]=size(C);. q, n% `( Z& z+ L/ D
nu=size(B,2);
$ U# B9 N' e3 I1 z( Zel=zeros(0,ny);
0 m. P' e4 F. ^* B Z3 c! H$ c0 \xic = zeros(nx,0);' t% c" N$ N9 @ s3 @
Ne = length(ze);
% j' W L! f! \ Ifor kexp = 1:Ne
; [5 \9 ]$ b) Y( X+ F' H j z = ze{kexp};1 v0 ?8 h/ Z( f
[Ncap,nz]=size(z);
3 B! l3 k, l; D if nu+ny~=nz
4 W' K' R+ i0 H4 C. k error('Ident:general:modelDataDimMismatch',...
|# \, ~. z$ b8 n$ g9 c9 ` 'The number of inputs and outputs of the model must match that of the data.')
) w) ~" V; J% ?2 A end
, M3 w4 C% M/ R1 t+ B nz=ny+nu; [Ncap,dum] = size(z); n = nx;- \ z; \1 X0 V+ |! N: _
rowmax = nx+nz; X0 = zeros(nx,1);" `3 C( }$ b7 [! T5 Y3 B1 X
M=floor(maxsize/rowmax);! f: E$ O) ?* R
if ny>1 || M<Ncap' @. }9 B+ |0 }1 j
R=zeros(n,n);Fcap=zeros(n,1);R1=[];5 t9 ~" c4 i( f) b; H% K) ^
for kc=1:M:Ncap2 c% C4 J+ p c! u% V( G7 B- W% {
jj=(kc:min(Ncap,kc-1+M));
) v) d' T" `* l$ C I( p ? if jj(length(jj))<Ncap
# g0 e. B, s9 r1 j( H jjz = [jj,jj(length(jj))+1];
. K5 }. ?( \9 f; E2 ` else
0 e5 c( C% g+ ^( m" v( f7 S( r jjz=jj;
# X' w& o4 M, G& e C) M8 l end$ b3 [ @* r9 F1 P7 r
psitemp=zeros(length(jj),ny);! H" N" w, Y7 ?$ L/ m( ]/ {
psi=zeros(ny*length(jj),n);. M* X* c# n* ]) `+ r) E$ y# x
x=ltitr(AKC,[K B-K*D],z(jjz,:),X0);
8 L% t, s4 z8 g yh=(C*x(1:length(jj),:).').';! S5 Q" A1 l d
nm=pvget(m,'NoiseVariance');
- X! H% f- n; c. k; W8 a if isempty(nm) || norm(nm)==0 % To handle models without noise
1 f- ]7 o# C7 ?/ `1 j& P nm = eye(ny);
7 z$ y& O, w: e end' J# z1 E3 o* ^# T4 X c; Y$ |5 J
sqrlam=pinv(sqrtm(nm));
2 ?4 f( C8 }6 A$ g7 O if ~isempty(D),yh=yh+(D*z(jj,ny+1:ny+nu).').';end* `+ i- f/ n' Z" S
e=(z(jj,1:ny)-yh)*sqrlam;* F1 j; G) t; k. Q4 U( U
[nxr,nxc]=size(x);X0=x(nxr,:).';* t; U2 T5 h. r$ M2 ~' g# n& }. I
evec=e(:);
* e% {0 R" y! ]" Y* N+ d& E4 [. y kl=1;
5 y$ |0 `) }# k' U# f for kx=1:nx
& `' v! s! A8 o Z( e if kc==1
6 R* ^- j5 f, B) O6 ` x0dum=zeros(nx,1);x0dum(kx,1)=1;# U9 ?: r: l: W- K, r3 t: {4 }8 W- O
else3 Q3 m. d: c9 P% Y5 J+ P. X; S4 M
x0dum=X00(:,kl);' n2 b0 H( {1 F$ ?: [
end- x E& X8 i: K" g4 t, u$ i
psix=ltitr(AKC,zeros(nx,1),zeros(length(jjz),1),x0dum);
5 _4 v( ~( ]) k [rp,cp]=size(psix);/ }) K! w. k' T( ~3 y
X00(:,kl)=psix(rp,:).';
7 s9 S( w- u" r% m; L; y$ U psitemp=(C*psix(1:length(jj),:).').'*sqrlam;& X1 t# L1 a) ^, O( i6 a Z
psi(:,kl)=psitemp(:);kl=kl+1;5 Q. N/ j: h; r4 j
end* R, f" e% j$ e) _
if ~isempty(R1)" ~- z3 a6 N1 o
if size(R1,1)<n+1
/ n# n T! {7 ~1 x) y" e; U error('Ident:estimation:predictSmallMaxSize',...) _7 k, y0 [# A) W
'The value of the algorithm property "MaxSize" is too small to estimate the initial states. Either increase MaxSize value in the model or set the "InitialState" option of the "predict" command to a value other than ''Estimate''.')
]" _( z6 w( S7 r) S end" P; t- [; G' R; E
R1=R1(1:n+1,:);
/ |5 X- g9 k6 G6 j+ B/ H end- V2 W, g3 i r, u4 D& C: D1 W8 o
H1 = [R1;[psi,evec] ];R1 = triu(qr(H1));
5 {/ L+ U( U2 l, k: p1 p- s% W end/ j B9 L& S: |2 i
try; c. l6 M' V4 E" L& J Y8 Z; o% v
xi(:,kexp) = pinv(R1(1:n,1:n))*R1(1:n,n+1);& \- W' x) h1 l+ C0 g% O
catch3 \" S9 Y7 f' j3 |/ c
warning('Ident:estimation:X0EstFailed',... s* j. ^' U! }4 S
'Failed to estimate initial conditions. Check model stability. \nThe "InitialState" option has been set to zero.')# a% ]. b/ ^% e, e% l. H
xi(:,kexp) = zeros(n,1);
1 B6 y$ ?" L: L9 n7 Y end
. `; }) u9 X7 a0 l3 Z else4 V2 H/ K$ V$ w( ~
%% First estimate new value of xi
. ~4 B, t, i/ c x=ltitr(AKC,[K B-K*D],z);! v0 J. D" |% b+ I# V2 O: n- N
y0=x*C';% Z- g( S* K: c' _. D, l; a% L
if ~isempty(D),
& A! Z8 [) q2 N6 G' h0 j y0=y0+(D*z(:,ny+1:ny+nu).').';+ m1 R6 Y+ \% O% n/ ~- p
end
7 l; _+ G; n# s2 |6 z: G psix0=ltitr(AKC.',C.',[1;zeros(Ncap,1)]);
- v" Y$ z+ g) H0 s. `; K1 E: H! n psix0=psix0(2:end,:);
- N' t. ?0 ^6 X( i try0 M7 L9 ?0 J1 j5 ~( f1 i
xi(:,kexp) = pinv(psix0)*(z(:,1)-y0);; j& B' f% @. L! k' n
catch
( E/ V+ k4 [- J7 ]" K1 N5 P warning('Ident:estimation:X0EstFailed',...
5 y; i) ~* M3 o1 t 'Failed to estimate initial conditions. Check model stability. \nThe "InitialState" option has been set to zero.')
2 m2 @9 N+ F: ~* R xi(:,kexp) = zeros(n,1);
# ]5 e; U3 i7 f& t5 t: \9 C end! G1 b0 L$ E& x$ i
end" S/ H; p3 ^3 B7 p7 u
end& _, q! V$ T3 w$ u' \
%%*************************************************************************
L+ f p' M' l" Y7 x/ Pfunction thpred = polypred(theta,m)
s1 [% x, Q/ s& g0 O% S% Note that cross couplings between output" E9 x( k8 v* x
% channels are ignored in these calculations.' R7 t9 U/ r8 u; h7 B8 D b1 Z
[ny,nu]= size(theta);
# j% a. S7 n& ]* kyna = pvget(theta,'OutputName');
' c/ x8 A) a# x1 H1 o! ~una = pvget(theta,'InputName');
* W& b5 J! k5 m! X8 y" \* M; dyu = pvget(theta,'OutputUnit');
* ^3 K+ o" X) J1 H) G" Wuu = pvget(theta,'InputUnit');
( M7 N. ^/ c+ x" b8 ~for ky = 1:ny8 ]2 l/ F G. m/ y' W- T$ B
[a,b,c,d,f] = polydata(theta(ky,:));
' N$ t+ x# c6 T0 K' N9 Y if nu>04 f5 m4 Z {9 }% t
ff = 1;
4 E7 K! K# v$ S3 ?, w" N) g for ku = 1:nu,
2 c$ D$ ^5 L( C5 M) |7 N bt = b(ku,:);( F Z2 J: z+ ~+ X
for kku = 1:nu, if kku~=ku, bt = conv(bt,f(kku,:)); end, end
, l2 t: `) [+ v# N( O. t bb(ku,:) = bt; U% H3 ~9 l7 W3 a s3 u% S' X
ff = conv(ff,f(ku,:)); k, H6 l; H. k+ ?$ g, G. A
end5 P# J9 Y, t% K6 Q- d$ p0 [# S
a = conv(conv(a,ff),d);c=conv(c,ff);
5 c( F+ y5 R+ a @+ V1 ]5 M else
0 [6 o$ ]* K% G! Q$ H) F2 Y, l( j# k a = conv(a,d);
( k2 J4 }8 {) k. x/ A end7 j* Z% `. l% _- {6 }5 A5 [
na = length(a); nc = length(c); nn = max(na,nc);7 ]5 b' T, C. n5 F
a = [a,zeros(1,nn-na)]; c = [c,zeros(1,nn-nc)];
6 c$ X: d ^, n U) _; ^/ A [f,g] = deconv(conv([1 zeros(1,m-1)],c),a);6 _3 _- y/ k/ ^) F
ng=length(g);
/ L- n0 }; D1 M. S& H7 p3 K/ l. g& D if nu>0,
3 D) f3 `" i! K; I" c+ y& u df=conv(d,f);/ Q/ {! A9 C `5 D
for ku=1:nu
% c5 ~( B* E) ] m% O bf(ku,:)=conv(bb(ku,:),df);( O9 c* @1 x4 P/ i- I
end
# B& o2 k( l5 b# m nbf=length(bf(1,:));nn=max(ng,nbf);
9 A' v" _0 E" y+ v gg=[[g,zeros(1,nn-ng)];[bf,zeros(nu,nn-nbf)]];
* k& e0 F$ r3 s. \6 H" E' Z else
4 Z' x4 q9 ]$ w2 J, [+ D gg=g;5 R( y3 Z- z1 x1 z2 _) v
end
% H! a F0 B, y4 O, o$ N7 } th1 = idpoly(c,gg);* R' B& |: ~+ \) O2 J
th1 = pvset(th1,'InputName',[yna(ky);una],'OutputName',[yna{ky},'p'],...
+ L0 p3 u/ t2 c7 Q/ s# }( ]2 D. \# l 'InputUnit',[yu(ky);uu],'OutputUnit',yu(ky),'Ts',pvget(theta,'Ts'),...
% E" ^% [: n. B4 Y# x; J 'TimeUnit',pvget(theta,'TimeUnit'),'EstimationInfo',pvget(theta,'EstimationInfo'));% T: w3 k3 S" u# T& b- t. s- V4 k( O
thpred{ky} = th1;
0 O( j5 t) L( _" Zend7 E2 l$ \# r, G# |$ k6 v
%%%************************************************************************ |
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