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我的代码如下:
0 D( H; ^) u1 F$ X5 z( R4 mclose all;1 ` C& E5 J" @* R8 `3 u
clear all;
* P$ v, w0 n" A; d' T$ q& p- Z% P' UL=1; EI=5; T=2; rho=2; M=6; W6 r3 ?( r6 R( [1 x
nt=80000; nx=20; tf=15; Ttr=50;
6 o3 D% U; m4 I/ f Fdx=L/nx; dt=tf/nt;+ k# m* O0 e* [% Z
x = linspace(0,L,nx+1); t_tr = linspace(0,tf,Ttr+1);9 ?3 x1 j5 A3 y+ q0 q& v1 ?+ Y
w=zeros(nx+1,nt+1);
% e A3 f" Q4 f6 k2 u4 [) cw3D_free=zeros(Ttr+1,nx+1);9 d* ~, z% R) ~6 `
d=zeros(nt+1,1);+ L' Y p7 _8 Q* O" \. E# z# \
for j=1:nt+1
0 t! m7 }# i% F+ ?1 p d(j) = 1 + sin(2*pi*(j-1)*dt) + cos(3*pi*(j-1)*dt) ;
+ H/ g8 B ^6 H6 j: W1 `end, P% c. f( Z6 K4 x/ y
Br=90;Bl=-90;k=100;k1=1;k2=4;r=1;m=1;
# \: P P0 K- fw=zeros(nx+1,nt+1); w3D_model=zeros(Ttr+1,nx+1);/ l" v* B# S: a' U2 l) ]/ i
u_model=zeros(nt+1,1);u3D_model=zeros(Ttr+1,1);& w8 Z* o9 K) P9 }3 a/ q
ua=zeros(nt+1,1); d_estimate=zeros(nt+1,1);$ K" i/ S% i& }; N2 k0 F1 H* N
d1=zeros(nt+1,1);+ ~. c1 m- E' Z- x- w% G
dbar=max(abs(d));
; L1 Z0 w* G4 P1 td_estimate(1:2)= dbar;- a: i7 o. E# |, K
for i=1:nx+1
& R( ?5 e: X A# ~6 h w(i,1)=(i-1)*dx;
, h/ b- U/ E' {0 `4 m+ X) } w(i,2)=w(i,1);6 ]) p1 b7 I: u( P3 J/ t- d9 N! N
end4 t" z+ w5 C5 {% X* N8 |
w(1, =0;w(2, =w(1, ;
( X( `, R' }8 \# `8 O0 gw3D_model(1,:)=w(:,1);w3D_model(2,:)=w(:,2);
8 d6 N' X4 f' X2 Zfor j=3:nt+1
! _. v: d" I: o" Z for i=3:nx-1* K1 N g u$ O
wxx=(w(i+1,j-1)-2*w(i,j-1)+w(i-1,j-1))/dx^2;; ^9 T8 y+ f: m6 b
wxxxx=(w(i+2,j-1)-4*w(i+1,j-1)+6*w(i,j-1)-4*w(i-1,j-1)+w(i-2,j-1))/dx^4;7 E: s5 \# H1 C1 ]
w(i,j)=2*w(i,j-1)-w(i,j-2)+(T*wxx-EI*wxxxx)*dt^2/rho;+ g3 \- W, D! i! E9 c6 k" {
end. r) k5 e+ w3 d7 m
8 u7 E6 w1 }, k, x7 a wxl=(w(nx+1,j-1)-w(nx,j-1))/dx;
( X4 d; C5 W% q$ X% ?2 p wxxxl=(w(nx+1,j-1)-3*w(nx,j-1)+3*w(nx-1,j-1)-w(nx-2,j-1))/dx^3;
4 S4 w7 Z# ]% f) k wxxxtl=(w(nx+1,j-1)-3*w(nx,j-1)+3*w(nx-1,j-1)-w(nx-2,j-1)-w(nx+1,j-2)+3*w(nx,j-2)-3*w(nx-1,j-2)+w(nx-2,j-2))/(dt*dx^3);/ Z% c2 ^' s( a2 B! N) c# Y d N
wxtl=(w(nx+1,j-1)-w(nx,j-1)-w(nx+1,j-2)+w(nx,j-2))/(dx*dt);
0 T6 E1 J6 H/ i9 Z i" y5 @8 p wtl=(w(nx+1,j-1)-w(nx+1,j-2))/dt;
! E% D- }% q. U9 W3 @) N ua(j)=wtl+k1*wxl-k2*wxxxl;
0 R$ P3 w- ~1 G: n& R" O d_estimate(j)= (abs(ua(j))+d_estimate(j-1))/(1+r*dt);$ x4 M- L6 |8 ~% P: G
u_model(j)= (-EI*wxxxl+T*wxl-k1*M*wxtl+k2*M*wxxxtl-k*ua(j)-sign(ua(j))*d_estimate(j))/m;
$ ^/ y) w1 T' l4 P3 a dv=(u_model(j)-u_model(j-1))/dt; B' k0 S9 A0 l
if dv>02 F5 B, Y' c! t* m- p! ^* L
d0=-m*Br;
* ]- u- x* i& |$ A# w else- P" r& S- g x) h& C
d0=-m*Bl;5 _; n1 ?. m0 p v' ^5 {/ m4 o4 i
end
! F/ k& j8 q; G, } P d1(j)=d0+d(j);
' k; K0 r u' l w(nx+1,j)=2*w(nx+1,j-1) - w(nx+1,j-2) + (m*u_model(j-1)+d1(j-1)+EI*wxxxl-T*wxl)*dt^2/M;
1 C1 }7 \9 z; F f w(nx,j)=(w(nx+1,j)+w(nx-1,j))/2;
. F8 I8 r; d: c1 o if mod(j-1,(nt/Ttr))==0, T9 @3 [3 a; X- n
w3D_model(1+(j-1)*Ttr/nt,:)=w(:,j);& C+ s! w) Z2 J) F/ `; L
u3D_model(1+(j-1)*Ttr/nt)=u_model(j);; C2 F* ^. C. H/ k* A5 g/ Q
end
7 p( a" A" l( hend6 m6 Q# [ f( `, I; |3 T3 |2 B) L5 ^
figure(1);4 }. ]3 D2 @- U/ q
suRF(x,t_tr,w3D_model);0 F( ?4 _! p( K% O i" E8 W- ]
title('Displacement of beam with robust boundary control');" }1 Q1 V; s1 Y6 [" K
ylabel('Time (s)','Fontsize',12);2 S8 I: L6 f0 ]
xlabel('x(m)','Fontsize',12);. x1 M3 f( U3 A E4 Z. |& \* i( K* k( ?+ J
zlabel('w(x,t)(m)','Fontsize',12);2 {) n1 N- r+ C3 a- a4 R9 ]
figure(2);& b# w1 U' `* B$ Q' j
plot(t_tr,u3D_model,'r')
& ?8 x# S- [; w& `5 Fxlabel('time');" b- a$ O( {# Z9 F/ v% `( o4 _
ylabel('u');8 K" F' [( U( C# W$ ?
1 f5 j: i- Q* Y5 O' d6 O$ z$ h. a' h0 |
以上我的代码没出问题,但图像出不来,求助!
% Q3 z: g: U$ r" e' R: O. s |
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