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我的代码如下:
1 B. _ U/ h- j5 vclose all;
: v& l, t4 i9 V T! V) i5 ~+ `clear all;
& N M" X( W6 p7 L2 Y+ ML=1; EI=5; T=2; rho=2; M=6;
1 L4 n- H# C) Y9 L; i5 xnt=80000; nx=20; tf=15; Ttr=50;
5 h" O8 Q# G. ]0 t$ K. w$ M1 Rdx=L/nx; dt=tf/nt;
! R0 p# y: r$ _5 ~, R! tx = linspace(0,L,nx+1); t_tr = linspace(0,tf,Ttr+1);
6 H# g& `3 T2 B: m9 X+ Vw=zeros(nx+1,nt+1);0 P+ C( D( n( u$ w, v9 j
w3D_free=zeros(Ttr+1,nx+1);" v) k, y: j! Z8 J' V3 |- ]* d L
d=zeros(nt+1,1);' f/ I: [! ~: n$ B6 o5 ~7 Z; ?) P5 T9 j
for j=1:nt+1' Q( `7 F1 v6 `% O, c9 w( `5 Y
d(j) = 1 + sin(2*pi*(j-1)*dt) + cos(3*pi*(j-1)*dt) ;
/ b- d- o& n1 h2 ?end
- C. I6 O: o3 D& K5 ZBr=90;Bl=-90;k=100;k1=1;k2=4;r=1;m=1;
0 i3 n" N B- D' M# ~) M8 {& |w=zeros(nx+1,nt+1); w3D_model=zeros(Ttr+1,nx+1);( E8 W5 P2 q! V7 A# \6 s7 D
u_model=zeros(nt+1,1);u3D_model=zeros(Ttr+1,1);
, n( J; c7 F2 _; _ua=zeros(nt+1,1); d_estimate=zeros(nt+1,1);
: q2 x' B# g3 I& Sd1=zeros(nt+1,1);
6 v0 i. k) z0 Odbar=max(abs(d));
+ h6 x- U1 u% Z' _d_estimate(1:2)= dbar;
f: z9 I2 j9 E' X, {for i=1:nx+1
% E2 W `% G2 S$ c8 W( H w(i,1)=(i-1)*dx;
" D7 {& m* p, r; \ w(i,2)=w(i,1);( ~3 j8 @/ p' b- G7 ^/ D
end8 M `5 F9 r( k. r4 ] p
w(1, =0;w(2, =w(1, ;
/ Y" W, g7 V- k- ~w3D_model(1,:)=w(:,1);w3D_model(2,:)=w(:,2);
C7 _. v9 T7 c6 G. Ifor j=3:nt+1
0 M1 n% P$ m" R' B& l for i=3:nx-1
" ]& o6 ~4 w5 D8 F6 I1 L/ O wxx=(w(i+1,j-1)-2*w(i,j-1)+w(i-1,j-1))/dx^2;/ b" o9 l$ h* ^) w. M) z. Z; z- n
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; S2 a0 N- Y4 v
w(i,j)=2*w(i,j-1)-w(i,j-2)+(T*wxx-EI*wxxxx)*dt^2/rho;
& i8 w* v& `) @6 p, J) e; C4 ` end
" d! l- Q2 k* @! S7 @" U
' t9 }% [8 n1 W wxl=(w(nx+1,j-1)-w(nx,j-1))/dx;0 ?# y0 Z' @2 L0 K: U1 h2 Z2 z
wxxxl=(w(nx+1,j-1)-3*w(nx,j-1)+3*w(nx-1,j-1)-w(nx-2,j-1))/dx^3;
) ^. p- x3 H& U- \4 k' M 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);$ M$ Z8 c9 ^$ |# k* R
wxtl=(w(nx+1,j-1)-w(nx,j-1)-w(nx+1,j-2)+w(nx,j-2))/(dx*dt);2 L+ l$ }7 f: d/ b# V" N! [
wtl=(w(nx+1,j-1)-w(nx+1,j-2))/dt;7 m" q# s* h, D! {( w+ }. r
ua(j)=wtl+k1*wxl-k2*wxxxl;% n1 h8 z. a; G
d_estimate(j)= (abs(ua(j))+d_estimate(j-1))/(1+r*dt);1 F: T+ T' @ P3 s& w
u_model(j)= (-EI*wxxxl+T*wxl-k1*M*wxtl+k2*M*wxxxtl-k*ua(j)-sign(ua(j))*d_estimate(j))/m;) N" I4 m% q' i# G
dv=(u_model(j)-u_model(j-1))/dt;
, S4 Q# m, F7 k7 w o3 f if dv>0. _0 ]# `* [. N& ]( `* D
d0=-m*Br;
( N6 F' Q8 F/ R4 k else
8 V6 N& m2 g! U: _/ N d0=-m*Bl;
W& J& v, u/ u+ |' [, X; i end
& ]0 |& \6 [ V: F: w d1(j)=d0+d(j);
3 L) g/ j- o7 t 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;
- `9 ]- X. d q8 Z w(nx,j)=(w(nx+1,j)+w(nx-1,j))/2;( p% v4 C+ i: ~! u6 v# n
if mod(j-1,(nt/Ttr))==0
9 S0 \1 r' f$ s$ G- V w3D_model(1+(j-1)*Ttr/nt,:)=w(:,j);" d4 q' r" e1 f, l9 o9 d# l
u3D_model(1+(j-1)*Ttr/nt)=u_model(j);
5 X! F7 {! \& Y6 e" Q7 R" \ end
3 z. Y9 f5 U4 ]; f) ?$ H+ @end) r3 ` c5 S) S% ^4 K2 p8 n
figure(1);
! p- O$ w; c* r0 m% A( ?) VsuRF(x,t_tr,w3D_model);
' [. R' O; s3 ^8 a4 @title('Displacement of beam with robust boundary control');7 B; k6 A1 z6 g
ylabel('Time (s)','Fontsize',12);
8 [1 X- f$ B8 S' C8 d Lxlabel('x(m)','Fontsize',12);7 ^( }0 g4 l& Q" @: V- U/ P
zlabel('w(x,t)(m)','Fontsize',12);
. h) ]7 b I* O8 c7 kfigure(2);5 \* D q5 d/ e$ R" c9 }! m
plot(t_tr,u3D_model,'r'). P* r# q3 d \! F c6 {
xlabel('time');# H- a0 a0 ^( i! c% G2 Q5 b \
ylabel('u');! ~3 P+ z* A! @1 k# ^$ a
0 v" C* }1 f4 b1 n
7 `+ `& Y7 J% o* m+ J4 T a以上我的代码没出问题,但图像出不来,求助!
/ N6 u: ~7 ]+ V" T' Q/ ~ |
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