ode45 error-time-dependent parameter

Question

Elahe S 2024-1-4

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2066326-ode45-error-time-dependent-parameter

编辑： Walter Roberson 2024-1-5

采纳的回答： Sam Chak

在 MATLAB Online 中打开

Dear all,

I would appreciate it if you could help me fix the error. 9 time-dependent parameter are existed (A_x, ..., D_t).

The error is:

Index exceeds matrix dimensions.

Error in STdof/MDOF3st3dof (line 56)

dg13=g(14);

Error in odearguments (line 87)

f0 = feval(ode,t0,y0,args{:}); % ODE15I sets args{1} to

yp0.

Error in ode45 (line 115)

odearguments(FcnHandlesUsed, solver_name, ode, tspan,

y0, options, varargin);

Error in STdof (line 34)

[t,g] =

ode45(@MDOF3st3dof,tspan,g0,options,tspan,A_x,V_x,D_x,A_z,V_z,D_z,A_t,V_t,D_t,m1x,m2x,m3x,m1z,m2z,m3z,I1,I2,I3,c1x,c2x,c3x,c1z,c2z,c3z,c1t,c2t,c3t,k1x,k2x,k3x,k1z,k2z,k3z,k1t,k2t,k3t);

function STdof
close all, clear,  clc
 
t_start=0;
t_end=32.82;
dt=0.02;
 
A_x=load ('D:\tax.out');  
V_x=load ('D:\tvx.out');  
D_x=load ('D:\tdx.out');  
A_z=load ('D:\taz.out');  
V_z=load ('D:\tvz.out');  
D_z=load ('D:\tdz.out');  
A_t=load ('D:\tat.out');  
V_t=load ('D:\tvt.out');  
D_t=load ('D:\tdt.out');  
L1=3;   L2=6; 
m1x=100;    m2x=150;    m3x=200;
m1z=400;    m2z=300;    m3z=210;
I1=130;     I2=160;     I3=190;
c1x=22000;  c2x=18000;  c3x=15000;
c1z=13000;  c2z=15000;  c3z=14000;
c1t=23000;  c2t=18000;  c3t=16000;
k1x=5000000;   k2x=4000000;    k3x=7600000;
k1z=6000000;   k2z=4400000;    k3z=7400000;
k1t=32000;     k2t=42000;      k3t=6500000;
%%========================================================== 
g0=[0,0,0,0,0,0,0,0,0,0,0,0];
Nstep=(t_end-t_start)/dt+1;
tspan=t_start:dt:t_end;
options = odeset('RelTol',1e-9,'AbsTol',1e-9);    
 
[t,g] = ode45(@MDOF3st3dof,tspan,g0,options,tspan,A_x,V_x,D_x,A_z,V_z,D_z,A_t,V_t,D_t,m1x,m2x,m3x,m1z,m2z,m3z,I1,I2,I3,c1x,c2x,c3x,c1z,c2z,c3z,c1t,c2t,c3t,k1x,k2x,k3x,k1z,k2z,k3z,k1t,k2t,k3t);
 
 function dg=MDOF3st3dof(t,g,t1,A_x,V_x,D_x,A_z,V_z,D_z,A_t,V_t,D_t,m1x,m2x,m3x,m1z,m2z,m3z,I1,I2,I3,c1x,c2x,c3x,c1z,c2z,c3z,c1t,c2t,c3t,k1x,k2x,k3x,k1z,k2z,k3z,k1t,k2t,k3t)
   
 A_x = interp1(t1,A_x,t)      
 V_x = interp1(t1,V_x,t) 
 D_x = interp1(t1,D_x,t) 
 A_z = interp1(t1,A_z,t) 
 V_z = interp1(t1,V_z,t) 
 D_z = interp1(t1,D_z,t) 
 A_t = interp1(t1,A_t,t) 
 V_t = interp1(t1,V_t,t) 
 D_t = interp1(t1,D_t,t) 
 
 dg1=g(2);
 dg2=(-1/m1x)*(c1x*g(2)-c1x*V_x+k1x*g(1)-k1x*D_x);
 dg5=g(6);
 dg6=(-1/m3x)*(m2x*A_x-c1x*g(2)+c1x*V_x-k1x*g(1)+k1x*D_x+c3x*g(6)+k3x*g(5));
 dg7=g(8);
 dg8=(-1/m1z)*(2*c1z*g(8)-2*c1z*V_z+2*k1z*g(7)-2*k1z*D_z);
 dg11=g(12);
 dg12=(-1/m3z)*(m2z*A_z-2*c1z*V_z-2*k1z*g(7)+2*k1z*D_z+c3z*g(12)+k3z*g(11));
 dg13=g(14);
 dg14=(-L1^2/(2*I1))*(c1z*g(14)-c1z*V_t+k1z*g(13)-k1z*D_t);
 dg17=g(18);
 dg18=(-1/I3)*(I2*A_t-L1^2/2*c1z*g(14)+L1^2/2*c1z*V_t-L1^2/2*k1z*g(13)+L1^2/2*k1z*D_t+c3t*g(18)+k3t*g(17));
 
dg=[dg1;dg2;dg5;dg6;dg7;dg8;dg11;dg12;dg13;dg14;dg17;dg18];
 
end
save('result.txt','g','-ASCII')
display 'Done!'
end

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Answer 1

Sam Chak 2024-1-4

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2066326-ode45-error-time-dependent-parameter#answer_1383131

在 MATLAB Online 中打开

Hi @Elahe S

You may not fully understand some of the MATLAB error messages if you are not a programmer or if you haven't encountered differential equations in matrix form. The code has been fixed now, and you can learn by example. However, you need to inject, feed, or load the time-dependent parameters into the Workspace.

%% §1: Time-dependent parameters

t_start = 0;

t_end = 6; % 32.82;

dt = 0.02;

tAVD = t_start:dt:t_end;

tx = tAVD; % should get time data from tax, tvx, tdx

tz = tAVD; % should get time data from taz, tvz, tdz

tt = tAVD; % should get time data from tat, tvt, tdt

A_x = tanh(tx); % load('D:\tax.out');

V_x = tanh(tx); % load('D:\tvx.out');

D_x = tanh(tx); % load('D:\tdx.out');

A_z = tanh(tz); % load('D:\taz.out');

V_z = tanh(tz); % load('D:\tvz.out');

D_z = tanh(tz); % load('D:\tdz.out');

A_t = tanh(tt); % load('D:\tat.out');

V_t = tanh(tt); % load('D:\tvt.out');

D_t = tanh(tt); % load('D:\tdt.out');

%% §2: Call ode solver

tspan = t_start:dt:t_end;

% Nstep = (t_end-t_start)/dt + 1;

g0 = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];

options = odeset('RelTol', 1e-9, 'AbsTol', 1e-9);

[t, g] = ode45(@(t, g) MDOF3st3dof(t, g, tAVD, A_x, V_x, D_x, A_z, V_z, D_z, A_t, V_t, D_t), tspan, g0, options);

%% §3: Plot results

tiledlayout(4, 3, 'TileSpacing', 'Compact');

nexttile, plot(t, g(:,1)), grid on, title('g1')

nexttile, plot(t, g(:,2)), grid on, title('g2')

nexttile, plot(t, g(:,3)), grid on, title('g3')

nexttile, plot(t, g(:,4)), grid on, title('g4')

nexttile, plot(t, g(:,5)), grid on, title('g5')

nexttile, plot(t, g(:,6)), grid on, title('g6')

nexttile, plot(t, g(:,7)), grid on, title('g7')

nexttile, plot(t, g(:,8)), grid on, title('g8')

nexttile, plot(t, g(:,9)), grid on, title('g9')

nexttile, plot(t, g(:,10)), grid on, title('g10')

nexttile, plot(t, g(:,11)), grid on, title('g11')

nexttile, plot(t, g(:,12)), grid on, title('g12')

%% §4: ODE function

function dg = MDOF3st3dof(t, g, t1, A_x, V_x, D_x, A_z, V_z, D_z, A_t, V_t, D_t)

%% §4.1: Interpolate time-dependent parameters

A_x = interp1(t1, A_x, t);

V_x = interp1(t1, V_x, t);

D_x = interp1(t1, D_x, t);

A_z = interp1(t1, A_z, t);

V_z = interp1(t1, V_z, t);

D_z = interp1(t1, D_z, t);

A_t = interp1(t1, A_t, t);

V_t = interp1(t1, V_t, t);

D_t = interp1(t1, D_t, t);

%% §4.2: Constants

L1 = 3; L2 = 6;

m1x = 100; m2x = 150; m3x = 200;

m1z = 400; m2z = 300; m3z = 210;

I1 = 130; I2 = 160; I3 = 190;

c1x = 22000; c2x = 18000; c3x = 15000;

c1z = 13000; c2z = 15000; c3z = 14000;

c1t = 23000; c2t = 18000; c3t = 16000;

k1x = 5000000; k2x = 4000000; k3x = 7600000;

k1z = 6000000; k2z = 4400000; k3z = 7400000;

k1t = 32000; k2t = 42000; k3t = 6500000;

%% §4.3: Differential equations

dg1 = g(2);

dg2 = (-1/m1x)*(c1x*g(2) - c1x*V_x + k1x*g(1) - k1x*D_x);

dg3 = g(4);

dg4 = (-1/m3x)*(m2x*A_x - c1x*g(2) + c1x*V_x - k1x*g(1) + k1x*D_x + c3x*g(4) + k3x*g(3));

dg5 = g(6);

dg6 = (-1/m1z)*(2*c1z*g(5) - 2*c1z*V_z + 2*k1z*g(5) - 2*k1z*D_z);

dg7 = g(8);

dg8 = (-1/m3z)*(m2z*A_z-2*c1z*V_z - 2*k1z*g(5) + 2*k1z*D_z + c3z*g(8) + k3z*g(7));

dg9 = g(10);

dg10= (-L1^2/(2*I1))*(c1z*g(10) - c1z*V_t + k1z*g(9) - k1z*D_t);

dg11= g(12);

dg12= (-1/I3)*(I2*A_t - L1^2/2*c1z*g(10) + L1^2/2*c1z*V_t - L1^2/2*k1z*g(9) + L1^2/2*k1z*D_t + c3t*g(12) + k3t*g(11));

dg = [dg1; dg2; dg3; dg4; dg5; dg6; dg7; dg8; dg9; dg10; dg11; dg12];

end

% save('result.txt','g','-ASCII')

% display 'Done!'

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Torsten 2024-1-5

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[t, g]  = ode45(@(t, g) MDOF3st3dof(t, g, tAVD, A_x, V_x, D_x, A_z, V_z, D_z, A_t, V_t, D_t), tspan, g0, options);
DG_SAVE = zeros(numel(t),12);
for i = 1:numel(t)
  dg = MDOF3st3dof(t(i), g(i,:), tAVD, A_x, V_x, D_x, A_z, V_z, D_z, A_t, V_t, D_t);
  DG_SAVE(i,:) = dg(1:12);
end

Elahe S 2024-1-5

Thank you.

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Answer 2

Rishi 2024-1-4

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2066326-ode45-error-time-dependent-parameter#answer_1383046

在 MATLAB Online 中打开

Hi Elahe,

I understand that you want to know why you are getting ‘Index exceeds matrix dimensions’ as an error.

This error message indicates that you are trying to access an element of a matrix using an index that does not exist. In your code, the error occurs at the following line:

d13 = g(14);

The function 'MDOF3st3dof' is called by the 'ode45' solver, which expects the function to return the derivatives of the state vector 'g'. However, the state vector 'g' is initialized with 12 elements (g0=[0,0,0,0,0,0,0,0,0,0,0,0];), and the code is trying to access the 14th element, which doesn't exist. This is the source of the error.

To resolve the error, you need to ensure that you are only accessing elements within the bounds of the g vector. Since g has 12 elements, you should only access indices 1 through 12. The differential equations need to be corrected to match the actual dimension of the system.

Hope this helps!