When simulating the response to a specific input signal, the input data U must be a matrix with as many rows as samples in the time vector T, and as many columns as input chan

Hi All, I got an error when trying to solve a 4 dof dynamic system with sinusoidal load on dof #1 and dof #3 using a state space model. I created the state space model and make sure that it follows the size appropriately, however the error still persists:

"When simulating the response to a specific input signal, the input data U must be a matrix with as many rows as samples in the time vector T, and as many columns as input channels."

I have checked that my U input and my T has the same rows. And the U has the same column as the same matrix size as input. What possibly can I improve from my code?

clc
clear
clc

%specify the timestep
dt = 0.1;
tmax = 10;
t = [0:dt:tmax]';
time = t'; 

%assemble the M matrix
m = [0.5 0.5 1.2 1.2];
M = diag(m);

%assemble the K matrix
k1 = 100; 
k2 = 80;
k3 = 70;
k4 = 50;
k5 = 80;
k6 = 60;

k11 = k1 + k2 + k5;
k12 = -k2;
k13 = 0;
k14 = -k5;
k22 = k2 + k3 + k6;
k23 = -k3;
k24 = k6;
k33 = k3+k4;
k34 = -k4;
k44 = k4 + k5 +k6;
k21 = k12;
k31 = k13;
k32 = k23;
k41 = k14;
k42 = k24;
k43 = k34;

K = [k11 k12 k13 k14; ...
     k21 k22 k23 k24; ...
     k31 k32 k33 k34; ...
     k41 k42 k43 k44];

%assemble the F matrix
b2 = [10 0 0 0; 0 0 -5 0; 0 0 0 0; 0 0 0 0]';

%assemble the C matrix
C = 0.01*K;

%assemble the state space model
MK = M\K;
MC = -M\C;
I = eye(length(M));
zer = zeros(length(M));


A = [zer I; -MK -MC];
B = [zeros(4) M\b2]';
C = [eye(length(A))];
D = zeros(8,4);
dyn = ss(A, B, C, D)

dyn =
 
  A = 
            x1       x2       x3       x4       x5       x6       x7       x8
   x1        0        0        0        0        1        0        0        0
   x2        0        0        0        0        0        1        0        0
   x3        0        0        0        0        0        0        1        0
   x4        0        0        0        0        0        0        0        1
   x5     -520      160        0      160      5.2     -1.6        0     -1.6
   x6      160     -420      140     -120     -1.6      4.2     -1.4      1.2
   x7        0    58.33     -100    41.67        0  -0.5833        1  -0.4167
   x8    66.67      -50    41.67   -158.3  -0.6667      0.5  -0.4167    1.583
 
  B = 
           u1      u2      u3      u4
   x1       0       0       0       0
   x2       0       0       0       0
   x3       0       0       0       0
   x4       0       0       0       0
   x5      20       0       0       0
   x6       0       0  -4.167       0
   x7       0       0       0       0
   x8       0       0       0       0
 
  C = 
       x1  x2  x3  x4  x5  x6  x7  x8
   y1   1   0   0   0   0   0   0   0
   y2   0   1   0   0   0   0   0   0
   y3   0   0   1   0   0   0   0   0
   y4   0   0   0   1   0   0   0   0
   y5   0   0   0   0   1   0   0   0
   y6   0   0   0   0   0   1   0   0
   y7   0   0   0   0   0   0   1   0
   y8   0   0   0   0   0   0   0   1
 
  D = 
       u1  u2  u3  u4
   y1   0   0   0   0
   y2   0   0   0   0
   y3   0   0   0   0
   y4   0   0   0   0
   y5   0   0   0   0
   y6   0   0   0   0
   y7   0   0   0   0
   y8   0   0   0   0
 
Continuous-time state-space model.

x0 = [0 0 0 0 0 0 0 0];

Tf = 10;
Ts = 0.1;
[u1,t] = gensig("sine",20,Tf,Ts);
[u2] = zeros(length(u1),1);
[u3,~]  = gensig("sine",12,Tf,Ts);
[u4]  = zeros(length(u1),1);
u = [u1 u2 u3 u4 u4 u4 u4 u4]';

size(A)

ans = 1×2

8 8

size(B)

ans = 1×2

8 4

size(C)

ans = 1×2

8 8

size(D)

ans = 1×2

8 4

size(time)

ans = 1×2

1 101

size(u)

ans = 1×2

8 101

y = lsim(dyn,u,x0,time);

Error using DynamicSystem/lsim (line 84)
When simulating the response to a specific input signal, the input data U must be a matrix with as many rows as samples in the time vector T, and as many columns as input channels.

plot(y(:,4))

Answer 1

[Paul]

The size of u is 8 x 101. But as the error message says, it must have the same number of rows as t has elements (101), and it must have the same number of columns as the system has inputs (4). So u should be 101 x 4. Perhaps it should be

u = [u1 u2 u3 u4]

[Raditya Danu]

Hi Paul,

Thank you for your answer. I tried it, however the problem still persists with the same error message.

[Paul]

The time and x0 inputs to lsim need to be reversed, as below. Note the warning recommending to use a smaller time step, but the code runs.

%specify the timestep
dt = 0.1;
tmax = 10;
t = [0:dt:tmax]';
time = t'; 
%assemble the M matrix
m = [0.5 0.5 1.2 1.2];
M = diag(m);
%assemble the K matrix
k1 = 100; 
k2 = 80;
k3 = 70;
k4 = 50;
k5 = 80;
k6 = 60;
k11 = k1 + k2 + k5;
k12 = -k2;
k13 = 0;
k14 = -k5;
k22 = k2 + k3 + k6;
k23 = -k3;
k24 = k6;
k33 = k3+k4;
k34 = -k4;
k44 = k4 + k5 +k6;
k21 = k12;
k31 = k13;
k32 = k23;
k41 = k14;
k42 = k24;
k43 = k34;
K = [k11 k12 k13 k14; ...
     k21 k22 k23 k24; ...
     k31 k32 k33 k34; ...
     k41 k42 k43 k44];
%assemble the F matrix
b2 = [10 0 0 0; 0 0 -5 0; 0 0 0 0; 0 0 0 0]';
%assemble the C matrix
C = 0.01*K;
%assemble the state space model
MK = M\K;
MC = -M\C;
I = eye(length(M));
zer = zeros(length(M));
A = [zer I; -MK -MC];
B = [zeros(4) M\b2]';
C = [eye(length(A))];
D = zeros(8,4);
dyn = ss(A, B, C, D);
x0 = [0 0 0 0 0 0 0 0];
Tf = 10;
Ts = 0.1;
[u1,t] = gensig("sine",20,Tf,Ts);
[u2] = zeros(length(u1),1);
[u3,~]  = gensig("sine",12,Tf,Ts);
[u4]  = zeros(length(u1),1);

u = [u1 u2 u3 u4];
y = lsim(dyn,u,time,x0);  % this line was incorrect

Warning: The input signal is undersampled. Use a sampling period smaller than 3.1e-02.

plot(time,y(:,4))