plotting an exponential will a matrix over time

Hi guys, i want to plot Y respect to time in 40 seconds. AF is a 4x4 matrix,

t= [0:2:40];
iden= eye(4);
AF= [ 0            1            0            0; 0.00010714      0.00275       10.049      0.98385;      0            0            0            1;   -7.6531e-05   -0.0019643     -0.17761     -0.70275];
meme=iden*AF;
figure(1)
Y = exp(AF.*meme);
plot(t,Y);

It results in vector must be in the same length, i do not know how to fix it.

[Image Analyst]

t= [0:2:40]
iden= eye(4)
AF= [ 0 1 0  0;
	0.00010714  0.00275  10.049  0.98385;
	0    0   0   1;
	-7.6531e-05   -0.0019643     -0.17761     -0.70275]
meme=iden*AF
figure(1)
Y = exp(AF.*meme)
plot(t,Y);

t =

Columns 1 through 20

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38

Column 21

40

iden =

1 0 0 0

0 1 0 0

0 0 1 0

0 0 0 1

AF =

0 1.0000 0 0

0.0001 0.0027 10.0490 0.9839

0 0 0 1.0000

-0.0001 -0.0020 -0.1776 -0.7027

meme =

0 1.0000 0 0

0.0001 0.0027 10.0490 0.9839

0 0 0 1.0000

-0.0001 -0.0020 -0.1776 -0.7027

Y =

1.0e+43 *

0.0000 0.0000 0.0000 0.0000

0.0000 0.0000 7.1796 0.0000

0.0000 0.0000 0.0000 0.0000

0.0000 0.0000 0.0000 0.0000

t is a 1-by-20 array, and Y is a 4-by-4 array, so exactly what do you want to plot?

[IP KWAN SO]

Sorry i have typing error,

i want to plot Y= exp(AF.*t) overtime in 40 seconds.

[Vineeth Nair]

The matrix dimensions must agree before multiplication can happen. Hence the above expression Y= exp(AF.*t) is incorrect.

To read more about elementwise multiplication please visty this link https://in.mathworks.com/help/matlab/ref/times.html

Answer 1

[David Wilson]

OK, your question is a bit vauge, and there are missing bits, i.e. the start point for y.

I'm assuming you are trying to solve a control problem. As mentioned above, you need to carefully look at dimensions, and I think you want the matrix exponental function, expm, (don't forget the "m").

I started my simulation below at some random point.

t= [0:2:40];  % time vector 

AF= [ 0            1            0            0; 
    0.00010714      0.00275       10.049      0.98385;      
    0            0            0            1;   
    -7.6531e-05   -0.0019643     -0.17761     -0.70275];

Y = randn(1,4); % start position (who knows??) 
for i=2:length(t)
   Y(i,:) = expm(AF*t(i))*Y(i-1,:)'; 
end 
plot(t,Y);

Of course if you have the control toolbox, there are many better ways to do this, e.g.

>> help lti/initial

or,

G = ss(AF, zeros(4,1), eye(4,4), 0)
Y0 = randn(1,4); % another random start poit 
[Y,t] = initial(G,Y0,t) % simulate the free response