simulate dynamic response to a state space differential equation

Hi guys!

I am a beginner with MATLAB, forgive me for any stupid expression and this terrible formatting. I am trying to get a dynamic response for a state space differential equation in a matrix form: Xdot=A*x+B*u (A is 4by4, B is 4by2)

The input u is [1;0] between interval [0,1], and is 0 everywhere else. I have used a stupid way to construct my u, but I guess it should work. Here's the code I have:

A=[-2.6 0.25 -38 0; -0.075 -0.27 4.4 0; 0.078 -0.99 -0.23 0.052; 1.0 0.078 0 0];

B=[17 7; 0.82 -3.2; 0 0.046; 0 0];

w1=zeros(1,10000);

w3=zeros(1,10000);

w2=ones(1,10001);

t=-1:0.0001:2.000;

u1=[w1 w2 w3];

u2=zeros(1,30001);

u=[u1; u2];

lsim(sys1,u,t)

However, the plot seems to be u(1:) of t only, and I would like to get a response for x1, x2, x3, and x4.

I then tried the following code:

A=[-2.6 0.25 -38 0; -0.075 -0.27 4.4 0; 0.078 -0.99 -0.23 0.052; 1.0 0.078 0 0];

B=[17 7; 0.82 -3.2; 0 0.046; 0 0];

w1=zeros(1,10000);

w3=zeros(1,10000);

w2=ones(1,10001);

t=-1:0.0001:2.0001;

u1=[w1 w2 w3];

u2=zeros(1,30001);

u=[u1; u2];

x=zeros(4,30001);

for k=1:1:30001

    x(:,k+1)=A*x(:,k)+B*u(:,k);

end

Then I have checked the values for x(:,10002) to x(:,11000) column by column, and found out that the values got too large that eventually MATLAB gave me NaN.

Is any of my approaches might work? Or either of them is correct...? Also, is there any more efficient way to solve this? Thanks!

[Jerry Zhang]

I think I understand what I want to ask....

Its a stupid question. I should set C=[1 0 0 1; 0 1 0 0; 0 0 1 0; 0 0 0 1] to output all 4 variables I want. Method one is obviously more efficient.

@coffee Murun Thanks for your help!

Answer 1

[bio lim]

How about defining your input like this.

u = [t <= 1 & t >= 0; zeros(size(t));];

I also have few comments.

• I don't understand why you would start your system with a 'negative' time. Why not simply start with 0?
• Your input, u, as you defined is u = [w1, w2, w3]. However, the size of your w2 is different than the other two, which doesn't make much sense to me.

[Jerry Zhang]

Thanks for that! u is a matrix of 2 rows. I think u should have 30001 columns, its [0;0] for col 1 to col 10000, which stands for time 0s to 0.9999s; and its [1;0] for time 1s to 2s, thus has 10001 elements.

[bio lim]

I see. Anyway, your entire expression could be simplified into a single one as shown above.

[Jerry Zhang]

I got what I want! Thanks for your help!