Plotting State Space Model with Disturbance

Hi! I am trying to simulate a very simple dynamical system with disturbance matrix u (Dirac function).

mx''+bx'+kx=u(t)

I want to drow the displacement(position) and velocity of the system. This is my code, which seems to be not completely correct:

m=5;

c=20;

k=100;

% solves m x''+ c x' + k x = f(t)

t=0:0.1:10

A=[0 1; -(-k/m) (-c/m)];

B=[0 ; (1/m)];

C=[1 0];

D=0;

u=ones(2,1)*(heaviside(t-2)-heaviside(t-2.5));

sys1=(ss(A,B,C,D);

step (sys1)

Any suggestion for completing the code?

Thanks Sam

Answer 1

[Sebastian Castro]

I see...

In your A matrix, your spring term is -(-k/m) , and that double negative makes it positive and therefore an unstable system. Try removing one of those minus signs and you should be good.

Also, couple other things:

1. You have an extra parenthesis when you define sys1
2. If you want to output both position and velocity, then your C matrix should be [1 0;0 1] , or eye(2)

- Sebastian

Answer 2

[Sam]

Dear Sebastian,

thank you for the answer. I corrected both of them, and it works now, but the excitation (U) seems not to be involved in the calculation.

U term can be a dirac impulse (as you see in my code), or a periodic function like sin. Actually I want to study the system response in underdamped, overdamped and critical situation.

• b2<4mk - underdamping;
• b2>4mk - overdamping;
• b2=4mk - critical damping.

[Sebastian Castro]

Ah, yes, didn't even notice that part! The step function will always input a step response. What you want to look into is the lsim function, where you can specify your own input vector.

http://www.mathworks.com/help/control/ref/lsim.html

- Sebastian

[Sam]

How could I combine ss and lsim? I receive two errors. first that u is not a matrix and another for the lsim function.

u is multiplied with one(2,1) so should actually be recognized as a matrix.

Sam

[Sebastian Castro]

Your system only has 1 input (B matrix has 1 column), while you defined "u" as having 2 rows (it's a 2x101 matrix). It worked for me with these changes:

u = heaviside(t-2)-heaviside(t-2.5);
lsim(sys1,u,t);

- Sebastian

[Sam]

solved. Thanks again.

Answer 3

[Marco Boutrus]

Hello! a very old page! but i hope u guys are still active!

i have the same formula that i need to plot (both the x and the v graphs). however i cant seem to change the stepsize, if i add

dt = 0.25; % Time step [s]

t = 0:dt:10; % Time range [s]

do i have to rewrite the whole ss form or is there a better way?

Marco