how to use ss and lsim for 1 dof differential equation

i want to solve 1 dof differential equation by using ss and lsim for just as an example.

probrem is the result calculated by ss&lsim and the result calcuated by matmatically analitically caliculation are different.

do you know why this things happen? if my code has some mistake, I want to know where is prob.

Best,

hiroki

---code---

M=4;

C=0;

K=2500;

A=[0 1; -K/M -C/M];

B=[0;1/M];

C=[1 0];

D=0;

sys=ss(A,B,C,D)

dt=0.001;

t=dt*[1:100];

w=100;

f=2*cos(w*t);

u=f;

x=2/(K-M*w^2)*cos(w*t);

y = lsim(sys,u,t);

plot(t,u)

hold on

yyaxis right

plot(t,y)

hold on

yyaxis right

plot(t,x);

legend('u:input','y:sys solution','x: analitical solution')

Answer 1

[Paul]

That lsim command calculates y using default initial conditions x(0) = xdot(0) = 0, but the analytical solution clearly doesn't satisfy those initial conditions. It looks like that solution satisfies the initial conditions x(0) = 2/(K-M*w^2), xdot(0) = 0. Try this:

y1 = lsim(sys,u,t,[2/(K-M*w^2) 0]);

and compare to x and y.

Alos, why not define t starting from 0?

t = dt*[0:100]

[Hiroki]

thank you so much! it works! your answer is perfect. I made two mistakes. first is initial condition of x(0) and second is starting definition of t!! thank!