[Help-gsl] ODE for state space system

[toso]

Hi all, 

I'm writing a code to compute the time response of a mechanical system 
written in a state space form 

dot(x) = A x + B u
y    = C x + D u 

I use for the first system of equation the gsl rk4 ode solver and an then I 
evaluate the system outputs (y). The problem arise when I compare the 
results with matlab (same system, same solver). 

I have tried two different ways t calculate y. The pseudo code that I use 
is: 

/* evaluate state evolution and then calculate outputs */ 

while( t < t_end )
{
  u = new_inputs();
  gsl_odeiv_step_apply( .. );
  update_state_derivatives( .. );
  y = C x + D u;
  t += dt;
} 

/* calculate outputs and then evaluate state evolution*/
while( t < t_end )
{
  u = new_inputs();
  y = C x + D u;
  gsl_odeiv_step_apply( .. );
  update_state_derivatives( .. );
  t += dt;
} 

I thought the second way was corrected but it gives worse results with 
respect to the first one. 

The example that I've tried has 4 states with natural frequencies 4 and 50 
Hz, the input is a chirp signal between 0.1 and 100 Hz, and if I sample it 
at 512 Hz the error is more than 40% while using 2048 Hz decrease to 4% but 
I think it's still a lot. 

Do anyone has any idea? 

Alessandro Toso