Different integration time step in Matlab and Simulink with ode45

Hi,

I am carrying out a comparison between Matlab and Simulink in order to learn more about how each works. I simulate a simple second order system using the following code in Matlab:

rhsfun = @(t,x) function_name(t,x);

[t,x] = ode45(rhsfun,[0 sim_time],x0);

I then simulate an equivalent system in Simulink, using the following call from the Matlab workspace:

sim('Model_name.mdl',sim_time);

What puzzles me is that after the simulation, the time vectors are very different. The vector from the Matlab simulation is approximately 6 times longer than that from the Simulink simulation, so obviously the integration time step in Simulink is greater.

I use the default options settings for the simulations. I am curious and would like to know the cause of this difference. Can someone enlighten me? Is there a way to have the solver use the same time steps in both cases?

Thank you,

Barry.

[Carlotta Mummolo]

Hi Barry, the problem may be in the Refine option in the ode45 in Matlab, which by default is 4, while in Simulink is 1.

Answer 1

[Kaustubha Govind]

In Simulink, ode45 is a variable-step solver, so depending on the dynamics of your system, it will take a time-step just small enough to achieve a certain level of tolerance. So your for your system, it appears that the Simulink solver decided that that many time-steps were enough to preserve the desired accuracy of the outputs. See Choosing a Solver for more information. To force the Simulink solver to take specified time-steps, please refer to my answer here: http://www.mathworks.com/matlabcentral/answers/11340-set-simulink-time-step

[Barry]

Thank you for the reply. If I am not mistaken, ode45 is a variable step solver regardless of whether it is implemented in Matlab or in Simulink. I would like to know from where the difference arises - perhaps from one of the many default settings within the continuous time integrator block in Simulink?

Answer 2

[Carlotta Mummolo]

Hi Barry, the problem may be in the Refine option in the ode45 in Matlab, which by default is 4, while in Simulink is 1.