Different time response using TF or IO system representation about python-control

[murrayrm]

I think the difference in the outputs is happening because forced_response and input_output_response use different methods to carry out the simulation:

• forced_response is intended for use with linear systems and does an exact calculation of the exponential response of the (time-discretized) input. (If you call forced_response with a nonlinear I/O system, it will call input_output_response.)
• input_output_response works on linear or nonlinear systems and calls the SciPy solve_ivp function.

The reason you may be getting different responses is because of the default settings for solve_ivp, which uses the RK45 integrator. Since you are simulating a high-Q system right at the resonant frequency, the default integrator with the default settings is not very accurate.

You can use the solve_ivp_method keyword to the input_output_response function to play around with different integrators (I tried using LSODA but that seemed to generate bigger differences) and the solve_ivp_kwargs keyword to pass different options to scipy.integrate.solve_ivp.

[murrayrm]

The following call to input_output_response gives results that are very close:

t, y_io = ct.input_output_response(
     io_cavity, t, np.sin(w0*t), solve_ivp_kwargs={'rtol': 1e-5})

(the default rol for RK45 is 1e-3).

[josujugo]

Thank you very much @murrayrm. I was sure that I was missing something.

Happy new year!