Step Response and step_info accuracy issue

Hi, I found an accuracy issue related to control.step_response and control.step_info. To be specific, the issue is in _default_response_times() function. I have two system transfer function sys1 and sys2.They both have exactly the same frequency response.
sys1: num1 = [1.067e+05, 5.791e+04], den1 = [10.67, 1.067e+05, 5.791e+04] OR k = 10000, zeros = [-0.5426], poles = [-1e+04, -0.5426 ]

sys2: num2 = [1.881e+06], den2 = [188.1, 1.881e+06] OR k = 10000, zeros = [], poles = [-1e+04, ]

As you notice, sys1 has extra pole and zero where both have the same value.

The issue

When I plot the step responses for both systems, the plots are not matched. Also when I used step_info() to get the characteristics of the systems, I got a different results.

The code:

here is the code

num1 = [1.067e+05, 5.791e+04]
den1 = [10.67, 1.067e+05, 5.791e+04]
num2 = [1.881e+06]
den2 = [188.1, 1.881e+06]
sys_1 = control.TransferFunction(num1, den1)
sys_2 = control.TransferFunction(num2, den2)
t1, y1 = control.step_response(sys_1)
t2, y2 = control.step_response(sys_2)
print(control.step_info(sys_1))
print(control.step_info(sys_2))
plt.plot(t1, y1, t2, y2)
plt.grid()
plt.show()

Test on Matlab;

I tested the two systems in Matlab. The step() function gives the same step response plot for both systems, and stepinfo() results exactly the same values for both systems.

[sawyerbfuller]

PR #454 , which incorporates @ilayn’s code seems to fix this (both step responses are perfectly overlaid):

code output:

{'RiseTime': 0.0002118493270188449, 'SettlingTime': 0.0003500119315963524, 'SettlingMin': 0.8953357369737194, 'SettlingMax': 0.9895824151834175, 'Overshoot': 0.0, 'Undershoot': 0.0, 'Peak': 0.9895824151834175, 'PeakTime': 0.0004559365951057749, 'SteadyStateValue': 0.9895824151834175}
{'RiseTime': 0.00021183782855545226, 'SettlingTime': 0.000349992934135095, 'SettlingMin': 0.8952871451949131, 'SettlingMax': 0.9895287145194958, 'Overshoot': 0.0, 'Undershoot': 0.0, 'Peak': 0.9895287145194958, 'PeakTime': 0.0004559118484128211, 'SteadyStateValue': 0.9895287145194958}

[ilayn]

I’ve tested for the given systems and indeed the responses are the same. The only remaining issue is when a system has Jordan blocks of significant poles but I think that is an open problem in the literature too. So with some reservation I would say it is robust but not fail-proof for every system.

Since we don’t have the commercial ODE solvers I think that would be all we can do for now via utilizing only pole-zero information.