SciPy step response plot seems to break for some values

Question

I'm using SciPy instead of MATLAB in a control systems class to plot the step responses of LTI systems. It's worked great so far, but I've run into an issue with a very specific system. With this code: ``` from numpy import min from scipy import linspace from scipy.signal import lti, step from matplotlib import pyplot as p # Create an LTI transfer function from coefficients tf = lti([64], [1, 16, 64]) # Step response (redo it to get better resolution) t, s = step(tf) t, s = step(tf, T = linspace(min(t), t[-1], 200)) # Plotting stuff p.plot(t, s) p.xlabel('Time / s') p.ylabel('Displacement / m') p.show() ``` The code as-is displays a flat line. If I modify the final coefficient of the denominator to `64.00000001` (i.e., `tf = lti([64], [1, 16, 64.0000001])`) then it works as it should, showing an underdamped step response. Setting the coefficient to `63.9999999` also works. Changing all the coefficients to have explicit decimal places (i.e., `tf = lti([64.0], [1.0, 16.0, 64.0])`) doesn…

Accepted Answer

This is a limitation of the implementation of the `step` function. It uses a matrix exponential to find the step response, and it doesn't handle repeated poles well. (Your system has a repeated pole at -8.)

Instead of using `step`, you can use the function scipy.signal.step2

```
In [253]: from scipy.signal import lti, step2

In [254]: sys = lti([64], [1, 16, 64])

In [255]: t, y = step2(sys)

In [256]: plot(t, y)
Out[256]: [<matplotlib.lines.Line2D at 0x5ec6b90>]
```

SciPy step response plot seems to break for some values

Solution

Problem