This PR fixes a problem where xferfcn._common_den was not properly padding the numerator coefficients and this was causing an apparent bug in tf2ss for MIMO systems (see issue #240). The issue occurred in the following code in xferfcn.py:

m = npmax - len(numpoly)
if m < 0:
    num[i,j,::-1] = numpoly
else:
    num[i,j,:m:-1] = numpoly

where npmax is the maximum number of poles across all inputs.

What this code is doing is putting the coefficients for numpoly at the right end of the array num[i,j], which has length npmax+1. However, what td04ad looks at is only the portion of the numerator array that is the order of the denominator array for that particular input (not the max across all inputs). So this code was shifting things too far to the right in the case where you had an input that had less than the maximum number of poles (discovered in issue #240, as part of a simulation bug).

The new code is

num[i, j, np+1-len(numpoly):np+1] = numpoly[::-1]

where np is the number of poles for this input (and hence np+1 is the portion of the input array that td04ad will use.

In addition to fixing this bug, two unit tests were added:

• control/tests/convert_test.py has a test to make sure that _common_den does the right thing.
• control/tests/timeresp_test.py has a test that corresponds to the original bug identified in issue Erroneous time-domain sim (because of ss2tf)  #240.

@repagh should have a look at this since it is in a section of code that he wrote.