add summing junction + implicit signal interconnection

[murrayrm]

This PR addresses the enhancement describe in issue #516 where signals with the same name are automatically interconnected by the interconnect function. It also defines a new function summation_block that addresses the request in issue #493. Together, these capabilities allow the following code to work for setting up a simple feedback system:

P = ct.ss2io(
    ct.rss(2, 1, 1, strictly_proper=True),
    inputs='u', outputs='y', name='P')
kp = ct.tf(random.uniform(1, 10), [1])
ki = ct.tf(random.uniform(1, 10), [1, 0])
C = ct.tf2io(kp + ki, inputs='e', outputs='u', name='C')
sumblk = ct.summation_block(inputs=['r', '-y'], output='e', name="sum")
Tio_sum = ct.interconnect(
    (C, P, sumblk), inplist=['r'], outlist=['y'])

Other minor changes:

• Added code to allow the iosys.feedback function to accept a float_like for the feedback system (so that feedback(P * C, 1) now works.

[coveralls]

Coverage increased (+0.1%) to 87.754% when pulling 791f7a6 on murrayrm:sumblk_implicit_interconnect into 1502d38 on python-control:master.

[sawyerbfuller]

Very cool!

I particularly like that it appears possible with this to leave out the ‘name’ keyword for the constitutive systems for simple interconnections like this. Am I correct in that? Nice to have that option because thst keyword is somewhat redundant and prone to errors when code gets modified.

If you give the sumblock more input names (eg 3 instead of 2), does it sum those three signals?

[murrayrm]

it appears possible with this to leave out the ‘name’ keyword for the constitutive systems for simple interconnections like this. Am I correct in that?

Correct. The following works just fine (from #516):

P = ct.tf2io(ct.tf(1, [1, 0]), inputs='u', outputs='y')
C = ct.tf2io(ct.tf(10, [1, 1]), inputs='e', outputs='u')
sumblk = ct.summation_block(inputs=['r', '-y'], output='e')
T = ct.interconnect((P, C, sumblk), inplist='r', outlist='y')

(P, C, and sumblk all have names automatically assigned, but not needed here).

If you give the sumblock more input names (eg 3 instead of 2), does it sum those three signals?

Yup. Any number of inputs can be summed together. The summation_block function does not require named signals, so you can also do ct.summation_block(7) if you want a LinearIOSystem that has 7 inputs and 1 output (sum of the inputs), for example).

Some possible tweaks:

• I think I may use the term summing_junction (instead of summation_block) to line up with the term we use in FBS.
• I will add a bit more documentation, both in docstrings and in the manual
• I want to switch all examples using InterconnectedSystem to use interconnect since using the class constructor since the function provides a slightly higher level interface (eg, the class constructor still requires the explicit signal name).

[sawyerbfuller]

Awesome.

New name for summer sounds better.

Hoping this will make creating simulink-like interconnected system simulations much easier. I will let you know how it goes once it’s been merged in.

[bnavigator]

Very nice!

(Now we will have users demanding a graphical editor next 😁. Implemented as jupyter notebook widget or the like.)

[sawyerbfuller]

I think the first step in that direction might be to add an option in interconnect to draw a block diagram. This could be done using matplotlibs pretty good capabilities for this.

…

-- Sawyer Fuller Assistant Professor of Mechanical Engineering Adjunct, Paul G Allen School of Computer Science University of Washington http://faculty.washington.edu/~minster/ (Typed with my thumbs)

[sawyerbfuller]

Nice that this summation effect is stated explicitly.