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• physics.control

  • Added support for using Feedback as a TransferFunction. (#26293 by @abhiphile)

  • Added methods to get the numerator and denominator of TransferFunction. (#26293 by @abhiphile)

  • Added function to get the expression for the Feedback object. (#26293 by @abhiphile)

This will be added to https://github.com/sympy/sympy/wiki/Release-Notes-for-1.13.

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#### References to other Issues or PRs
Fixes Discussion in https://github.com/sympy/sympy/pull/26228
Fixes Issue https://github.com/sympy/sympy/issues/26161

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#### Brief description of what is fixed or changed
1. Feedback in Control Systems will now be used with TransferFunctions easily without affecting the system's overall structure.
2. Added method to find out the numerator and denominator of TransferFunction.
3. Added a method to convert the Feedback system to expression.

#### Other comments


#### Release Notes

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<!-- BEGIN RELEASE NOTES -->
* physics.control
  * Added support for using Feedback as a TransferFunction.
  * Added methods to get the numerator and denominator of TransferFunction.
  * Added function to get the expression for the Feedback object.
<!-- END RELEASE NOTES -->

Update

The release notes on the wiki have been updated.

@moorepants, Sir, can you please review this PR? I've made sure that everything is correct here.
This can possibly close the issue.

It would be good to have a test showing that you can combine with another transfer function (like putting two a feedback in series with a tf) and show that is works in regular assembly operations.

It would be good to have a test showing that you can combine with another transfer function (like putting two a feedback in series with a tf) and show that is works in regular assembly operations.

Sir, Are you talking about this?
tf3 = TransferFunction(tf1 * fd1, tf2, s)

Sir, Are you talking about this?

I was thinking just Series(Feedback(tf1, tf2), tf3) then check the num and den are correct and maybe that doit works.

I was thinking just Series(Feedback(tf1, tf2), tf3)

I can see that num and den property are not available in Series so do I've to implement them inside of Series?
I think that will be lots of work and out of scope for this PR and reviewing everything will be difficult, maybe I can work on it by opening a new PR.

I've just used doit() and written the tests.

I can see that num and den property are not available in Series so do I've to implement them inside of Series?

If making Feedback work as a transfer function means that other things have to be fixed too, then we need to do that. This PR doesn't address the primary issue if you can't use Feedback as a transfer function.

My original example does seem to work with this PR:

In [1]: %paste
import sympy as sm
import sympy.physics.control as cn

Ib, Is, c, m, h, g, l2, l1 = sm.symbols('I_b, I_s, c, m, h, g, l2, l1',
                                        real=True, nonnegative=True)
KD, KP, v = sm.symbols('K_D, K_P, v', real=True)
s = sm.symbols('s')

tau1_sq = (Ib + m*h**2)/m/g/h
tau2 = l2/v
tau3 = v/(l1 + l2)
K = v**2/g/(l1 + l2)

Gtheta = cn.TransferFunction(-K*(tau2*s + 1), tau1_sq*s**2 - 1, s)
Gdelta = cn.TransferFunction(1, Is*s**2 + c*s, s)
Gpsi = cn.TransferFunction(1, tau3*s, s)
Dcont = cn.TransferFunction(KD*s, 1, s)
PIcont = cn.TransferFunction(KP, s, s)
Gunity = cn.TransferFunction(1, 1, s)

Ginner = cn.Feedback(Dcont*Gdelta, Gtheta)

Gouter = cn.Feedback(PIcont*Ginner*Gpsi, Gunity)

## -- End pasted text --

In [2]: Gouter
Out[2]: Feedback(Series(TransferFunction(K_P, s, s), Feedback(Series(TransferFunction(K_D*s, 1, s), TransferFunction(1, I_s*s**2 + c*s, s)), TransferFunction(-v**2*(l2*s/v + 1)/(g*(l1 + l2)), -1 + s**2*(I_b + h**2*m)/(g*h*m), s), -1), TransferFunction(1, s*v/(l1 + l2), s)), TransferFunction(1, 1, s), -1)

In [3]: Gouter.num
Out[3]: Series(TransferFunction(K_P, s, s), Feedback(Series(TransferFunction(K_D*s, 1, s), TransferFunction(1, I_s*s**2 + c*s, s)), TransferFunction(-v**2*(l2*s/v + 1)/(g*(l1 + l2)), -1 + s**2*(I_b + h**2*m)/(g*h*m), s), -1), TransferFunction(1, s*v/(l1 + l2), s))

In [4]: Gouter.doit()
Out[4]: TransferFunction(K_D*K_P*g*s**3*v**2*(l1 + l2)*(I_s*s**2 + c*s)**2*(-g*h*m + s**2*(I_b + h**2*m))*(-K_D*g*h*m*s*v**2*(l2*s + v) + g*v*(l1 + l2)*(I_s*s**2 + c*s)*(-g*h*m + s**2*(I_b + h**2*m))), s**2*v*(I_s*s**2 + c*s)*(-K_D*g*h*m*s*v**2*(l2*s + v) + g*v*(l1 + l2)*(I_s*s**2 + c*s)*(-g*h*m + s**2*(I_b + h**2*m)))*(K_D*K_P*g*s*v*(l1 + l2)**2*(I_s*s**2 + c*s)*(-g*h*m + s**2*(I_b + h**2*m)) + s**2*v*(I_s*s**2 + c*s)*(-K_D*g*h*m*s*v**2*(l2*s + v) + g*v*(l1 + l2)*(I_s*s**2 + c*s)*(-g*h*m + s**2*(I_b + h**2*m))))/(l1 + l2), s)

In [5]: Gouter.doit().to_expr()
Out[5]: (K_D*K_P*g*s**3*v**2*(l1 + l2)*(I_s*s**2 + c*s)**2*(-g*h*m + s**2*(I_b + h**2*m))*(-K_D*g*h*m*s*v**2*(l2*s + v) + g*v*(l1 + l2)*(I_s*s**2 + c*s)*(-g*h*m + s**2*(I_b + h**2*m))))/((s**2*v*(I_s*s**2 + c*s)*(-K_D*g*h*m*s*v**2*(l2*s + v) + g*v*(l1 + l2)*(I_s*s**2 + c*s)*(-g*h*m + s**2*(I_b + h**2*m)))*(K_D*K_P*g*s*v*(l1 + l2)**2*(I_s*s**2 + c*s)*(-g*h*m + s**2*(I_b + h**2*m)) + s**2*v*(I_s*s**2 + c*s)*(-K_D*g*h*m*s*v**2*(l2*s + v) + g*v*(l1 + l2)*(I_s*s**2 + c*s)*(-g*h*m + s**2*(I_b + h**2*m))))/(l1 + l2)))

In [6]: Gouter.doit().to_expr().simplify()
Out[6]: K_D*K_P*(l1 + l2)**2*(g*h*m - s**2*(I_b + h**2*m))/(K_D*K_P*(l1 + l2)**2*(g*h*m - s**2*(I_b + h**2*m)) + s**2*v*(K_D*h*m*v*(l2*s + v) - (l1 + l2)*(I_s*s + c)*(-g*h*m + s**2*(I_b + h**2*m))))

which is nice. It is also a useful test case for the unit tests.

So I guess we can merge this without making Series and Parallel act like a transfer function also. It can be solved separately.

tau1_sq = (Ib + m*h2)/m/g/h
tau2 = l2/v
tau3 = v/(l1 + l2)
K = v2/g/(l1 + l2)

Thank you for your time. I will also write a unit test for this.
But I've already included a similar test here https://github.com/sympy/sympy/pull/26293/files#diff-f148f25c5f8d301ec215df3efcee817b486b0a760284872c93395c19d2a08e29R1036
If it is still needed, I'll include this in the unit test

LGTM, nice work!

Failing test here doesn't seem to be related. Thanks for your contributions, merging !

Failing test here doesn't seem to be unrelated.

That particular pypy test just fails randomly since some recent pypy release (a few months ago?). I can't reproduce the failure outside of CI so I haven't opened a PyPy issue about it. The problem is something to do with pytest's assertion rewriting which presumably messes with PyPy's AST.

pypy/pypy#3959
pytest-dev/pytest#11168

Sorry, mentioned "doesn't" and "unrelated" together by mistake. Did not mean to cause a confusion 😄