[GSoC] Added PIDController class to control module.

[abhiphile]

PIDController Class Added to Control Module

• Introduced a new PIDController class in the control module.
  • The PIDController class allows for the creation of PID controllers with the following parameters:
    • kp : Proportional gain (defaults to Symbol('kp') if not provided).
    • ki : Integral gain (defaults to Symbol('ki') if not provided).
    • kd : Derivative gain (defaults to Symbol('kd') if not provided).
    • tf : Derivative filter time constant (defaults to 0 if not provided).
    • var : The complex frequency variable (defaults to s if not provided).

References to other Issues or PRs

Fixes: #26163

Brief description of what is fixed or changed

Other comments

Release Notes

• physics.control
  • Introduced a PIDController class in the control module.

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• physics.control
  • Introduced a PIDController class in the control module. (#26781 by @abhiphile)

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<!-- Your title above should be a short description of what
was changed. Do not include the issue number in the title. -->

**PIDController Class Added to Control Module**
- Introduced a new `PIDController` class in the control module.
   - The `PIDController` class allows for the creation of PID controllers with the following parameters:
        - `kp` : Proportional gain (defaults to `Symbol('kp')` if not provided).
        - `ki` : Integral gain (defaults to `Symbol('ki')` if not provided).
        - `kd` : Derivative gain (defaults to `Symbol('kd')` if not provided).
        - `tf` : Derivative filter time constant (defaults to 0 if not provided).
        - `var` : The complex frequency variable (defaults to `s` if not provided).

#### References to other Issues or PRs
Fixes: https://github.com/sympy/sympy/issues/26163

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#### Brief description of what is fixed or changed


#### Other comments


#### Release Notes

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* physics.control
  * Introduced a `PIDController` class in the control module. 
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Update

The release notes on the wiki have been updated.

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[faze-geek]

Not sure if we should add the pid-controller image at doc/src/modules/physics/control/pid-controller.png, that is a place for our technical documentation .rst files.

[faze-geek]

You can also showcase solving a good symbolic question on the pid-controller at doc/src/guides/physics/control_problems.rst using sympy. Maybe after this PR is merged.

[moorepants]

Not sure if we should add the pid-controller image at doc/src/modules/physics/control/pid-controller.png, that is a place for our technical documentation .rst files.

Also, do not commit binary image files. This PR needs to be reopened without the png or it needs to be removed, squashed, and force pushed.

[moorepants]

Make sure that comments are address from the prior attempts:

#26287
#26285
#26175

[moorepants]

What happens when you have a symbolic transferfunction:

 >>> tf1 = TransferFunction(a, s + a, s)

?

[moorepants]

Also, for a symbolic power_gain=Symbol('b')?

[moorepants]

Please cite a reference for this "bandwidth" calculation. I'm not immediately familiar with this and what the "power gain" is.

Also, this should be in a separate PR, as it is not related to PID.

[abhiphile]

Not sure if we should add the pid-controller image at doc/src/modules/physics/control/pid-controller.png, that is a place for our technical documentation .rst files.

I've seen a similar thing in

sympy/sympy/physics/continuum_mechanics/beam.py

Line 61 in 958cc95

.. image:: allowed-sign-conventions.png

And the image file is located in doc/src/modules/physics/continumm_mechanics/allowed-sign-conventions.png. Using this as a reference I've put my image file in doc/src/modules/physics/control/pid-controller.png