:py:mod:`dysys.transferfunctionsymbolic`
========================================

.. py:module:: dysys.transferfunctionsymbolic


Module Contents
---------------

Classes
~~~~~~~

.. autoapisummary::

   dysys.transferfunctionsymbolic.TransferFunctionSymbolic



Functions
~~~~~~~~~

.. autoapisummary::

   dysys.transferfunctionsymbolic.tfs



Attributes
~~~~~~~~~~

.. autoapisummary::

   dysys.transferfunctionsymbolic.s


.. py:class:: TransferFunctionSymbolic(H, s=None)


   Represents a SISO continuous LTI transfer function model in symbolic form

   .. py:method:: __call__(s)

      Evaluate the transfer function at a complex frequency s


   .. py:method:: __str__()

      Return str(self).


   .. py:method:: __factor_p(p, poles=True)


   .. py:method:: factor()

      Returns an overall gain and a list of standard-form terms


   .. py:method:: __num_den_lists(params = {})

      Returns num and den coefficients as lists


   .. py:method:: to_control(params = {})

      Returns an equivalent Control Systems package control.TransferFunction object


   .. py:method:: poles()

      Returns a dict of the symbolic poles as keys and multiplicity as values


   .. py:method:: zeros()

      Returns a dict of the symbolic zeros as keys and multiplicity as values


   .. py:method:: dc_gain()

      Returns the DC gain of the transfer function


   .. py:method:: frequency_response_function(w = sp.symbols('w', real=True))

      Returns the symbolic frequency response function (FRF)

      Evaluates H(jw). Assumes the region of convergence for the corresponding
      Fourier transform is congruent with that of the Laplace transform.

      :param w: The frequency symbol


   .. py:method:: forced_response(t, u = None, U = None, laplace = False)

      Returns the forced response of a SISO system

      The inverse Laplace transform is used to compute the forced response.
      Exactly one of arguments u or U may be provided.

      :param t: The time symbol
      :param u: The input as a time-dependent expression
      :param U: The input as a Laplace transform (must use
                symbolic sp.symbols("s") if using this option)
      :param laplace: If True, returns Laplace transform Y(s) of the output



.. py:function:: tfs(H, s=None)

   Create a TransferFunctionSymbolic object


.. py:data:: s