control.initial_response

control.initial_response(sysdata, T=None, X0=0, output=None, T_num=None, params=None, transpose=False, return_x=False, squeeze=None)[source]

Compute the initial condition response for a linear system.

If the system has multiple outputs (MIMO), optionally, one output may be selected. If no selection is made for the output, all outputs are given.

For information on the shape of parameters T, X0 and return values T, yout, see Time series data.

Parameters

  • sysdata (I/O system or list of I/O systems) – I/O system(s) for which initial response is computed.

  • sys (StateSpace or TransferFunction) – LTI system to simulate

  • T (array_like or float, optional) – Time vector, or simulation time duration if a number (time vector is autocomputed if not given; see step_response() for more detail)

  • X0 (array_like or float, optional) – Initial condition (default = 0). Numbers are converted to constant arrays with the correct shape.

  • output (int) – Index of the output that will be used in this simulation. Set to None to not trim outputs.

  • T_num (int, optional) – Number of time steps to use in simulation if T is not provided as an array (autocomputed if not given); ignored if sys is discrete-time.

  • params (dict, optional) – If system is a nonlinear I/O system, set parameter values.

  • transpose (bool, optional) – If True, transpose all input and output arrays (for backward compatibility with MATLAB and scipy.signal.lsim()). Default value is False.

  • return_x (bool, optional) – If True, return the state vector when assigning to a tuple (default = False). See forced_response() for more details.

  • squeeze (bool, optional) – By default, if a system is single-input, single-output (SISO) then the output response is returned as a 1D array (indexed by time). If squeeze=True, remove single-dimensional entries from the shape of the output even if the system is not SISO. If squeeze=False, keep the output as a 2D array (indexed by the output number and time) even if the system is SISO. The default value can be set using config.defaults[‘control.squeeze_time_response’].

Returns

results – Time response represented as a TimeResponseData object or list of TimeResponseData objects. See forced_response() for additional information.

Return type

TimeResponseData or TimeResponseList

See also

forced_response, impulse_response, step_response

Notes

This function uses the forced_response function with the input set to zero.

Examples

>>> G = ct.rss(4)
>>> T, yout = ct.initial_response(G)