control.impulse_response

control.impulse_response(sysdata, timepts=None, input_indices=None, output_indices=None, timepts_num=None, transpose=False, return_states=False, squeeze=None, **kwargs)

Compute the impulse response for a linear system.

If the system has multiple inputs and/or multiple outputs, the impulse response is computed for each input/output pair, with all other inputs set to zero. Optionally, a single input and/or single output can be selected, in which case all other inputs are set to 0 and all other outputs are ignored.

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

Parameters

sysdataI/O system or list of I/O systems

I/O system(s) for which impulse response is computed.

timepts (or T)array_like or float, optional

Time vector, or simulation time duration if a scalar (time vector is auto-computed if not given; see step_response for more detail).

input_indices (or input)int, optional

Only compute the impulse response for the listed input. If not specified, the impulse responses for each independent input are computed.

output_indices (or output)int, optional

Only report the step response for the listed output. If not specified, all outputs are reported.

timepts_num (or T_num)int, optional

Number of time steps to use in simulation if T is not provided as an array (auto-computed if not given); ignored if the system is discrete time.

transposebool, optional

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

return_states (or return_x)bool, optional

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

squeezebool, 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

resultsTimeResponseData or TimeResponseList

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

See also

forced_response, initial_response, step_response

Notes

This function uses the forced_response function to compute the time response. For continuous-time systems, the initial condition is altered to account for the initial impulse. For discrete-time systems, the impulse is sized so that it has unit area. The impulse response for nonlinear systems is not implemented.

Examples

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