control.input_output_response

control.input_output_response(sys, timepts=None, inputs=0.0, initial_state=0.0, params=None, ignore_errors=False, transpose=False, return_states=False, squeeze=None, solve_ivp_kwargs=None, evaluation_times='T', **kwargs)

Compute the output response of a system to a given input.

Simulate a dynamical system with a given input and return its output and state values.

Parameters

sysNonlinearIOSystem or list of NonlinearIOSystem

I/O system(s) for which input/output response is simulated.

timepts (or T)array_like

Time steps at which the input is defined; values must be evenly spaced.

inputs (or U)array_like, list, or number, optional

Input array giving input at each time in timepts (default = 0). If a list is specified, each element in the list will be treated as a portion of the input and broadcast (if necessary) to match the time vector.

initial_state (or X0)array_like, list, or number, optional

Initial condition (default = 0). If a list is given, each element in the list will be flattened and stacked into the initial condition. If a smaller number of elements are given that the number of states in the system, the initial condition will be padded with zeros.

evaluation_times (or t_eval)array-list, optional

List of times at which the time response should be computed. Defaults to timepts.

return_states (or return_x)bool, optional

If True, return the state vector when assigning to a tuple. See forced_response for more details. If True, return the values of the state at each time Default is False.

paramsdict, optional

Parameter values for the system. Passed to the evaluation functions for the system as default values, overriding internal defaults.

squeezebool, optional

If True and if the system has a single output, return the system output as a 1D array rather than a 2D array. If False, return the system output as a 2D array even if the system is SISO. Default value set by config.defaults['control.squeeze_time_response'].

Returns

responseTimeResponseData

Time response data object representing the input/output response. When accessed as a tuple, returns (time, outputs) or (time, outputs, states if return_x is True. If the input/output system signals are named, these names will be used as labels for the time response. If sys is a list of systems, returns a TimeResponseList object. Results can be plotted using the plot method. See TimeResponseData for more detailed information.

response.timearray

Time values of the output.

response.outputsarray

Response of the system. If the system is SISO and squeeze is not True, the array is 1D (indexed by time). If the system is not SISO or squeeze is False, the array is 2D (indexed by output and time).

response.statesarray

Time evolution of the state vector, represented as a 2D array indexed by state and time.

response.inputsarray

Input(s) to the system, indexed by input and time.

response.paramsdict

Parameters values used for the simulation.

Other Parameters

ignore_errorsbool, optional

If False (default), errors during computation of the trajectory will raise a RuntimeError exception. If True, do not raise an exception and instead set response.success to False and place an error message in response.message.

solve_ivp_methodstr, optional

Set the method used by scipy.integrate.solve_ivp. Defaults to ‘RK45’.

solve_ivp_kwargsdict, optional

Pass additional keywords to scipy.integrate.solve_ivp.

transposebool, default=False

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

Raises

TypeError

If the system is not an input/output system.

ValueError

If time step does not match sampling time (for discrete-time systems).

Notes

If a smaller number of initial conditions are given than the number of states in the system, the initial conditions will be padded with zeros. This is often useful for interconnected control systems where the process dynamics are the first system and all other components start with zero initial condition since this can be specified as [xsys_0, 0]. A warning is issued if the initial conditions are padded and and the final listed initial state is not zero.

If discontinuous inputs are given, the underlying SciPy numerical integration algorithms can sometimes produce erroneous results due to the default tolerances that are used. The ivp_method and ivp_keywords parameters can be used to tune the ODE solver and produce better results. In particular, using ‘LSODA’ as the ivp_method or setting the rtol parameter to a smaller value (e.g. using ivp_kwargs={'rtol': 1e-4}) can provide more accurate results.