control.describing_function_response

control.describing_function_response(H, F, A, omega=None, refine=True, warn_nyquist=None, _check_kwargs=True, **kwargs)[source]

Compute the describing function response of a system.

This function uses describing function analysis to analyze a closed loop system consisting of a linear system with a nonlinear function in the feedback path.

Parameters
HLTI system

Linear time-invariant (LTI) system (state space, transfer function, or FRD).

Fnonlinear function

Feedback nonlinearity, either a scalar function or a single-input, single-output, static input/output system.

Alist

List of amplitudes to be used for the describing function plot.

omegalist, optional

List of frequencies to be used for the linear system Nyquist curve.

warn_nyquistbool, optional

Set to True to turn on warnings generated by nyquist_plot or False to turn off warnings. If not set (or set to None), warnings are turned off if omega is specified, otherwise they are turned on.

refinebool, optional

If True, scipy.optimize.minimize to refine the estimate of the intersection of the frequency response and the describing function.

Returns
responseDescribingFunctionResponse object

Response object that contains the result of the describing function analysis. The results can plotted using the plot method.

response.intersections1D ndarray of 2-tuples or None

A list of all amplitudes and frequencies in which H(j\omega) N(a) = -1, where N(a) is the describing function associated with F, or None if there are no such points. Each pair represents a potential limit cycle for the closed loop system with amplitude given by the first value of the tuple and frequency given by the second value.

response.Nvalscomplex ndarray

Complex value of the describing function, indexed by amplitude.

See also

DescribingFunctionResponse, describing_function_plot

Examples

>>> H_simple = ct.tf([8], [1, 2, 2, 1])
>>> F_saturation = ct.saturation_nonlinearity(1)
>>> amp = np.linspace(1, 4, 10)
>>> response = ct.describing_function_response(H_simple, F_saturation, amp)
>>> response.intersections  
[(3.343844998258643, 1.4142293090899216)]
>>> cplt = response.plot()