control.nlsys

control.nlsys(updfcn, outfcn=None, **kwargs)[source]

Create a nonlinear input/output system.

Creates an InputOutputSystem for a nonlinear system by specifying a state update function and an output function. The new system can be a continuous or discrete-time system.

Parameters

updfcncallable (or StateSpace)

Function returning the state update function

updfcn(t, x, u, params) -> array

where x is a 1-D array with shape (nstates,), u is a 1-D array with shape (ninputs,), t is a float representing the current time, and params is a dict containing the values of parameters used by the function.

If a StateSpace system is passed as the update function, then a nonlinear I/O system is created that implements the linear dynamics of the state space system.

outfcncallable

Function returning the output at the given state

outfcn(t, x, u, params) -> array

where the arguments are the same as for updfcn.

inputsint, list of str or None, optional

Description of the system inputs. This can be given as an integer count or as a list of strings that name the individual signals. If an integer count is specified, the names of the signal will be of the form ‘s[i]’ (where ‘s’ is one of ‘u’, ‘y’, or ‘x’). If this parameter is not given or given as None, the relevant quantity will be determined when possible based on other information provided to functions using the system.

outputsint, list of str or None, optional

Description of the system outputs. Same format as inputs.

statesint, list of str, or None, optional

Description of the system states. Same format as inputs.

dttimebase, optional

The timebase for the system, used to specify whether the system is operating in continuous or discrete time. It can have the following values:

dt = 0: continuous-time system (default)
dt > 0: discrete-time system with sampling period dt
dt = True: discrete time with unspecified sampling period
dt = None: no timebase specified

namestring, optional

System name (used for specifying signals). If unspecified, a generic name ‘sys[id]’ is generated with a unique integer id.

paramsdict, optional

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

Returns

sysNonlinearIOSystem: Nonlinear input/output system.

Other Parameters

input_prefix, output_prefix, state_prefixstring, optional: Set the prefix for input, output, and state signals. Defaults = ‘u’, ‘y’, ‘x’.

See also

ss, tf

Examples

>>> def kincar_update(t, x, u, params):
...     l = params['l']              # wheelbase
...     return np.array([
...         np.cos(x[2]) * u[0],     # x velocity
...         np.sin(x[2]) * u[0],     # y velocity
...         np.tan(u[1]) * u[0] / l  # angular velocity
...     ])
>>>
>>> def kincar_output(t, x, u, params):
...     return x[0:2]  # x, y position
>>>
>>> kincar = ct.nlsys(
...     kincar_update, kincar_output, states=3, inputs=2, outputs=2,
...     params={'l': 1})
>>>
>>> timepts = np.linspace(0, 10)
>>> response = ct.input_output_response(
...     kincar, timepts, [10, 0.05 * np.sin(timepts)])