control.NonlinearIOSystem

class control.NonlinearIOSystem(updfcn, outfcn=None, params=None, **kwargs)

Nonlinear I/O 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 (Note: discrete-time systems are not yet supported by most functions.)

Parameters

• updfcn (callable) –

  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 currrent time, and params is a dict containing the values of parameters used by the function.

• outfcn (callable) –

  Function returning the output at the given state

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

  where the arguments are the same as for upfcn.

• inputs (int, 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.

• outputs (int, list of str or None, optional) – Description of the system outputs. Same format as inputs.

• states (int, list of str, or None, optional) – Description of the system states. Same format as inputs.

• dt (timebase, 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

• name (string, optional) – System name (used for specifying signals). If unspecified, a generic name <sys[id]> is generated with a unique integer id.

• params (dict, optional) – Parameter values for the systems. Passed to the evaluation functions for the system as default values, overriding internal defaults.

__init__(updfcn, outfcn=None, params=None, **kwargs)

Create a nonlinear I/O system given update and output functions.

Methods

__init__(updfcn[, outfcn, params])	Create a nonlinear I/O system given update and output functions.
copy([name, use_prefix_suffix])	Make a copy of an input/output system
dynamics(t, x, u[, params])	Compute the dynamics of a differential or difference equation.
feedback([other, sign, params])	Feedback interconnection between two input/output systems
find_input(name)	Find the index for an input given its name (None if not found)
find_output(name)	Find the index for an output given its name (None if not found)
find_state(name)	Find the index for a state given its name (None if not found)
isctime([strict])	Check to see if a system is a continuous-time system
isdtime([strict])	Check to see if a system is a discrete-time system
issiso()	Check to see if a system is single input, single output
linearize(x0, u0[, t, params, eps, name, ...])	Linearize an input/output system at a given state and input.
output(t, x, u[, params])	Compute the output of the system
set_inputs(inputs[, prefix])	Set the number/names of the system inputs.
set_outputs(outputs[, prefix])	Set the number/names of the system outputs.
set_states(states[, prefix])	Set the number/names of the system states.

Attributes

input_labels
ninputs	Number of system inputs.
noutputs	Number of system outputs.
nstates	Number of system states.
output_labels
state_labels

copy(name=None, use_prefix_suffix=True)

Make a copy of an input/output system

A copy of the system is made, with a new name. The name keyword can be used to specify a specific name for the system. If no name is given and use_prefix_suffix is True, the name is constructed by prepending config.defaults[‘namedio.duplicate_system_name_prefix’] and appending config.defaults[‘namedio.duplicate_system_name_suffix’]. Otherwise, a generic system name of the form sys[<id>] is used, where <id> is based on an internal counter.

dynamics(t, x, u, params=None)

Compute the dynamics of a differential or difference equation.

Given time t, input u and state x, returns the value of the right hand side of the dynamical system. If the system is continuous, returns the time derivative

dx/dt = f(t, x, u[, params])

where f is the system’s (possibly nonlinear) dynamics function. If the system is discrete-time, returns the next value of x:

x[t+dt] = f(t, x[t], u[t][, params])

where t is a scalar.

The inputs x and u must be of the correct length. The params argument is an optional dictionary of parameter values.

Parameters

• t (float) – the time at which to evaluate

• x (array_like) – current state

• u (array_like) – input

• params (dict (optional)) – system parameter values

Returns

dx/dt or x[t+dt]

Return type

ndarray

feedback(other=1, sign=-1, params=None)

Feedback interconnection between two input/output systems

Parameters

• sys1 (InputOutputSystem) – The primary process.

• sys2 (InputOutputSystem) – The feedback process (often a feedback controller).

• sign (scalar, optional) – The sign of feedback. sign = -1 indicates negative feedback, and sign = 1 indicates positive feedback. sign is an optional argument; it assumes a value of -1 if not specified.

Returns

out

Return type

InputOutputSystem

Raises

ValueError – if the inputs, outputs, or timebases of the systems are incompatible.

find_input(name)

Find the index for an input given its name (None if not found)

find_output(name)

Find the index for an output given its name (None if not found)

find_state(name)

Find the index for a state given its name (None if not found)

isctime(strict=False)

Check to see if a system is a continuous-time system

Parameters

• sys (Named I/O system) – System to be checked

• strict (bool, optional) – If strict is True, make sure that timebase is not None. Default is False.

isdtime(strict=False)

Check to see if a system is a discrete-time system

Parameters

strict (bool, optional) – If strict is True, make sure that timebase is not None. Default is False.

issiso()

Check to see if a system is single input, single output

linearize(x0, u0, t=0, params=None, eps=1e-06, name=None, copy_names=False, **kwargs)

Linearize an input/output system at a given state and input.

Return the linearization of an input/output system at a given state and input value as a StateSpace system. See linearize() for complete documentation.

ninputs

Number of system inputs.

noutputs

Number of system outputs.

nstates

Number of system states.

output(t, x, u, params=None)

Compute the output of the system

Given time t, input u and state x, returns the output of the system:

y = g(t, x, u[, params])

The inputs x and u must be of the correct length.

Parameters

• t (float) – the time at which to evaluate

• x (array_like) – current state

• u (array_like) – input

• params (dict (optional)) – system parameter values

Returns

y

Return type

ndarray

set_inputs(inputs, prefix='u')

Set the number/names of the system inputs.

Parameters

• inputs (int, list of str, or None) – 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 u[i] (where the prefix u can be changed using the optional prefix parameter).

• prefix (string, optional) – If inputs is an integer, create the names of the states using the given prefix (default = ‘u’). The names of the input will be of the form prefix[i].

set_outputs(outputs, prefix='y')

Set the number/names of the system outputs.

Parameters

• outputs (int, list of str, or None) – Description of the system outputs. 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 u[i] (where the prefix u can be changed using the optional prefix parameter).

• prefix (string, optional) – If outputs is an integer, create the names of the states using the given prefix (default = ‘y’). The names of the input will be of the form prefix[i].

set_states(states, prefix='x')

Set the number/names of the system states.

Parameters

• states (int, list of str, or None) – Description of the system states. 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 u[i] (where the prefix u can be changed using the optional prefix parameter).

• prefix (string, optional) – If states is an integer, create the names of the states using the given prefix (default = ‘x’). The names of the input will be of the form prefix[i].