control.NonlinearIOSystem

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

Bases: InputOutputSystem

Nonlinear input/output system model.

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. Nonlinear I/O systems are usually created with the nlsys factory function.

Parameters:

updfcncallable

Function returning the state update function

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

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

outfcncallable

Function returning the output at the given state

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

where the arguments are the same as for updfcn.

inputs, outputs, statesint, list of str or None, optional

Description of the system inputs, outputs, and states. See control.nlsys for more details.

paramsdict, optional

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

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

Attributes:

ninputs, noutputs, nstatesint

Number of input, output and state variables.

shapetuple

2-tuple of I/O system dimension, (noutputs, ninputs).

input_labels, output_labels, state_labelslist of str

Names for the input, output, and state variables.

namestring, optional

System name.

See also

nlsys, InputOutputSystem

Notes

The InputOutputSystem class (and its subclasses) makes use of two special methods for implementing much of the work of the class:

• _rhs(t, x, u): compute the right hand side of the differential or difference equation for the system. If not specified, the system has no state.

• _out(t, x, u): compute the output for the current state of the system. The default is to return the entire system state.

Attributes

dt	System timebase.
input_labels	List of labels for the input signals.
ninputs	Number of system inputs.
noutputs	Number of system outputs.
nstates	Number of system states.
output_labels	List of labels for the output signals.
repr_format	String representation format.
shape	2-tuple of I/O system dimension, (noutputs, ninputs).
state_labels	List of labels for the state signals.

Methods

__call__	Evaluate a (static) nonlinearity at a given input value.
copy	Make a copy of an input/output system.
dynamics	Dynamics of a differential or difference equation.
feedback	Feedback interconnection between two I/O systems.
find_input	Find the index for an input given its name (None if not found).
find_inputs	Return list of indices matching input spec (None if not found).
find_output	Find the index for a output given its name (None if not found).
find_outputs	Return list of indices matching output spec (None if not found).
find_state	Find the index for a state given its name (None if not found).
find_states	Return list of indices matching state spec (None if not found).
isctime	Check to see if a system is a continuous-time system.
isdtime	Check to see if a system is a discrete-time system.
issiso	Check to see if a system is single input, single output.
linearize	Linearize an input/output system at a given state and input.
output	Compute the output of the system.
set_inputs	Set the number/names of the system inputs.
set_outputs	Set the number/names of the system outputs.
set_states	Set the number/names of the system states.
update_names	Update signal and system names for an I/O system.

__add__(other)

Add two input/output systems (parallel interconnection)

__call__(u, params=None, squeeze=None)

Evaluate a (static) nonlinearity at a given input value.

If a nonlinear I/O system has no internal state, then evaluating the system at an input u gives the output y = F(u), determined by the output function.

Parameters:

paramsdict, optional

Parameter values for the system. Passed to the evaluation function 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'].

__mul__(other)

Multiply two input/output systems (series interconnection)

__neg__()

Negate an input/output system (rescale)

__radd__(other)

Parallel addition of input/output system to a compatible object.

__rmul__(other)

Pre-multiply an input/output systems by a scalar/matrix

__rsub__(other)

Parallel subtraction of I/O system to a compatible object.

__sub__(other)

Subtract two input/output systems (parallel interconnection)

__truediv__(other)

Division of input/output system (by scalar or array)

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['iosys.duplicate_system_name_prefix'] and appending config.defaults['iosys.duplicate_system_name_suffix']. Otherwise, a generic system name of the form ‘sys[<id>]’ is used, where ‘<id>’ is based on an internal counter.

Parameters:

namestr, optional

Name of the newly created system.

use_prefix_suffixbool, optional

If True and name is None, set the name of the new system to the name of the original system with prefix config.defaults['duplicate_system_name_prefix'] and suffix config.defaults['duplicate_system_name_suffix'].

Returns:

InputOutputSystem

dt

System timebase.

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

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 a continuous-time system, returns the time derivative:

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

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

x[t+dt] = updfcn(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:

tfloat

Time at which to evaluate.

xarray_like

Current state.

uarray_like

Current input.

paramsdict, optional

System parameter values.

Returns:

dx/dt or x[t+dt]ndarray

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

Feedback interconnection between two I/O systems.

Parameters:

otherInputOutputSystem

System in the feedback path.

signfloat, optional

Gain to use in feedback path. Defaults to -1.

paramsdict, optional

Parameter values for the overall system. Passed to the evaluation functions for the system as default values, overriding defaults for the individual systems.

Returns:

NonlinearIOSystem

find_input(name)

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

Parameters:

namestr

Signal name for the desired input.

Returns:

int

Index of the named input.

find_inputs(name_list)

Return list of indices matching input spec (None if not found).

Parameters:

name_liststr or list of str

List of signal specifications for the desired inputs. A signal can be described by its name or by a slice-like description of the form ‘start:end` where ‘start’ and ‘end’ are signal names. If either is omitted, it is taken as the first or last signal, respectively.

Returns:

list of int

List of indices for the specified inputs.

find_output(name)

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

Parameters:

namestr

Signal name for the desired output.

Returns:

int

Index of the named output.

find_outputs(name_list)

Return list of indices matching output spec (None if not found).

Parameters:

name_liststr or list of str

List of signal specifications for the desired outputs. A signal can be described by its name or by a slice-like description of the form ‘start:end` where ‘start’ and ‘end’ are signal names. If either is omitted, it is taken as the first or last signal, respectively.

Returns:

list of int

List of indices for the specified outputs.

find_state(name)

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

Parameters:

namestr

Signal name for the desired state.

Returns:

int

Index of the named state.

find_states(name_list)

Return list of indices matching state spec (None if not found).

Parameters:

name_liststr or list of str

List of signal specifications for the desired states. A signal can be described by its name or by a slice-like description of the form ‘start:end` where ‘start’ and ‘end’ are signal names. If either is omitted, it is taken as the first or last signal, respectively.

Returns:

list of int

List of indices for the specified states..

property input_labels

List of labels for the input signals.

isctime(strict=False)

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

Parameters:

strictbool, 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:

strictbool, 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=None, t=0, params=None, eps=1e-06, 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 operating point (or 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 = outfcn(t, x, u[, params])

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

Parameters:

tfloat

The time at which to evaluate.

xarray_like

Current state.

uarray_like

Current input.

paramsdict, optional

System parameter values.

Returns:

yndarray

property output_labels

List of labels for the output signals.

property repr_format

String representation format.

Format used in creating the representation for the system:

• ‘info’ : <IOSystemType sysname: [inputs] -> [outputs]>

• ‘eval’ : system specific, loadable representation

• ‘latex’ : HTML/LaTeX representation of the object

The default representation for an input/output is set to ‘eval’. This value can be changed for an individual system by setting the repr_format parameter when the system is created or by setting the repr_format property after system creation. Set config.defaults['iosys.repr_format'] to change for all I/O systems or use the repr_format parameter/attribute for a single system.

set_inputs(inputs, prefix='u')

Set the number/names of the system inputs.

Parameters:

inputsint, 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).

prefixstring, 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:

outputsint, 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 ‘y[i]’ (where the prefix ‘y’ can be changed using the optional prefix parameter).

prefixstring, 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:

statesint, 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 ‘x[i]’ (where the prefix ‘x’ can be changed using the optional prefix parameter).

prefixstring, 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]’.

property shape

2-tuple of I/O system dimension, (noutputs, ninputs).

property state_labels

List of labels for the state signals.

update_names([name, inputs, outputs, states])

Update signal and system names for an I/O system.

Parameters:

namestr, optional

New system name.

inputslist of str, int, or None, optional

List of strings that name the individual input signals. If given as an integer or None, signal names default to the form ‘u[i]’. See InputOutputSystem for more information.

outputslist of str, int, or None, optional

Description of output signals; defaults to ‘y[i]’.

statesint, list of str, int, or None, optional

Description of system states; defaults to ‘x[i]’.

input_prefixstring, optional

Set the prefix for input signals. Default = ‘u’.

output_prefixstring, optional

Set the prefix for output signals. Default = ‘y’.

state_prefixstring, optional

Set the prefix for state signals. Default = ‘x’.