control.NonlinearIOSystem

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

Bases: InputOutputSystem

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

See also

InputOutputSystem

Input/output system class.

Notes

The InputOuputSystem 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.

Methods

copy	Make a copy of an input/output system
dynamics	Compute the dynamics of a differential or difference equation.
feedback	Feedback interconnection between two input/output 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 an 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

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

• squeeze (bool, 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.

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_inputs(name_list)

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

find_output(name)

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

find_outputs(name_list)

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

find_state(name)

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

find_states(name_list)

Return list of indices matching state spec (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, 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].

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

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

Parameters

• name (str, optional) – New system name.

• inputs (list 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.

• outputs (list of str, int, or None, optional) – Description of output signals; defaults to y[i].

• states (int, list of str, int, or None, optional) – Description of system states; defaults to x[i].