control.NonlinearIOSystem

class control.NonlinearIOSystem(updfcn, outfcn=None, inputs=None, outputs=None, states=None, params={}, name=None, **kwargs)

Bases: control.iosys.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.

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

  • 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.

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_output

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

find_state

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

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.

__add__(sys2)

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 not 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__(sys1)

Multiply two input/output systems (series interconnection)

__neg__()

Negate an input/output systems (rescale)

__rmul__(sys2)

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

copy(newname=None)

Make a copy of an input/output system.

dynamics(t, x, u)

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)

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])

Where t is a scalar.

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

Returns

dx/dt or x[t+dt]

Return type

ndarray

feedback(other=1, sign=- 1, params={})

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)

issiso()

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

linearize(x0, u0, t=0, params={}, eps=1e-06, name=None, copy=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.

output(t, x, u)

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)

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

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].