control.InputOutputSystem

class control.InputOutputSystem(params={}, **kwargs)

Bases: NamedIOSystem

A class for representing input/output systems.

The InputOutputSystem class allows (possibly nonlinear) input/output systems to be represented in Python. It is intended as a parent class for a set of subclasses that are used to implement specific structures and operations for different types of input/output dynamical systems.

Parameters
  • inputs (int, list of str, or None) – Description of the system inputs. This can be given as an integer count or 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) – Description of the system outputs. Same format as inputs.

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

  • dt (None, True or float, optional) – System timebase. 0 (default) indicates continuous time, True indicates discrete time with unspecified sampling time, positive number is discrete time with specified sampling time, None indicates unspecified timebase (either continuous or discrete time).

  • 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.

ninputs, noutputs, nstates

Number of input, output and state variables

Type

int

input_index, output_index, state_index

Dictionary of signal names for the inputs, outputs and states and the index of the corresponding array

Type

dict

dt

System timebase. 0 (default) indicates continuous time, True indicates discrete time with unspecified sampling time, positive number is discrete time with specified sampling time, None indicates unspecified timebase (either continuous or discrete time).

Type

None, True or float

params

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

Type

dict, optional

name

System name (used for specifying signals)

Type

string, optional

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. This must be specified by the subclass for the system.

  • _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_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)

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.

__add__(sys2)

Add two input/output systems (parallel interconnection)

__mul__(sys1)

Multiply two input/output systems (series interconnection)

__neg__()

Negate an input/output systems (rescale)

__radd__(sys2)

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

__rmul__(sys2)

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

__rsub__(sys2)

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

__sub__(sys2)

Subtract two input/output systems (parallel interconnection)

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)

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)

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={}, 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.

ninputs

Number of system inputs.

noutputs

Number of system outputs.

nstates

Number of system states.

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].