control.InputOutputSystem¶

class
control.
InputOutputSystem
(inputs=None, outputs=None, states=None, params={}, name=None, **kwargs)¶ 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 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) – 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).
params (dict, optional) – Parameter values for the systems. Passed to the evaluation functions for the system as default values, overriding internal defaults.
name (string, optional) – System name (used for specifying signals). If unspecified, a generic name <sys[id]> is generated with a unique integer id.

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.

__init__
(inputs=None, outputs=None, states=None, params={}, name=None, **kwargs)¶ Create an input/output system.
The InputOutputSystem contructor is used to create an input/output object with the core information required for all input/output systems. Instances of this class are normally created by one of the input/output subclasses:
LinearICSystem
,LinearIOSystem
,NonlinearIOSystem
,InterconnectedSystem
. 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 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).
params (dict, optional) – Parameter values for the systems. Passed to the evaluation functions for the system as default values, overriding internal defaults.
name (string, optional) – System name (used for specifying signals). If unspecified, a generic name <sys[id]> is generated with a unique integer id.
 Returns
Input/output system object
 Return type
Methods
__init__
([inputs, outputs, states, params, name])Create an input/output system.
copy
([newname])Make a copy of an input/output system.
dynamics
(t, x, u)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)
issiso
()Check to see if a system is single input, single output
linearize
(x0, u0[, t, params, eps, name, copy])Linearize an input/output system at a given state and input.
name_or_default
([name])output
(t, x, u)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
idCounter

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 discretetime, 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
 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=1e06, 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].