control.NonlinearIOSystem¶

class
control.
NonlinearIOSystem
(updfcn, outfcn=None, inputs=None, outputs=None, states=None, params={}, name=None, **kwargs)¶ Nonlinear I/O system.
This class is used to implement a system that is a nonlinear state space system (defined by and update function and an output function).

__init__
(updfcn, outfcn=None, inputs=None, outputs=None, states=None, params={}, name=None, **kwargs)¶ Create a nonlinear I/O system given update and output functions.
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: discretetime systems not yet supported by most function.) Parameters
updfcn (callable) –
Function returning the state update function
updfcn(t, x, u[, param]) > array
where x is a 1D array with shape (nstates,), u is a 1D array with shape (ninputs,), t is a float representing the currrent time, and param is an optional dict containing the values of parameters used by the function.
outfcn (callable) –
Function returning the output at the given state
outfcn(t, x, u[, param]) > 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.
 Returns
iosys – Nonlinear system represented as an input/output system.
 Return type
Methods
__init__
(updfcn[, outfcn, inputs, outputs, …])Create a nonlinear I/O system given update and output functions.
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].
