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# iosys.py - input/output system module
#
# RMM, 28 April 2019
#
# Additional features to add
# * Allow constant inputs for MIMO input_output_response (w/out ones)
# * Add support for constants/matrices as part of operators (1 + P)
# * Add unit tests (and example?) for time-varying systems
# * Allow time vector for discrete time simulations to be multiples of dt
# * Check the way initial outputs for discrete time systems are handled
#
"""The :mod:`~control.iosys` module contains the
:class:`~control.InputOutputSystem` class that represents (possibly nonlinear)
input/output systems. The :class:`~control.InputOutputSystem` class is a
general class that defines any continuous or discrete time dynamical system.
Input/output systems can be simulated and also used to compute equilibrium
points and linearizations.
"""
__author__ = "Richard Murray"
__copyright__ = "Copyright 2019, California Institute of Technology"
__credits__ = ["Richard Murray"]
__license__ = "BSD"
__maintainer__ = "Richard Murray"
__email__ = "murray@cds.caltech.edu"
import numpy as np
import scipy as sp
import copy
from warnings import warn
from .lti import LTI
from .namedio import NamedIOSystem, _process_signal_list, \
_process_namedio_keywords, isctime, isdtime, common_timebase
from .statesp import StateSpace, tf2ss, _convert_to_statespace
from .statesp import _rss_generate
from .xferfcn import TransferFunction
from .timeresp import _check_convert_array, _process_time_response, \
TimeResponseData
from . import config
__all__ = ['InputOutputSystem', 'LinearIOSystem', 'NonlinearIOSystem',
'InterconnectedSystem', 'LinearICSystem', 'input_output_response',
'find_eqpt', 'linearize', 'ss', 'rss', 'drss', 'ss2io', 'tf2io',
'interconnect', 'summing_junction']
# Define module default parameter values
_iosys_defaults = {}
class InputOutputSystem(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 system. Passed to the evaluation functions
for the system as default values, overriding internal defaults.
Attributes
----------
ninputs, noutputs, nstates : int
Number of input, output and state variables
input_index, output_index, state_index : dict
Dictionary of signal names for the inputs, outputs and states and the
index of the corresponding array
dt : None, True or float
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)
Notes
-----
The :class:`~control.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.
"""
# Allow ndarray * InputOutputSystem to give IOSystem._rmul_() priority
__array_priority__ = 12 # override ndarray, matrix, SS types
def __init__(self, params=None, **kwargs):
"""Create an input/output system.
The InputOutputSystem constructor 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: :class:`~control.LinearICSystem`,
:class:`~control.LinearIOSystem`, :class:`~control.NonlinearIOSystem`,
:class:`~control.InterconnectedSystem`.
"""
# Store the system name, inputs, outputs, and states
name, inputs, outputs, states, dt = _process_namedio_keywords(
kwargs, end=True)
# Initialize the data structure
# Note: don't use super() to override LinearIOSystem/StateSpace MRO
NamedIOSystem.__init__(
self, inputs=inputs, outputs=outputs,
states=states, name=name, dt=dt)
# default parameters
self.params = {} if params is None else params.copy()
def __mul__(sys2, sys1):
"""Multiply two input/output systems (series interconnection)"""
# Note: order of arguments is flipped so that self = sys2,
# corresponding to the ordering convention of sys2 * sys1
# Convert sys1 to an I/O system if needed
if isinstance(sys1, (int, float, np.number)):
sys1 = LinearIOSystem(StateSpace(
[], [], [], sys1 * np.eye(sys2.ninputs)))
elif isinstance(sys1, np.ndarray):
sys1 = LinearIOSystem(StateSpace([], [], [], sys1))
elif isinstance(sys1, (StateSpace, TransferFunction)) and \
not isinstance(sys1, LinearIOSystem):
sys1 = LinearIOSystem(sys1)
elif not isinstance(sys1, InputOutputSystem):
raise TypeError("Unknown I/O system object ", sys1)
# Make sure systems can be interconnected
if sys1.noutputs != sys2.ninputs:
raise ValueError("Can't multiply systems with incompatible "
"inputs and outputs")
# Make sure timebase are compatible
dt = common_timebase(sys1.dt, sys2.dt)
# Create a new system to handle the composition
inplist = [(0, i) for i in range(sys1.ninputs)]
outlist = [(1, i) for i in range(sys2.noutputs)]
newsys = InterconnectedSystem(
(sys1, sys2), inplist=inplist, outlist=outlist)
# Set up the connection map manually
newsys.set_connect_map(np.block(
[[np.zeros((sys1.ninputs, sys1.noutputs)),
np.zeros((sys1.ninputs, sys2.noutputs))],
[np.eye(sys2.ninputs, sys1.noutputs),
np.zeros((sys2.ninputs, sys2.noutputs))]]
))
# If both systems are linear, create LinearICSystem
if isinstance(sys1, StateSpace) and isinstance(sys2, StateSpace):
ss_sys = StateSpace.__mul__(sys2, sys1)
return LinearICSystem(newsys, ss_sys)
# Return the newly created InterconnectedSystem
return newsys
def __rmul__(sys1, sys2):
"""Pre-multiply an input/output systems by a scalar/matrix"""
# Convert sys2 to an I/O system if needed
if isinstance(sys2, (int, float, np.number)):
sys2 = LinearIOSystem(StateSpace(
[], [], [], sys2 * np.eye(sys1.noutputs)))
elif isinstance(sys2, np.ndarray):
sys2 = LinearIOSystem(StateSpace([], [], [], sys2))
elif isinstance(sys2, (StateSpace, TransferFunction)) and \
not isinstance(sys2, LinearIOSystem):
sys2 = LinearIOSystem(sys2)
elif not isinstance(sys2, InputOutputSystem):
raise TypeError("Unknown I/O system object ", sys2)
return InputOutputSystem.__mul__(sys2, sys1)
def __add__(sys1, sys2):
"""Add two input/output systems (parallel interconnection)"""
# Convert sys1 to an I/O system if needed
if isinstance(sys2, (int, float, np.number)):
sys2 = LinearIOSystem(StateSpace(
[], [], [], sys2 * np.eye(sys1.ninputs)))
elif isinstance(sys2, np.ndarray):
sys2 = LinearIOSystem(StateSpace([], [], [], sys2))
elif isinstance(sys2, (StateSpace, TransferFunction)) and \
not isinstance(sys2, LinearIOSystem):
sys2 = LinearIOSystem(sys2)
elif not isinstance(sys2, InputOutputSystem):
raise TypeError("Unknown I/O system object ", sys2)
# Make sure number of input and outputs match
if sys1.ninputs != sys2.ninputs or sys1.noutputs != sys2.noutputs:
raise ValueError("Can't add systems with incompatible numbers of "
"inputs or outputs.")
ninputs = sys1.ninputs
noutputs = sys1.noutputs
# Create a new system to handle the composition
inplist = [[(0, i), (1, i)] for i in range(ninputs)]
outlist = [[(0, i), (1, i)] for i in range(noutputs)]
newsys = InterconnectedSystem(
(sys1, sys2), inplist=inplist, outlist=outlist)
# If both systems are linear, create LinearICSystem
if isinstance(sys1, StateSpace) and isinstance(sys2, StateSpace):
ss_sys = StateSpace.__add__(sys2, sys1)
return LinearICSystem(newsys, ss_sys)
# Return the newly created InterconnectedSystem
return newsys
def __radd__(sys1, sys2):
"""Parallel addition of input/output system to a compatible object."""
# Convert sys2 to an I/O system if needed
if isinstance(sys2, (int, float, np.number)):
sys2 = LinearIOSystem(StateSpace(
[], [], [], sys2 * np.eye(sys1.noutputs)))
elif isinstance(sys2, np.ndarray):
sys2 = LinearIOSystem(StateSpace([], [], [], sys2))
elif isinstance(sys2, (StateSpace, TransferFunction)) and \
not isinstance(sys2, LinearIOSystem):
sys2 = LinearIOSystem(sys2)
elif not isinstance(sys2, InputOutputSystem):
raise TypeError("Unknown I/O system object ", sys2)
return InputOutputSystem.__add__(sys2, sys1)
def __sub__(sys1, sys2):
"""Subtract two input/output systems (parallel interconnection)"""
# Convert sys1 to an I/O system if needed
if isinstance(sys2, (int, float, np.number)):
sys2 = LinearIOSystem(StateSpace(
[], [], [], sys2 * np.eye(sys1.ninputs)))
elif isinstance(sys2, np.ndarray):
sys2 = LinearIOSystem(StateSpace([], [], [], sys2))
elif isinstance(sys2, (StateSpace, TransferFunction)) and \
not isinstance(sys2, LinearIOSystem):
sys2 = LinearIOSystem(sys2)
elif not isinstance(sys2, InputOutputSystem):
raise TypeError("Unknown I/O system object ", sys2)
# Make sure number of input and outputs match
if sys1.ninputs != sys2.ninputs or sys1.noutputs != sys2.noutputs:
raise ValueError("Can't add systems with incompatible numbers of "
"inputs or outputs.")
ninputs = sys1.ninputs
noutputs = sys1.noutputs
# Create a new system to handle the composition
inplist = [[(0, i), (1, i)] for i in range(ninputs)]
outlist = [[(0, i), (1, i, -1)] for i in range(noutputs)]
newsys = InterconnectedSystem(
(sys1, sys2), inplist=inplist, outlist=outlist)
# If both systems are linear, create LinearICSystem
if isinstance(sys1, StateSpace) and isinstance(sys2, StateSpace):
ss_sys = StateSpace.__sub__(sys1, sys2)
return LinearICSystem(newsys, ss_sys)
# Return the newly created InterconnectedSystem
return newsys
def __rsub__(sys1, sys2):
"""Parallel subtraction of I/O system to a compatible object."""
# Convert sys2 to an I/O system if needed
if isinstance(sys2, (int, float, np.number)):
sys2 = LinearIOSystem(StateSpace(
[], [], [], sys2 * np.eye(sys1.noutputs)))
elif isinstance(sys2, np.ndarray):
sys2 = LinearIOSystem(StateSpace([], [], [], sys2))
elif isinstance(sys2, (StateSpace, TransferFunction)) and \
not isinstance(sys2, LinearIOSystem):
sys2 = LinearIOSystem(sys2)
elif not isinstance(sys2, InputOutputSystem):
raise TypeError("Unknown I/O system object ", sys2)
return InputOutputSystem.__sub__(sys2, sys1)
def __neg__(sys):
"""Negate an input/output systems (rescale)"""
if sys.ninputs is None or sys.noutputs is None:
raise ValueError("Can't determine number of inputs or outputs")
# Create a new system to hold the negation
inplist = [(0, i) for i in range(sys.ninputs)]
outlist = [(0, i, -1) for i in range(sys.noutputs)]
newsys = InterconnectedSystem(
(sys,), dt=sys.dt, inplist=inplist, outlist=outlist)
# If the system is linear, create LinearICSystem
if isinstance(sys, StateSpace):
ss_sys = StateSpace.__neg__(sys)
return LinearICSystem(newsys, ss_sys)
# Return the newly created system
return newsys
def __truediv__(sys2, sys1):
"""Division of input/output systems
Only division by scalars and arrays of scalars is supported"""
# Note: order of arguments is flipped so that self = sys2,
# corresponding to the ordering convention of sys2 * sys1
if not isinstance(sys1, (LTI, NamedIOSystem)):
return sys2 * (1/sys1)
else:
return NotImplemented
# Update parameters used for _rhs, _out (used by subclasses)
def _update_params(self, params, warning=False):
if warning:
warn("Parameters passed to InputOutputSystem ignored.")
def _rhs(self, t, x, u):
"""Evaluate right hand side of a differential or difference equation.
Private function used to compute the right hand side of an
input/output system model. Intended for fast
evaluation; for a more user-friendly interface
you may want to use :meth:`dynamics`.
"""
raise NotImplementedError("Evaluation not implemented for system of type ",
type(self))
def dynamics(self, 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] : ndarray
"""
self._update_params(params)
return self._rhs(t, x, u)
def _out(self, t, x, u):
"""Evaluate the output of a system at a given state, input, and time
Private function used to compute the output of of an input/output
system model given the state, input, parameters. Intended for fast
evaluation; for a more user-friendly interface you may want to use
:meth:`output`.
"""
# If no output function was defined in subclass, return state
return x
def output(self, 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 : ndarray
"""
self._update_params(params)
return self._out(t, x, u)
def feedback(self, 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: InputOutputSystem
Raises
------
ValueError
if the inputs, outputs, or timebases of the systems are
incompatible.
"""
# TODO: add conversion to I/O system when needed
if not isinstance(other, InputOutputSystem):
# Try converting to a state space system
try:
other = _convert_to_statespace(other)
except TypeError:
raise TypeError(
"Feedback around I/O system must be an I/O system "
"or convertable to an I/O system.")
other = LinearIOSystem(other)
# Make sure systems can be interconnected
if self.noutputs != other.ninputs or other.noutputs != self.ninputs:
raise ValueError("Can't connect systems with incompatible "
"inputs and outputs")
# Make sure timebases are compatible
dt = common_timebase(self.dt, other.dt)
inplist = [(0, i) for i in range(self.ninputs)]
outlist = [(0, i) for i in range(self.noutputs)]
# Return the series interconnection between the systems
newsys = InterconnectedSystem(
(self, other), inplist=inplist, outlist=outlist,
params=params, dt=dt)
# Set up the connecton map manually
newsys.set_connect_map(np.block(
[[np.zeros((self.ninputs, self.noutputs)),
sign * np.eye(self.ninputs, other.noutputs)],
[np.eye(other.ninputs, self.noutputs),
np.zeros((other.ninputs, other.noutputs))]]
))
if isinstance(self, StateSpace) and isinstance(other, StateSpace):
# Special case: maintain linear systems structure
ss_sys = StateSpace.feedback(self, other, sign=sign)
return LinearICSystem(newsys, ss_sys)
# Return the newly created system
return newsys
def linearize(self, x0, u0, t=0, params=None, eps=1e-6,
name=None, 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
:func:`~control.linearize` for complete documentation.
"""
#
# If the linearization is not defined by the subclass, perform a
# numerical linearization use the `_rhs()` and `_out()` member
# functions.
#
# If x0 and u0 are specified as lists, concatenate the elements
x0 = _concatenate_list_elements(x0, 'x0')
u0 = _concatenate_list_elements(u0, 'u0')
# Figure out dimensions if they were not specified.
nstates = _find_size(self.nstates, x0)
ninputs = _find_size(self.ninputs, u0)
# Convert x0, u0 to arrays, if needed
if np.isscalar(x0):
x0 = np.ones((nstates,)) * x0
if np.isscalar(u0):
u0 = np.ones((ninputs,)) * u0
# Compute number of outputs by evaluating the output function
noutputs = _find_size(self.noutputs, self._out(t, x0, u0))
# Update the current parameters
self._update_params(params)
# Compute the nominal value of the update law and output
F0 = self._rhs(t, x0, u0)
H0 = self._out(t, x0, u0)
# Create empty matrices that we can fill up with linearizations
A = np.zeros((nstates, nstates)) # Dynamics matrix
B = np.zeros((nstates, ninputs)) # Input matrix
C = np.zeros((noutputs, nstates)) # Output matrix
D = np.zeros((noutputs, ninputs)) # Direct term
# Perturb each of the state variables and compute linearization
for i in range(nstates):
dx = np.zeros((nstates,))
dx[i] = eps
A[:, i] = (self._rhs(t, x0 + dx, u0) - F0) / eps
C[:, i] = (self._out(t, x0 + dx, u0) - H0) / eps
# Perturb each of the input variables and compute linearization
for i in range(ninputs):
du = np.zeros((ninputs,))
du[i] = eps
B[:, i] = (self._rhs(t, x0, u0 + du) - F0) / eps
D[:, i] = (self._out(t, x0, u0 + du) - H0) / eps
# Create the state space system
linsys = LinearIOSystem(
StateSpace(A, B, C, D, self.dt, remove_useless_states=False))
# Set the system name, inputs, outputs, and states
if 'copy' in kwargs:
copy_names = kwargs.pop('copy')
warn("keyword 'copy' is deprecated. please use 'copy_names'",
DeprecationWarning)
if copy_names:
linsys._copy_names(self, prefix_suffix_name='linearized')
if name is not None:
linsys.name = name
# re-init to include desired signal names if names were provided
return LinearIOSystem(linsys, **kwargs)
class LinearIOSystem(InputOutputSystem, StateSpace):
"""Input/output representation of a linear (state space) system.
This class is used to implement a system that is a linear state
space system (defined by the StateSpace system object).
Parameters
----------
linsys : StateSpace or TransferFunction
LTI system to be converted
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 : 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.
Attributes
----------
ninputs, noutputs, nstates, dt, etc
See :class:`InputOutputSystem` for inherited attributes.
A, B, C, D
See :class:`~control.StateSpace` for inherited attributes.
"""
def __init__(self, linsys, **kwargs):
"""Create an I/O system from a state space linear system.
Converts a :class:`~control.StateSpace` system into an
:class:`~control.InputOutputSystem` with the same inputs, outputs, and
states. The new system can be a continuous or discrete time system.
"""
if isinstance(linsys, TransferFunction):
# Convert system to StateSpace
linsys = _convert_to_statespace(linsys)
elif not isinstance(linsys, StateSpace):
raise TypeError("Linear I/O system must be a state space "
"or transfer function object")
# Process keyword arguments
name, inputs, outputs, states, dt = _process_namedio_keywords(
kwargs, linsys, end=True)
# Create the I/O system object
# Note: don't use super() to override StateSpace MRO
InputOutputSystem.__init__(
self, inputs=inputs, outputs=outputs, states=states,
params=None, dt=dt, name=name)
# Initalize additional state space variables
StateSpace.__init__(
self, linsys, remove_useless_states=False, init_namedio=False)
# When sampling a LinearIO system, return a LinearIOSystem
def sample(self, *args, **kwargs):
return LinearIOSystem(StateSpace.sample(self, *args, **kwargs))
sample.__doc__ = StateSpace.sample.__doc__
# The following text needs to be replicated from StateSpace in order for
# this entry to show up properly in sphinx doccumentation (not sure why,
# but it was the only way to get it to work).
#
#: Deprecated attribute; use :attr:`nstates` instead.
#:
#: The ``state`` attribute was used to store the number of states for : a
#: state space system. It is no longer used. If you need to access the
#: number of states, use :attr:`nstates`.
states = property(StateSpace._get_states, StateSpace._set_states)
def _update_params(self, params=None, warning=True):
# Parameters not supported; issue a warning
if params and warning:
warn("Parameters passed to LinearIOSystems are ignored.")
def _rhs(self, t, x, u):
# Convert input to column vector and then change output to 1D array
xdot = self.A @ np.reshape(x, (-1, 1)) \
+ self.B @ np.reshape(u, (-1, 1))
return np.array(xdot).reshape((-1,))
def _out(self, t, x, u):
# Convert input to column vector and then change output to 1D array
y = self.C @ np.reshape(x, (-1, 1)) \
+ self.D @ np.reshape(u, (-1, 1))
return np.array(y).reshape((-1,))
def __repr__(self):
# Need to define so that I/O system gets used instead of StateSpace
return InputOutputSystem.__repr__(self)
def __str__(self):
return InputOutputSystem.__str__(self) + "\n\n" \
+ StateSpace.__str__(self)
class NonlinearIOSystem(InputOutputSystem):
"""Nonlinear I/O system.
Creates an :class:`~control.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 systems. Passed to the evaluation
functions for the system as default values, overriding internal
defaults.
"""
def __init__(self, updfcn, outfcn=None, params=None, **kwargs):
"""Create a nonlinear I/O system given update and output functions."""
# Process keyword arguments
name, inputs, outputs, states, dt = _process_namedio_keywords(
kwargs, end=True)
# Initialize the rest of the structure
super().__init__(
inputs=inputs, outputs=outputs, states=states,
params=params, dt=dt, name=name
)
# Store the update and output functions
self.updfcn = updfcn
self.outfcn = outfcn
# Check to make sure arguments are consistent
if updfcn is None:
if self.nstates is None:
self.nstates = 0
else:
raise ValueError("States specified but no update function "
"given.")
if outfcn is None:
# No output function specified => outputs = states
if self.noutputs is None and self.nstates is not None:
self.noutputs = self.nstates
elif self.noutputs is not None and self.noutputs == self.nstates:
# Number of outputs = number of states => all is OK
pass
elif self.noutputs is not None and self.noutputs != 0:
raise ValueError("Outputs specified but no output function "
"(and nstates not known).")
# Initialize current parameters to default parameters
self._current_params = {} if params is None else params.copy()
def __str__(self):
return f"{InputOutputSystem.__str__(self)}\n\n" + \
f"Update: {self.updfcn}\n" + \
f"Output: {self.outfcn}"
# Return the value of a static nonlinear system
def __call__(sys, 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'].
"""
# Make sure the call makes sense
if not sys._isstatic():
raise TypeError(
"function evaluation is only supported for static "
"input/output systems")
# If we received any parameters, update them before calling _out()
if params is not None:
sys._update_params(params)
# Evaluate the function on the argument
out = sys._out(0, np.array((0,)), np.asarray(u))
_, out = _process_time_response(
None, out, issiso=sys.issiso(), squeeze=squeeze)
return out
def _update_params(self, params, warning=False):
# Update the current parameter values
self._current_params = self.params.copy()
if params:
self._current_params.update(params)
def _rhs(self, t, x, u):
xdot = self.updfcn(t, x, u, self._current_params) \
if self.updfcn is not None else []
return np.array(xdot).reshape((-1,))
def _out(self, t, x, u):
y = self.outfcn(t, x, u, self._current_params) \
if self.outfcn is not None else x
return np.array(y).reshape((-1,))
class InterconnectedSystem(InputOutputSystem):
"""Interconnection of a set of input/output systems.
This class is used to implement a system that is an interconnection of
input/output systems. The sys consists of a collection of subsystems
whose inputs and outputs are connected via a connection map. The overall
system inputs and outputs are subsets of the subsystem inputs and outputs.
See :func:`~control.interconnect` for a list of parameters.
"""
def __init__(self, syslist, connections=None, inplist=None, outlist=None,
params=None, warn_duplicate=None, **kwargs):
"""Create an I/O system from a list of systems + connection info."""
# Convert input and output names to lists if they aren't already
if inplist is not None and not isinstance(inplist, (list, tuple)):
inplist = [inplist]
if outlist is not None and not isinstance(outlist, (list, tuple)):
outlist = [outlist]
# Check if dt argument was given; if not, pull from systems
dt = kwargs.pop('dt', None)
# Process keyword arguments (except dt)
defaults = {
'inputs': len(inplist or []),
'outputs': len(outlist or [])}
name, inputs, outputs, states, _ = _process_namedio_keywords(
kwargs, defaults, end=True)
# Initialize the system list and index
self.syslist = list(syslist) # insure modifications can be made
self.syslist_index = {}
# Initialize the input, output, and state counts, indices
nstates, self.state_offset = 0, []
ninputs, self.input_offset = 0, []
noutputs, self.output_offset = 0, []
# Keep track of system objects and names we have already seen
sysobj_name_dct = {}
sysname_count_dct = {}
# Go through the system list and keep track of counts, offsets
for sysidx, sys in enumerate(self.syslist):
# If we were passed a SS or TF system, convert to LinearIOSystem
if isinstance(sys, (StateSpace, TransferFunction)) and \
not isinstance(sys, LinearIOSystem):
sys = LinearIOSystem(sys, name=sys.name)
self.syslist[sysidx] = sys
# Make sure time bases are consistent
dt = common_timebase(dt, sys.dt)
# Make sure number of inputs, outputs, states is given
if sys.ninputs is None or sys.noutputs is None or \
sys.nstates is None:
raise TypeError("System '%s' must define number of inputs, "
"outputs, states in order to be connected" %
sys.name)
# Keep track of the offsets into the states, inputs, outputs
self.input_offset.append(ninputs)
self.output_offset.append(noutputs)
self.state_offset.append(nstates)
# Keep track of the total number of states, inputs, outputs
nstates += sys.nstates
ninputs += sys.ninputs
noutputs += sys.noutputs
# Check for duplicate systems or duplicate names
# Duplicates are renamed sysname_1, sysname_2, etc.
if sys in sysobj_name_dct:
# Make a copy of the object using a new name
if warn_duplicate is None and sys._generic_name_check():
# Make a copy w/out warning, using generic format
sys = sys.copy(use_prefix_suffix=False)
warn_flag = False
else:
sys = sys.copy()
warn_flag = warn_duplicate
# Warn the user about the new object
if warn_flag is not False:
warn("duplicate object found in system list; "
"created copy: %s" % str(sys.name), stacklevel=2)
# Check to see if the system name shows up more than once
if sys.name is not None and sys.name in sysname_count_dct:
count = sysname_count_dct[sys.name]
sysname_count_dct[sys.name] += 1
sysname = sys.name + "_" + str(count)
sysobj_name_dct[sys] = sysname
self.syslist_index[sysname] = sysidx
if warn_duplicate is not False:
warn("duplicate name found in system list; "
"renamed to {}".format(sysname), stacklevel=2)
else:
sysname_count_dct[sys.name] = 1
sysobj_name_dct[sys] = sys.name
self.syslist_index[sys.name] = sysidx
if states is None:
states = []
state_name_delim = config.defaults['namedio.state_name_delim']
for sys, sysname in sysobj_name_dct.items():
states += [sysname + state_name_delim +
statename for statename in sys.state_index.keys()]
# Make sure we the state list is the right length (internal check)
if isinstance(states, list) and len(states) != nstates:
raise RuntimeError(
f"construction of state labels failed; found: "
f"{len(states)} labels; expecting {nstates}")
# Create the I/O system
# Note: don't use super() to override LinearICSystem/StateSpace MRO
InputOutputSystem.__init__(
self, inputs=inputs, outputs=outputs,
states=states, params=params, dt=dt, name=name)
# Convert the list of interconnections to a connection map (matrix)
self.connect_map = np.zeros((ninputs, noutputs))