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# nlsys.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.nlsys` module contains the
:class:`~control.NonlinearIOSystem` class that represents (possibly nonlinear)
input/output systems. The :class:`~control.NonlinearIOSystem` 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.
"""
import numpy as np
import scipy as sp
import copy
from warnings import warn
from . import config
from .iosys import InputOutputSystem, _process_signal_list, \
_process_iosys_keywords, isctime, isdtime, common_timebase, _parse_spec
from .timeresp import _check_convert_array, _process_time_response, \
TimeResponseData
__all__ = ['NonlinearIOSystem', 'InterconnectedSystem', 'nlsys',
'input_output_response', 'find_eqpt', 'linearize',
'interconnect', 'connection_table']
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.
See Also
--------
InputOutputSystem : Input/output system class.
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. If not specified, the system
has no state.
* _out(t, x, u): compute the output for the current state of the system.
The default is to return the entire system state.
"""
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_iosys_keywords(kwargs)
# Initialize the rest of the structure
super().__init__(
inputs=inputs, outputs=outputs, states=states, dt=dt, name=name,
**kwargs
)
self.params = {} if params is None else params.copy()
# 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 __mul__(self, other):
"""Multiply two input/output systems (series interconnection)"""
# Convert 'other' to an I/O system if needed
other = _convert_static_iosystem(other)
if not isinstance(other, InputOutputSystem):
return NotImplemented
# Make sure systems can be interconnected
if other.noutputs != self.ninputs:
raise ValueError(
"can't multiply systems with incompatible inputs and outputs")
# Make sure timebase are compatible
dt = common_timebase(other.dt, self.dt)
# Create a new system to handle the composition
inplist = [(0, i) for i in range(other.ninputs)]
outlist = [(1, i) for i in range(self.noutputs)]
newsys = InterconnectedSystem(
(other, self), inplist=inplist, outlist=outlist)
# Set up the connection map manually
newsys.set_connect_map(np.block(
[[np.zeros((other.ninputs, other.noutputs)),
np.zeros((other.ninputs, self.noutputs))],
[np.eye(self.ninputs, other.noutputs),
np.zeros((self.ninputs, self.noutputs))]]
))
# Return the newly created InterconnectedSystem
return newsys
def __rmul__(self, other):
"""Pre-multiply an input/output systems by a scalar/matrix"""
# Convert other to an I/O system if needed
other = _convert_static_iosystem(other)
if not isinstance(other, InputOutputSystem):
return NotImplemented
# Make sure systems can be interconnected
if self.noutputs != other.ninputs:
raise ValueError("Can't multiply systems with incompatible "
"inputs and outputs")
# Make sure timebase are compatible
dt = common_timebase(self.dt, other.dt)
# Create a new system to handle the composition
inplist = [(0, i) for i in range(self.ninputs)]
outlist = [(1, i) for i in range(other.noutputs)]
newsys = InterconnectedSystem(
(self, other), inplist=inplist, outlist=outlist)
# Set up the connection map manually
newsys.set_connect_map(np.block(
[[np.zeros((self.ninputs, self.noutputs)),
np.zeros((self.ninputs, other.noutputs))],
[np.eye(self.ninputs, self.noutputs),
np.zeros((other.ninputs, other.noutputs))]]
))
# Return the newly created InterconnectedSystem
return newsys
def __add__(self, other):
"""Add two input/output systems (parallel interconnection)"""
# Convert other to an I/O system if needed
other = _convert_static_iosystem(other)
if not isinstance(other, InputOutputSystem):
return NotImplemented
# Make sure number of input and outputs match
if self.ninputs != other.ninputs or self.noutputs != other.noutputs:
raise ValueError("Can't add systems with incompatible numbers of "
"inputs or outputs")
# Create a new system to handle the composition
inplist = [[(0, i), (1, i)] for i in range(self.ninputs)]
outlist = [[(0, i), (1, i)] for i in range(self.noutputs)]
newsys = InterconnectedSystem(
(self, other), inplist=inplist, outlist=outlist)
# Return the newly created InterconnectedSystem
return newsys
def __radd__(self, other):
"""Parallel addition of input/output system to a compatible object."""
# Convert other to an I/O system if needed
other = _convert_static_iosystem(other)
if not isinstance(other, InputOutputSystem):
return NotImplemented
# Make sure number of input and outputs match
if self.ninputs != other.ninputs or self.noutputs != other.noutputs:
raise ValueError("can't add systems with incompatible numbers of "
"inputs or outputs")
# Create a new system to handle the composition
inplist = [[(0, i), (1, i)] for i in range(other.ninputs)]
outlist = [[(0, i), (1, i)] for i in range(other.noutputs)]
newsys = InterconnectedSystem(
(other, self), inplist=inplist, outlist=outlist)
# Return the newly created InterconnectedSystem
return newsys
def __sub__(self, other):
"""Subtract two input/output systems (parallel interconnection)"""
# Convert other to an I/O system if needed
other = _convert_static_iosystem(other)
if not isinstance(other, InputOutputSystem):
return NotImplemented
# Make sure number of input and outputs match
if self.ninputs != other.ninputs or self.noutputs != other.noutputs:
raise ValueError(
"can't substract systems with incompatible numbers of "
"inputs or outputs")
ninputs = self.ninputs
noutputs = self.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(
(self, other), inplist=inplist, outlist=outlist)
# Return the newly created InterconnectedSystem
return newsys
def __rsub__(self, other):
"""Parallel subtraction of I/O system to a compatible object."""
# Convert other to an I/O system if needed
other = _convert_static_iosystem(other)
if not isinstance(other, InputOutputSystem):
return NotImplemented
return other - self
def __neg__(self):
"""Negate an input/output system (rescale)"""
if self.ninputs is None or self.noutputs is None:
raise ValueError("Can't determine number of inputs or outputs")
# Create a new selftem to hold the negation
inplist = [(0, i) for i in range(self.ninputs)]
outlist = [(0, i, -1) for i in range(self.noutputs)]
newsys = InterconnectedSystem(
(self,), dt=self.dt, inplist=inplist, outlist=outlist)
# Return the newly created system
return newsys
def __truediv__(self, other):
"""Division of input/output system (by scalar or array)"""
if not isinstance(other, InputOutputSystem):
return self * (1/other)
else:
return NotImplemented
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):
"""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`.
"""
xdot = self.updfcn(t, x, u, self._current_params) \
if self.updfcn is not None else []
return np.array(xdot).reshape((-1,))
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`.
"""
y = self.outfcn(t, x, u, self._current_params) \
if self.outfcn is not None else x
return np.array(y).reshape((-1,))
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.
"""
# Convert sys2 to an I/O system if needed
other = _convert_static_iosystem(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))]]
))
# 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.
"""
from .statesp import StateSpace
#
# 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 = StateSpace(A, B, C, D, self.dt, remove_useless_states=False)
# Set the system name, inputs, outputs, and states
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 StateSpace(linsys, **kwargs)
class InterconnectedSystem(NonlinearIOSystem):
"""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.
The function :func:`~control.interconnect` should be used to create an
interconnected I/O system since it performs additional argument
processing and checking.
"""
def __init__(self, syslist, connections=None, inplist=None, outlist=None,
params=None, warn_duplicate=None, connection_type=None,
**kwargs):
"""Create an I/O system from a list of systems + connection info."""
from .statesp import _convert_to_statespace
from .xferfcn import TransferFunction
self.connection_type = connection_type # explicit, implicit, or None
# Convert input and output names to lists if they aren't already
if inplist is not None and not isinstance(inplist, list):
inplist = [inplist]
if outlist is not None and not isinstance(outlist, list):
outlist = [outlist]
# Check if dt argument was given; if not, pull from systems
dt = kwargs.pop('dt', None)
# Process keyword arguments (except dt)
name, inputs, outputs, states, _ = _process_iosys_keywords(kwargs)
# Initialize the system list and index
self.syslist = list(syslist) # ensure 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):
# Convert transfer functions to state space
if isinstance(sys, TransferFunction):
sys = _convert_to_statespace(sys)
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:
raise TypeError("system '%s' must define number of inputs, "
"outputs, states in order to be connected" %
sys.name)
elif sys.nstates is None:
raise TypeError("can't interconnect systems with no state")
# 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['iosys.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}")
# Figure out what the inputs and outputs are
if inputs is None and inplist is not None:
inputs = len(inplist)
if outputs is None and outlist is not None:
outputs = len(outlist)
# Create updfcn and outfcn
def updfcn(t, x, u, params):
self.update_params(params)
return self._rhs(t, x, u)
def outfcn(t, x, u, params):
self.update_params(params)
return self._out(t, x, u)
# Initialize NonlinearIOSystem object
super().__init__(
updfcn, outfcn, inputs=inputs, outputs=outputs,
states=states, dt=dt, name=name, params=params, **kwargs)
# Convert the list of interconnections to a connection map (matrix)
self.connect_map = np.zeros((ninputs, noutputs))
for connection in connections or []:
input_indices = self._parse_input_spec(connection[0])
for output_spec in connection[1:]:
output_indices, gain = self._parse_output_spec(output_spec)
if len(output_indices) != len(input_indices):
raise ValueError(
f"inconsistent number of signals in connecting"
f" '{output_spec}' to '{connection[0]}'")
for input_index, output_index in zip(
input_indices, output_indices):
if self.connect_map[input_index, output_index] != 0:
warn("multiple connections given for input %d" %
input_index + "; combining with previous entries")
self.connect_map[input_index, output_index] += gain
# Convert the input list to a matrix: maps system to subsystems
self.input_map = np.zeros((ninputs, self.ninputs))
for index, inpspec in enumerate(inplist or []):
if isinstance(inpspec, (int, str, tuple)):
inpspec = [inpspec]
if not isinstance(inpspec, list):
raise ValueError("specifications in inplist must be of type "
"int, str, tuple or list")
for spec in inpspec:
ulist_indices = self._parse_input_spec(spec)
for j, ulist_index in enumerate(ulist_indices):
if self.input_map[ulist_index, index] != 0:
warn("multiple connections given for input %d" %
index + "; combining with previous entries.")
self.input_map[ulist_index, index + j] += 1
# Convert the output list to a matrix: maps subsystems to system
self.output_map = np.zeros((self.noutputs, noutputs + ninputs))
for index, outspec in enumerate(outlist or []):
if isinstance(outspec, (int, str, tuple)):
outspec = [outspec]
if not isinstance(outspec, list):
raise ValueError("specifications in outlist must be of type "
"int, str, tuple or list")
for spec in outspec:
ylist_indices, gain = self._parse_output_spec(spec)
for j, ylist_index in enumerate(ylist_indices):
if self.output_map[index, ylist_index] != 0:
warn("multiple connections given for output %d" %
index + "; combining with previous entries")
self.output_map[index + j, ylist_index] += gain
def _update_params(self, params, warning=False):
for sys in self.syslist:
local = sys.params.copy() # start with system parameters
local.update(self.params) # update with global params
if params:
local.update(params) # update with locally passed parameters
sys._update_params(local, warning=warning)
def _rhs(self, t, x, u):
# Make sure state and input are vectors
x = np.array(x, ndmin=1)
u = np.array(u, ndmin=1)
# Compute the input and output vectors
ulist, ylist = self._compute_static_io(t, x, u)
# Go through each system and update the right hand side for that system
xdot = np.zeros((self.nstates,)) # Array to hold results
state_index, input_index = 0, 0 # Start at the beginning
for sys in self.syslist:
# Update the right hand side for this subsystem
if sys.nstates != 0:
xdot[state_index:state_index + sys.nstates] = sys._rhs(
t, x[state_index:state_index + sys.nstates],
ulist[input_index:input_index + sys.ninputs])
# Update the state and input index counters
state_index += sys.nstates
input_index += sys.ninputs
return xdot
def _out(self, t, x, u):
# Make sure state and input are vectors
x = np.array(x, ndmin=1)
u = np.array(u, ndmin=1)
# Compute the input and output vectors
ulist, ylist = self._compute_static_io(t, x, u)
# Make the full set of subsystem outputs to system output
return self.output_map @ ylist
def _compute_static_io(self, t, x, u):
# Figure out the total number of inputs and outputs
(ninputs, noutputs) = self.connect_map.shape
#
# Get the outputs and inputs at the current system state
#
# Initialize the lists used to keep track of internal signals
ulist = np.dot(self.input_map, u)
ylist = np.zeros((noutputs + ninputs,))
# To allow for feedthrough terms, iterate multiple times to allow
# feedthrough elements to propagate. For n systems, we could need to
# cycle through n+1 times before reaching steady state
# TODO (later): see if there is a more efficient way to compute
cycle_count = len(self.syslist) + 1
while cycle_count > 0:
state_index, input_index, output_index = 0, 0, 0
for sys in self.syslist:
# Compute outputs for each system from current state
ysys = sys._out(
t, x[state_index:state_index + sys.nstates],
ulist[input_index:input_index + sys.ninputs])
# Store the outputs at the start of ylist
ylist[output_index:output_index + sys.noutputs] = \
ysys.reshape((-1,))
# Store the input in the second part of ylist
ylist[noutputs + input_index:
noutputs + input_index + sys.ninputs] = \
ulist[input_index:input_index + sys.ninputs]
# Increment the index pointers
state_index += sys.nstates
input_index += sys.ninputs
output_index += sys.noutputs
# Compute inputs based on connection map
new_ulist = self.connect_map @ ylist[:noutputs] \
+ np.dot(self.input_map, u)
# Check to see if any of the inputs changed
if (ulist == new_ulist).all():
break
else:
ulist = new_ulist
# Decrease the cycle counter
cycle_count -= 1
# Make sure that we stopped before detecting an algebraic loop
if cycle_count == 0:
raise RuntimeError("algebraic loop detected")
return ulist, ylist
def _parse_input_spec(self, spec):
"""Parse an input specification and returns the indices."""
# Parse the signal that we received
subsys_index, input_indices, gain = _parse_spec(
self.syslist, spec, 'input')
if gain != 1:
raise ValueError("gain not allowed in spec '%s'" % str(spec))
# Return the indices into the input vector list (ylist)
return [self.input_offset[subsys_index] + i for i in input_indices]
def _parse_output_spec(self, spec):
"""Parse an output specification and returns the indices and gain."""
# Parse the rest of the spec with standard signal parsing routine
try:
# Start by looking in the set of subsystem outputs
subsys_index, output_indices, gain = \
_parse_spec(self.syslist, spec, 'output')
output_offset = self.output_offset[subsys_index]
except ValueError:
# Try looking in the set of subsystem *inputs*
subsys_index, output_indices, gain = _parse_spec(
self.syslist, spec, 'input or output', dictname='input_index')
# Return the index into the input vector list (ylist)
output_offset = sum(sys.noutputs for sys in self.syslist) + \
self.input_offset[subsys_index]
return [output_offset + i for i in output_indices], gain
def _find_system(self, name):
return self.syslist_index.get(name, None)
def set_connect_map(self, connect_map):
"""Set the connection map for an interconnected I/O system.
Parameters
----------
connect_map : 2D array
Specify the matrix that will be used to multiply the vector of
subsystem outputs to obtain the vector of subsystem inputs.
"""
# Make sure the connection map is the right size
if connect_map.shape != self.connect_map.shape:
ValueError("Connection map is not the right shape")
self.connect_map = connect_map
def set_input_map(self, input_map):
"""Set the input map for an interconnected I/O system.
Parameters
----------
input_map : 2D array
Specify the matrix that will be used to multiply the vector of
system inputs to obtain the vector of subsystem inputs. These
values are added to the inputs specified in the connection map.
"""
# Figure out the number of internal inputs
ninputs = sum(sys.ninputs for sys in self.syslist)
# Make sure the input map is the right size
if input_map.shape[0] != ninputs:
ValueError("Input map is not the right shape")
self.input_map = input_map
self.ninputs = input_map.shape[1]
def set_output_map(self, output_map):
"""Set the output map for an interconnected I/O system.
Parameters
----------
output_map : 2D array
Specify the matrix that will be used to multiply the vector of
subsystem outputs concatenated with subsystem inputs to obtain
the vector of system outputs.
"""
# Figure out the number of internal inputs and outputs
ninputs = sum(sys.ninputs for sys in self.syslist)
noutputs = sum(sys.noutputs for sys in self.syslist)
# Make sure the output map is the right size
if output_map.shape[1] == noutputs:
# For backward compatibility, add zeros to the end of the array
output_map = np.concatenate(
(output_map,
np.zeros((output_map.shape[0], ninputs))),
axis=1)
if output_map.shape[1] != noutputs + ninputs:
ValueError("Output map is not the right shape")
self.output_map = output_map
self.noutputs = output_map.shape[0]
def unused_signals(self):
"""Find unused subsystem inputs and outputs
Returns
-------
unused_inputs : dict
A mapping from tuple of indices (isys, isig) to string
'{sys}.{sig}', for all unused subsystem inputs.
unused_outputs : dict
A mapping from tuple of indices (osys, osig) to string
'{sys}.{sig}', for all unused subsystem outputs.
"""
used_sysinp_via_inp = np.nonzero(self.input_map)[0]
used_sysout_via_out = np.nonzero(self.output_map)[1]
used_sysinp_via_con, used_sysout_via_con = np.nonzero(self.connect_map)
used_sysinp = set(used_sysinp_via_inp) | set(used_sysinp_via_con)
used_sysout = set(used_sysout_via_out) | set(used_sysout_via_con)
nsubsysinp = sum(sys.ninputs for sys in self.syslist)
nsubsysout = sum(sys.noutputs for sys in self.syslist)
unused_sysinp = sorted(set(range(nsubsysinp)) - used_sysinp)
unused_sysout = sorted(set(range(nsubsysout)) - used_sysout)
inputs = [(isys, isig, f'{sys.name}.{sig}')
for isys, sys in enumerate(self.syslist)
for sig, isig in sys.input_index.items()]
outputs = [(isys, isig, f'{sys.name}.{sig}')