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2418 lines (2007 loc) · 99.2 KB
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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 .statesp import StateSpace, tf2ss, _convert_to_statespace
from .timeresp import _check_convert_array, _process_time_response
from .lti import isctime, isdtime, common_timebase
from . import config
__all__ = ['InputOutputSystem', 'LinearIOSystem', 'NonlinearIOSystem',
'InterconnectedSystem', 'LinearICSystem', 'input_output_response',
'find_eqpt', 'linearize', 'ss2io', 'tf2io', 'interconnect',
'summing_junction']
# Define module default parameter values
_iosys_defaults = {
'iosys.state_name_delim': '_',
'iosys.duplicate_system_name_prefix': '',
'iosys.duplicate_system_name_suffix': '$copy',
'iosys.linearized_system_name_prefix': '',
'iosys.linearized_system_name_suffix': '$linearized'
}
class InputOutputSystem(object):
"""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.
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.
"""
idCounter = 0
def name_or_default(self, name=None):
if name is None:
name = "sys[{}]".format(InputOutputSystem.idCounter)
InputOutputSystem.idCounter += 1
return name
def __init__(self, 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: :class:`~control.LinearICSystem`,
:class:`~control.LinearIOSystem`, :class:`~control.NonlinearIOSystem`,
:class:`~control.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
-------
InputOutputSystem
Input/output system object
"""
# Store the input arguments
# default parameters
self.params = params.copy()
# timebase
self.dt = kwargs.get('dt', config.defaults['control.default_dt'])
# system name
self.name = self.name_or_default(name)
# Parse and store the number of inputs, outputs, and states
self.set_inputs(inputs)
self.set_outputs(outputs)
self.set_states(states)
def __repr__(self):
return self.name if self.name is not None else str(type(self))
def __str__(self):
"""String representation of an input/output system"""
str = "System: " + (self.name if self.name else "(None)") + "\n"
str += "Inputs (%s): " % self.ninputs
for key in self.input_index:
str += key + ", "
str += "\nOutputs (%s): " % self.noutputs
for key in self.output_index:
str += key + ", "
str += "\nStates (%s): " % self.nstates
for key in self.state_index:
str += key + ", "
return str
def __mul__(sys2, sys1):
"""Multiply two input/output systems (series interconnection)"""
if isinstance(sys1, (int, float, np.number)):
# TODO: Scale the output
raise NotImplemented("Scalar multiplication not yet implemented")
elif isinstance(sys1, np.ndarray):
# TODO: Post-multiply by a matrix
raise NotImplemented("Matrix multiplication not yet implemented")
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"""
if isinstance(sys2, InputOutputSystem):
# Both systems are InputOutputSystems => use __mul__
return InputOutputSystem.__mul__(sys2, sys1)
elif isinstance(sys2, (int, float, np.number)):
# TODO: Scale the output
raise NotImplemented("Scalar multiplication not yet implemented")
elif isinstance(sys2, np.ndarray):
# TODO: Post-multiply by a matrix
raise NotImplemented("Matrix multiplication not yet implemented")
elif isinstance(sys2, StateSpace):
# TODO: Should eventuall preserve LinearIOSystem structure
return StateSpace.__mul__(sys2, sys1)
else:
raise TypeError("Unknown I/O system object ", sys1)
def __add__(sys1, sys2):
"""Add two input/output systems (parallel interconnection)"""
# TODO: Allow addition of scalars and matrices
if isinstance(sys2, (int, float, np.number)):
# TODO: Scale the output
raise NotImplemented("Scalar addition not yet implemented")
elif isinstance(sys2, np.ndarray):
# TODO: Post-multiply by a matrix
raise NotImplemented("Matrix addition not yet implemented")
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 different 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
# TODO: add __radd__ to allow postaddition by scalars and matrices
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")
inplist = [(0, i) for i in range(sys.ninputs)]
outlist = [(0, i, -1) for i in range(sys.noutputs)]
# Create a new system to hold the negation
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 _isstatic(self):
"""Check to see if a system is a static system (no states)"""
return self.nstates == 0
# Utility function to parse a list of signals
def _process_signal_list(self, signals, prefix='s'):
if signals is None:
# No information provided; try and make it up later
return None, {}
elif isinstance(signals, int):
# Number of signals given; make up the names
return signals, {'%s[%d]' % (prefix, i): i for i in range(signals)}
elif isinstance(signals, str):
# Single string given => single signal with given name
return 1, {signals: 0}
elif all(isinstance(s, str) for s in signals):
# Use the list of strings as the signal names
return len(signals), {signals[i]: i for i in range(len(signals))}
else:
raise TypeError("Can't parse signal list %s" % str(signals))
# Find a signal by name
def _find_signal(self, name, sigdict): return sigdict.get(name, None)
# 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, params={}):
"""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`.
"""
NotImplemented("Evaluation not implemented for system of type ",
type(self))
def dynamics(self, 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] : ndarray
"""
return self._rhs(t, x, u)
def _out(self, t, x, u, params={}):
"""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):
"""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 : ndarray
"""
return self._out(t, x, u)
def set_inputs(self, 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]`.
"""
self.ninputs, self.input_index = \
self._process_signal_list(inputs, prefix=prefix)
def set_outputs(self, 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]`.
"""
self.noutputs, self.output_index = \
self._process_signal_list(outputs, prefix=prefix)
def set_states(self, 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]`.
"""
self.nstates, self.state_index = \
self._process_signal_list(states, prefix=prefix)
def find_input(self, name):
"""Find the index for an input given its name (`None` if not found)"""
return self.input_index.get(name, None)
def find_output(self, name):
"""Find the index for an output given its name (`None` if not found)"""
return self.output_index.get(name, None)
def find_state(self, name):
"""Find the index for a state given its name (`None` if not found)"""
return self.state_index.get(name, None)
def issiso(self):
"""Check to see if a system is single input, single output"""
return self.ninputs == 1 and self.noutputs == 1
def feedback(self, 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: 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={}, eps=1e-6,
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
: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.
#
# 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=False),
name=name, **kwargs)
# Set the names the system, inputs, outputs, and states
if copy:
if name is None:
linsys.name = \
config.defaults['iosys.linearized_system_name_prefix'] + \
self.name + \
config.defaults['iosys.linearized_system_name_suffix']
linsys.ninputs, linsys.input_index = self.ninputs, \
self.input_index.copy()
linsys.noutputs, linsys.output_index = \
self.noutputs, self.output_index.copy()
linsys.nstates, linsys.state_index = \
self.nstates, self.state_index.copy()
return linsys
def copy(self, newname=None):
"""Make a copy of an input/output system."""
dup_prefix = config.defaults['iosys.duplicate_system_name_prefix']
dup_suffix = config.defaults['iosys.duplicate_system_name_suffix']
newsys = copy.copy(self)
newsys.name = self.name_or_default(
dup_prefix + self.name + dup_suffix if not newname else newname)
return newsys
class LinearIOSystem(InputOutputSystem, StateSpace):
"""Input/output representation of a linear (state space) system.
This class is used to implementat a system that is a linear state
space system (defined by the StateSpace system object).
"""
def __init__(self, linsys, inputs=None, outputs=None, states=None,
name=None, **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
Parameters
----------
linsys : StateSpace
LTI StateSpace 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).
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
-------
iosys : LinearIOSystem
Linear system represented as an input/output system
"""
if not isinstance(linsys, StateSpace):
raise TypeError("Linear I/O system must be a state space object")
# Look for 'input' and 'output' parameter name variants
inputs = _parse_signal_parameter(inputs, 'input', kwargs)
outputs = _parse_signal_parameter(outputs, 'output', kwargs, end=True)
# Create the I/O system object
super(LinearIOSystem, self).__init__(
inputs=linsys.ninputs, outputs=linsys.noutputs,
states=linsys.nstates, params={}, dt=linsys.dt, name=name)
# Initalize additional state space variables
StateSpace.__init__(self, linsys, remove_useless=False)
# Process input, output, state lists, if given
# Make sure they match the size of the linear system
ninputs, self.input_index = self._process_signal_list(
inputs if inputs is not None else linsys.ninputs, prefix='u')
if ninputs is not None and linsys.ninputs != ninputs:
raise ValueError("Wrong number/type of inputs given.")
noutputs, self.output_index = self._process_signal_list(
outputs if outputs is not None else linsys.noutputs, prefix='y')
if noutputs is not None and linsys.noutputs != noutputs:
raise ValueError("Wrong number/type of outputs given.")
nstates, self.state_index = self._process_signal_list(
states if states is not None else linsys.nstates, prefix='x')
if nstates is not None and linsys.nstates != nstates:
raise ValueError("Wrong number/type of states given.")
def _update_params(self, params={}, 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 = np.dot(self.A, np.reshape(x, (-1, 1))) \
+ np.dot(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 = np.dot(self.C, np.reshape(x, (-1, 1))) \
+ np.dot(self.D, np.reshape(u, (-1, 1)))
return np.array(y).reshape((-1,))
class NonlinearIOSystem(InputOutputSystem):
"""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).
"""
def __init__(self, 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 :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 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 1-D array with shape (nstates,), `u` is a 1-D 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 : NonlinearIOSystem
Nonlinear system represented as an input/output system.
"""
# Look for 'input' and 'output' parameter name variants
inputs = _parse_signal_parameter(inputs, 'input', kwargs)
outputs = _parse_signal_parameter(outputs, 'output', kwargs)
# Store the update and output functions
self.updfcn = updfcn
self.outfcn = outfcn
# Initialize the rest of the structure
dt = kwargs.pop('dt', config.defaults['control.default_dt'])
super(NonlinearIOSystem, self).__init__(
inputs=inputs, outputs=outputs, states=states,
params=params, dt=dt, name=name
)
# Make sure all input arguments got parsed
if kwargs:
raise TypeError("unknown parameters %s" % kwargs)
# 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 = params.copy()
# 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 not 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(sys, None, out, None, squeeze=squeeze)
return out
def _update_params(self, params, warning=False):
# Update the current parameter values
self._current_params = self.params.copy()
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.
"""
def __init__(self, syslist, connections=[], inplist=[], outlist=[],
inputs=None, outputs=None, states=None,
params={}, dt=None, name=None, **kwargs):
"""Create an I/O system from a list of systems + connection info.
The InterconnectedSystem class is used to represent an input/output
system that consists of an interconnection between a set of subystems.
The outputs of each subsystem can be summed together to provide
inputs to other subsystems. The overall system inputs and outputs can
be any subset of subsystem inputs and outputs.
See :func:`~control.interconnect` for a list of parameters.
"""
# Look for 'input' and 'output' parameter name variants
inputs = _parse_signal_parameter(inputs, 'input', kwargs)
outputs = _parse_signal_parameter(outputs, 'output', kwargs, end=True)
# Convert input and output names to lists if they aren't already
if not isinstance(inplist, (list, tuple)):
inplist = [inplist]
if not isinstance(outlist, (list, tuple)):
outlist = [outlist]
# Check to make sure all systems are consistent
self.syslist = syslist
self.syslist_index = {}
nstates = 0
self.state_offset = []
ninputs = 0
self.input_offset = []
noutputs = 0
self.output_offset = []
sysobj_name_dct = {}
sysname_count_dct = {}
for sysidx, sys in enumerate(syslist):
# 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