control.InterconnectedSystem

class control.InterconnectedSystem(syslist, connections=None, inplist=None, outlist=None, params=None, warn_duplicate=None, connection_type=None, **kwargs)[source]

Bases: 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 system 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 interconnect factory function should be used to create an interconnected I/O system since it performs additional argument processing and checking.

Parameters:

syslistlist of NonlinearIOSystem: List of state space systems to interconnect.
connectionslist of connections: Description of the internal connections between the subsystem. See interconnect for details.
inplist, outlistlist of input and output connections: Description of the inputs and outputs for the overall system. See interconnect for details.
inputs, outputs, statesint, list of str or None, optional: Description of the system inputs, outputs, and states. See control.nlsys for more details.
paramsdict, optional: Parameter values for the systems. Passed to the evaluation functions for the system as default values, overriding internal defaults.
connection_typestr: Type of connection: ‘explicit’ (or None) for explicitly listed set of connections, ‘implicit’ for connections made via signal names.

Attributes:

ninputs, noutputs, nstatesint: Number of input, output and state variables.
shapetuple: 2-tuple of I/O system dimension, (noutputs, ninputs).
namestring, optional: System name.
connect_map2D array: Mapping of subsystem outputs to subsystem inputs.
input_map2D array: Mapping of system inputs to subsystem inputs.
output_map2D array: Mapping of (stacked) subsystem outputs and inputs to system outputs.
input_labels, output_labels, state_labelslist of str: Names for the input, output, and state variables.
input_offset, output_offset, state_offsetlist of int: Offset to the subsystem inputs, outputs, and states in the overall system input, output, and state arrays.
syslist_indexdict: Index of the subsystem with key given by the name of the subsystem.

See also

interconnect, NonlinearIOSystem, LinearICSystem

Attributes

`dt`	System timebase.
`input_labels`	List of labels for the input signals.
`ninputs`	Number of system inputs.
`noutputs`	Number of system outputs.
`nstates`	Number of system states.
`output_labels`	List of labels for the output signals.
`repr_format`	String representation format.
`shape`	2-tuple of I/O system dimension, (noutputs, ninputs).
`state_labels`	List of labels for the state signals.

Methods

`__call__`	Evaluate a (static) nonlinearity at a given input value.
`check_unused_signals`	Check for unused subsystem inputs and outputs.
`connection_table`	Table of connections inside an interconnected system.
`copy`	Make a copy of an input/output system.
`dynamics`	Dynamics of a differential or difference equation.
`feedback`	Feedback interconnection between two I/O systems.
`find_input`	Find the index for an input given its name (None if not found).
`find_inputs`	Return list of indices matching input spec (None if not found).
`find_output`	Find the index for a output given its name (None if not found).
`find_outputs`	Return list of indices matching output spec (None if not found).
`find_state`	Find the index for a state given its name (None if not found).
`find_states`	Return list of indices matching state spec (None if not found).
`isctime`	Check to see if a system is a continuous-time system.
`isdtime`	Check to see if a system is a discrete-time system.
`issiso`	Check to see if a system is single input, single output.
`linearize`	Linearize an input/output system at a given state and input.
`output`	Compute the output of the system.
`set_connect_map`	Set the connection map for an interconnected I/O system.
`set_input_map`	Set the input map for an interconnected I/O system.
`set_inputs`	Set the number/names of the system inputs.
`set_output_map`	Set the output map for an interconnected I/O system.
`set_outputs`	Set the number/names of the system outputs.
`set_states`	Set the number/names of the system states.
`unused_signals`	Find unused subsystem inputs and outputs.
`update_names`	Update signal and system names for an I/O system.

__add__(other)[source]: Add two input/output systems (parallel interconnection)

__call__(u, params=None, squeeze=None)[source]

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:

paramsdict, optional: Parameter values for the system. Passed to the evaluation function for the system as default values, overriding internal defaults.
squeezebool, 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'].

__mul__(other)[source]: Multiply two input/output systems (series interconnection)

__neg__()[source]: Negate an input/output system (rescale)

__radd__(other)[source]: Parallel addition of input/output system to a compatible object.

__rmul__(other)[source]: Pre-multiply an input/output systems by a scalar/matrix

__rsub__(other)[source]: Parallel subtraction of I/O system to a compatible object.

__sub__(other)[source]: Subtract two input/output systems (parallel interconnection)

__truediv__(other)[source]: Division of input/output system (by scalar or array)

check_unused_signals(ignore_inputs=None, ignore_outputs=None, print_warning=True)[source]

Check for unused subsystem inputs and outputs.

Check to see if there are any unused signals and return a list of unused input and output signal descriptions. If warning is True and any unused inputs or outputs are found, emit a warning.

Parameters:

ignore_inputslist of input-spec

Subsystem inputs known to be unused. input-spec can be any of:: ‘sig’, ‘sys.sig’, (isys, isig), (‘sys’, isig)

If the ‘sig’ form is used, all subsystem inputs with that name are considered ignored.

ignore_outputslist of output-spec

Subsystem outputs known to be unused. output-spec can be any of:: ‘sig’, ‘sys.sig’, (isys, isig), (‘sys’, isig)

If the ‘sig’ form is used, all subsystem outputs with that name are considered ignored.

print_warningbool, optional

If True, print a warning listing any unused signals.

Returns:

dropped_inputslist of tuples: A list of the dropped input signals, with each element of the list in the form of (isys, isig).
dropped_outputslist of tuples: A list of the dropped output signals, with each element of the list in the form of (osys, osig).

connection_table(show_names=False, column_width=32)[source]

Table of connections inside an interconnected system.

Intended primarily for InterconnectedSystem’s that have been connected implicitly using signal names.

Parameters:

show_namesbool, optional: Instead of printing out the system number, print out the name of each system. Default is False because system name is not usually specified when performing implicit interconnection using interconnect.
column_widthint, optional: Character width of printed columns.

Examples

>>> P = ct.ss(1,1,1,0, inputs='u', outputs='y', name='P')
>>> C = ct.tf(10, [.1, 1], inputs='e', outputs='u', name='C')
>>> L = ct.interconnect([C, P], inputs='e', outputs='y')
>>> L.connection_table(show_names=True) 
signal    | source                        | destination
--------------------------------------------------------------------
e         | input                         | C
u         | C                             | P
y         | P                             | output

copy(name=None, use_prefix_suffix=True)[source]

Make a copy of an input/output system.

A copy of the system is made, with a new name. The name keyword can be used to specify a specific name for the system. If no name is given and use_prefix_suffix is True, the name is constructed by prepending config.defaults['iosys.duplicate_system_name_prefix'] and appending config.defaults['iosys.duplicate_system_name_suffix']. Otherwise, a generic system name of the form ‘sys[<id>]’ is used, where ‘<id>’ is based on an internal counter.

Parameters:

namestr, optional: Name of the newly created system.
use_prefix_suffixbool, optional: If True and name is None, set the name of the new system to the name of the original system with prefix config.defaults['duplicate_system_name_prefix'] and suffix config.defaults['duplicate_system_name_suffix'].

Returns:

InputOutputSystem

dt

System timebase.

dynamics(t, x, u, params=None)[source]

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 a continuous-time system, returns the time derivative:

dx/dt = updfcn(t, x, u[, params])

where updfcn is the system’s (possibly nonlinear) update function. If the system is discrete time, returns the next value of x:

x[t+dt] = updfcn(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:

tfloat: Time at which to evaluate.
xarray_like: Current state.
uarray_like: Current input.
paramsdict, optional: System parameter values.

Returns:

dx/dt or x[t+dt]ndarray

feedback(other=1, sign=-1, params=None)[source]

Feedback interconnection between two I/O systems.

Parameters:

otherInputOutputSystem: System in the feedback path.
signfloat, optional: Gain to use in feedback path. Defaults to -1.
paramsdict, optional: Parameter values for the overall system. Passed to the evaluation functions for the system as default values, overriding defaults for the individual systems.

Returns:

NonlinearIOSystem

find_input(name)[source]

Find the index for an input given its name (None if not found).

Parameters:

namestr: Signal name for the desired input.

Returns:

int: Index of the named input.

find_inputs(name_list)[source]

Return list of indices matching input spec (None if not found).

Parameters:

name_liststr or list of str: List of signal specifications for the desired inputs. A signal can be described by its name or by a slice-like description of the form ‘start:end` where ‘start’ and ‘end’ are signal names. If either is omitted, it is taken as the first or last signal, respectively.

Returns:

list of int: List of indices for the specified inputs.

find_output(name)[source]

Find the index for a output given its name (None if not found).

Parameters:

namestr: Signal name for the desired output.

Returns:

int: Index of the named output.

find_outputs(name_list)[source]

Return list of indices matching output spec (None if not found).

Parameters:

name_liststr or list of str: List of signal specifications for the desired outputs. A signal can be described by its name or by a slice-like description of the form ‘start:end` where ‘start’ and ‘end’ are signal names. If either is omitted, it is taken as the first or last signal, respectively.

Returns:

list of int: List of indices for the specified outputs.

find_state(name)[source]

Find the index for a state given its name (None if not found).

Parameters:

namestr: Signal name for the desired state.

Returns:

int: Index of the named state.

find_states(name_list)[source]

Return list of indices matching state spec (None if not found).

Parameters:

name_liststr or list of str: List of signal specifications for the desired states. A signal can be described by its name or by a slice-like description of the form ‘start:end` where ‘start’ and ‘end’ are signal names. If either is omitted, it is taken as the first or last signal, respectively.

Returns:

list of int: List of indices for the specified states..

property input_labels: List of labels for the input signals.

isctime(strict=False)[source]

Check to see if a system is a continuous-time system.

Parameters:

strictbool, optional: If strict is True, make sure that timebase is not None. Default is False.

isdtime(strict=False)[source]

Check to see if a system is a discrete-time system.

Parameters:

strictbool, optional: If strict is True, make sure that timebase is not None. Default is False.

issiso()[source]: Check to see if a system is single input, single output.

linearize(x0, u0=None, t=0, params=None, eps=1e-06, copy_names=False, **kwargs)[source]

Linearize an input/output system at a given state and input.

Return the linearization of an input/output system at a given operating point (or state and input value) as a StateSpace system. See linearize for complete documentation.

ninputs

Number of system inputs.

noutputs

Number of system outputs.

nstates

Number of system states.

output(t, x, u, params=None)[source]

Compute the output of the system.

Given time t, input u and state x, returns the output of the system:

y = outfcn(t, x, u[, params])

The inputs x and u must be of the correct length.

Parameters:

tfloat: The time at which to evaluate.
xarray_like: Current state.
uarray_like: Current input.
paramsdict, optional: System parameter values.

Returns:

yndarray

property output_labels: List of labels for the output signals.

property repr_format

String representation format.

Format used in creating the representation for the system:

‘info’ : <IOSystemType sysname: [inputs] -> [outputs]>

‘eval’ : system specific, loadable representation

‘latex’ : HTML/LaTeX representation of the object

The default representation for an input/output is set to ‘eval’. This value can be changed for an individual system by setting the repr_format parameter when the system is created or by setting the repr_format property after system creation. Set config.defaults['iosys.repr_format'] to change for all I/O systems or use the repr_format parameter/attribute for a single system.

set_connect_map(connect_map)[source]

Set the connection map for an interconnected I/O system.

Parameters:

connect_map2D array: Specify the matrix that will be used to multiply the vector of subsystem outputs to obtain the vector of subsystem inputs.

set_input_map(input_map)[source]

Set the input map for an interconnected I/O system.

Parameters:

input_map2D 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.

set_inputs(inputs, prefix='u')[source]

Set the number/names of the system inputs.

Parameters:

inputsint, 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).
prefixstring, optional: If inputs is an integer, create the names of the states using the given prefix (default = ‘u’). The names of the input will be of the form ‘prefix[i]’.

set_output_map(output_map)[source]

Set the output map for an interconnected I/O system.

Parameters:

output_map2D 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.

set_outputs(outputs, prefix='y')[source]

Set the number/names of the system outputs.

Parameters:

outputsint, 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 ‘y[i]’ (where the prefix ‘y’ can be changed using the optional prefix parameter).
prefixstring, optional: If outputs is an integer, create the names of the states using the given prefix (default = ‘y’). The names of the input will be of the form ‘prefix[i]’.

set_states(states, prefix='x')[source]

Set the number/names of the system states.

Parameters:

statesint, 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 ‘x[i]’ (where the prefix ‘x’ can be changed using the optional prefix parameter).
prefixstring, 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]’.

property shape: 2-tuple of I/O system dimension, (noutputs, ninputs).

property state_labels: List of labels for the state signals.

unused_signals()[source]

Find unused subsystem inputs and outputs.

Returns:

unused_inputsdict: A mapping from tuple of indices (isys, isig) to string ‘{sys}.{sig}’, for all unused subsystem inputs.
unused_outputsdict: A mapping from tuple of indices (osys, osig) to string ‘{sys}.{sig}’, for all unused subsystem outputs.

update_names([name, inputs, outputs, states])[source]

Update signal and system names for an I/O system.

Parameters:

namestr, optional: New system name.
inputslist of str, int, or None, optional: List of strings that name the individual input signals. If given as an integer or None, signal names default to the form ‘u[i]’. See InputOutputSystem for more information.
outputslist of str, int, or None, optional: Description of output signals; defaults to ‘y[i]’.
statesint, list of str, int, or None, optional: Description of system states; defaults to ‘x[i]’.
input_prefixstring, optional: Set the prefix for input signals. Default = ‘u’.
output_prefixstring, optional: Set the prefix for output signals. Default = ‘y’.
state_prefixstring, optional: Set the prefix for state signals. Default = ‘x’.