control.InterconnectedSystem

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

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 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 interconnect() should be used to create an interconnected I/O system since it performs additional argument processing and checking.

Methods

check_unused_signals	Check for unused subsystem inputs and outputs
connection_table	Print table of connections inside an interconnected system model.
copy	Make a copy of an input/output system
dynamics	Compute the dynamics of a differential or difference equation.
feedback	Feedback interconnection between two input/output 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 an 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)

Add two input/output systems (parallel interconnection)

__call__(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’].

__mul__(other)

Multiply two input/output systems (series interconnection)

__neg__()

Negate an input/output system (rescale)

__radd__(other)

Parallel addition of input/output system to a compatible object.

__rmul__(other)

Pre-multiply an input/output systems by a scalar/matrix

__rsub__(other)

Parallel subtraction of I/O system to a compatible object.

__sub__(other)

Subtract two input/output systems (parallel interconnection)

__truediv__(other)

Division of input/output system (by scalar or array)

check_unused_signals(ignore_inputs=None, ignore_outputs=None, warning=True)

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_inputs (list 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_outputs (list 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.

Returns

• dropped_inputs (list of tuples) – A list of the dropped input signals, with each element of the list in the form of (isys, isig).

• dropped_outputs (list 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)

Print table of connections inside an interconnected system model.

Intended primarily for InterconnectedSystems that have been connected implicitly using signal names.

Parameters

• show_names (bool, 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_width (int, 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)

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.

dynamics(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]

Return type

ndarray

feedback(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

Return type

InputOutputSystem

Raises

ValueError – if the inputs, outputs, or timebases of the systems are incompatible.

find_input(name)

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

find_inputs(name_list)

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

find_output(name)

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

find_outputs(name_list)

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

find_state(name)

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

find_states(name_list)

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

isctime(strict=False)

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

Parameters

• sys (Named I/O system) – System to be checked

• strict (bool, optional) – If strict is True, make sure that timebase is not None. Default is False.

isdtime(strict=False)

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

Parameters

strict (bool, optional) – If strict is True, make sure that timebase is not None. Default is False.

issiso()

Check to see if a system is single input, single output.

linearize(x0, u0, t=0, params=None, eps=1e-06, 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 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)

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

Return type

ndarray

set_connect_map(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.

set_input_map(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.

set_inputs(inputs, prefix='u')

Set the number/names of the system inputs.

Parameters

• inputs (int, list of str, or None) – Description of the system inputs. This can be given as an integer count or as a list of strings that name the individual signals. If an integer count is specified, the names of the signal will be of the form u[i] (where the prefix u can be changed using the optional prefix parameter).

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

set_output_map(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.

set_outputs(outputs, prefix='y')

Set the number/names of the system outputs.

Parameters

• outputs (int, list of str, or None) – Description of the system outputs. This can be given as an integer count or as a list of strings that name the individual signals. If an integer count is specified, the names of the signal will be of the form u[i] (where the prefix u can be changed using the optional prefix parameter).

• prefix (string, optional) – If outputs is an integer, create the names of the states using the given prefix (default = ‘y’). The names of the input will be of the form prefix[i].

set_states(states, prefix='x')

Set the number/names of the system states.

Parameters

• states (int, list of str, or None) – Description of the system states. This can be given as an integer count or as a list of strings that name the individual signals. If an integer count is specified, the names of the signal will be of the form u[i] (where the prefix u can be changed using the optional prefix parameter).

• prefix (string, optional) – If states is an integer, create the names of the states using the given prefix (default = ‘x’). The names of the input will be of the form prefix[i].

unused_signals()

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.

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

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

Parameters

• name (str, optional) – New system name.

• inputs (list 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.

• outputs (list of str, int, or None, optional) – Description of output signals; defaults to y[i].

• states (int, list of str, int, or None, optional) – Description of system states; defaults to x[i].