MIMOStateSpace

Defined in module: wield.control.MIMO.ss.MIMOStateSpace

class MIMOStateSpace(*args, A=None, B=None, C=None, D=None, E=None, inputs=None, outputs=None, inout=None, hermitian=True, time_symm=False, dt=None, fiducial_rtol=None, fiducial_atol=None, algorithm_choices=None, algorithm_ranking=None)

Bases: BareStateSpaceUser, MIMO

State space class to represent MIMO Transfer functions using dense matrix representations

This class allows both string-based and number based indexing

inputs and outputs can either be a list of names or a dictionary of names to indices.

inputs and outputs can contain overlapping indices

__init__(*args, A=None, B=None, C=None, D=None, E=None, inputs=None, outputs=None, inout=None, hermitian=True, time_symm=False, dt=None, fiducial_rtol=None, fiducial_atol=None, algorithm_choices=None, algorithm_ranking=None)

Form a MIMO LTI system from statespace matrices.

There are lots of ways to create LTI systems. From the arguments

Methods

L2_norm(**kwargs)
Linf_norm(**kwargs)
__init__(*args[, A, B, C, D, E, inputs, ...])	Form a MIMO LTI system from statespace matrices.
balance([inputs, outputs])	Balance the system matrix.
balanceABC(**kwargs)
balance_and_truncate(**kwargs)	TODO rename as Gramian order reduction
block_diagonalize(**kwargs)
constraint([outputs, matrix])	Adds an output constraint to the system and returns the altered system
constraints([output_matrix])	Adds multiple output constraints to the system and returns the altered system
dissect(*, ilists, inames, olists, onames)	This implements the dissection interface to break the statespace into blocks.
dissectB(iname)
dissectC(oname)
dissectD(iname, oname)
extend_io(*[, inputs, outputs, overwrite])	Extends individual inputs or outputs with shaped SISO statespaces, single gains, or defaults to gain of 1.
feedback_connect(*[, connections, gain])	Feedback linkage for a single statespace.
fresponse(*[, f, w, s])
grammian_order_reduction([inputs, outputs])	Balance the system matrix.
inverse(inputs, outputs)	Creates the inverse between the set of inputs and outputs.
minreal([job, scale, rescale_in, ...])
namespace(ns)	prepend a namespace to all inputs and outputs and return the new system
permute_UT(**kwargs)	TODO remove
print_nonzero()
reduceE(**kwargs)
reduceE2(**kwargs)
reduceE3(**kwargs)
rename(renames[, which])	Rename inputs and outputs of the statespace and return the new systems
rename_inputs(renames)
rename_outputs(renames)
rescale()
scale_io([inputs, outputs, scale_in, scale_out])	Balance the system matrix.
schur_form(**kwargs)
secondaries([outputs])	Return a new system with additional inputs and outputs created from the names of the originals
series_connect(*[, input_connections, ...])	Like feedback but extends inputs and outputs through gain or gain systems in series
set_algorithm_choices(algorithm_choices)
similarity_diagonal(D, **kw)
similarity_triangular_left(S, **kw)
similarity_triangular_right(S, **kw)
siso(row, col)	convert a single output (row) and input (col) into a SISO representation
stochastic_balance_and_truncate(**kwargs)
topological_sort(**kwargs)

Attributes

A
ABCD
ABCDE
ABCDe
AE
Ae
B
C
D
E
algorithm_choices
algorithm_ranking
as_controlLTI
dt
e
hermitian
input_dissections_byname
isEeye
output_dissections_byname
p
poles
structure_flags
time_symm

property input_dissections_byname

property output_dissections_byname

secondaries(outputs=None)

Return a new system with additional inputs and outputs created from the names of the originals

Properly implementing should use a topological sort on inputs and outputs to check for cycles and ensure that the index dependency is resolvable

siso(row, col)

convert a single output (row) and input (col) into a SISO representation

dissect(*, ilists, inames, olists, onames)

This implements the dissection interface to break the statespace into blocks. This is useful for a number of advanced control synthesis and analysis routines that depend on categories of input and output blocks

dissectB(iname)

dissectC(oname)

dissectD(iname, oname)

namespace(ns)

prepend a namespace to all inputs and outputs and return the new system

TODO: rename this as prefix

rename(renames, which='both')

Rename inputs and outputs of the statespace and return the new systems

renames: dictionary mapping from:to name pairs or a function(from) -> to which: can be “inputs”, “outputs”, or “both” (the default).

rename_inputs(renames)

rename_outputs(renames)

fresponse(*, f=None, w=None, s=None, **kwargs)

balance(inputs=None, outputs=None, **kwargs)

Balance the system matrix.

TODO: Document

grammian_order_reduction(inputs=None, outputs=None, **kwargs)

Balance the system matrix.

TODO: Document

scale_io(inputs=None, outputs=None, scale_in=None, scale_out=None)

Balance the system matrix.

TODO: Document

constraint(outputs=None, matrix=None)

Adds an output constraint to the system and returns the altered system

outputs: this is a list of outputs which establishes an order matrix: this is a matrix for the list of outputs which adds the system constraint G:=matrix -> G @ C @ x = 0 by augmenting the A and E matrices

constraints(output_matrix=[])

Adds multiple output constraints to the system and returns the altered system

output_matrix is a list of output, matrix pairs. This function is equivalent to calling constraint many times with the list, but is faster to perform all at once

inverse(inputs, outputs)

Creates the inverse between the set of inputs and outputs. the size of inputs and outputs must be the same.

series_connect(*, input_connections=None, output_connections=None, gain=1)

Like feedback but extends inputs and outputs through gain or gain systems in series

the gain terms can be SISO systems, StateSpaceRaw, D, ABCD, or ABCDE blocks

extend_io(*, inputs=[], outputs=[], overwrite=False)

Extends individual inputs or outputs with shaped SISO statespaces, single gains, or defaults to gain of 1.

Parameters:

• inputs (list) – list of tuples describing the inputs to extend. Each tuple is a (newname, oldname, gain) triple. The gain term can be ignored and will default to 1 if not included. The gain term can be a number or a SISO system.

• outputs (list) – list of tuples describing the outputs to extend. Each tuple is a (newname, oldname, gain) triple. The gain term can be ignored and will default to 1 if not included. The gain term can be a number or a SISO system.

each tuple can instead be a dictionary with the following arguments inside

new (str): old (str): gain (SISO or Number, optional): overwrite (bool, False): if a newname overlaps with an existing name, it will drop the existing name and replace it with

the new one which this is True. Otherwise (default) name clashes throw an error. This can be used to rename outputs.

rename (bool): rename the old to the new after applying the gain.

for inputs, the newname will pass through the gain and plug into the oldname. For outputs, the oldname output will pass through the gain to form the newname output.

TODO: support vector IO TODO: example

feedback_connect(*, connections=None, gain=1, **kw)

Feedback linkage for a single statespace.

connections is a list of row, col pairs or row,col,gain tuples

gain is the connection gain to apply. It can be a scalar or a matrix

TODO: allow gain to be a SISO response, StateSpaceRaw, D, ABCD, or ABCDE blocks TODO: add a feedback_connectE TODO: automatic conditioning

property A

property ABCD

property ABCDE

property ABCDe

property AE

property Ae

property B

property C

property D

property E

L2_norm(**kwargs)

Linf_norm(**kwargs)

property algorithm_choices

property algorithm_ranking

property as_controlLTI

balanceABC(**kwargs)

balance_and_truncate(**kwargs)

TODO rename as Gramian order reduction

block_diagonalize(**kwargs)

property dt

property e

property hermitian

property isEeye

minreal(job='minimal', scale=True, rescale_in=None, rescale_out=None, tol=None)

property p

permute_UT(**kwargs)

TODO remove

property poles

print_nonzero()

reduceE(**kwargs)

reduceE2(**kwargs)

reduceE3(**kwargs)

rescale()

schur_form(**kwargs)

set_algorithm_choices(algorithm_choices)

similarity_diagonal(D, **kw)

similarity_triangular_left(S, **kw)

similarity_triangular_right(S, **kw)

stochastic_balance_and_truncate(**kwargs)

property structure_flags

property time_symm

topological_sort(**kwargs)