def balred(sys, orders, method='truncate', alpha=None):
"""
Balanced reduced order model of sys of a given order.
States are eliminated based on Hankel singular value.
If sys has unstable modes, they are removed, the
balanced realization is done on the stable part, then
reinserted in accordance with the reference below.
Reference: Hsu,C.S., and Hou,D., 1991,
Reducing unstable linear control systems via real Schur transformation.
Electronics Letters, 27, 984-986.
Parameters
----------
sys: StateSpace
Original system to reduce
orders: integer or array of integer
Desired order of reduced order model (if a vector, returns a vector
of systems)
method: string
Method of removing states, either ``'truncate'`` or ``'matchdc'``.
alpha: float
Redefines the stability boundary for eigenvalues of the system matrix A.
By default for continuous-time systems, alpha <= 0 defines the stability
boundary for the real part of A's eigenvalues and for discrete-time
systems, 0 <= alpha <= 1 defines the stability boundary for the modulus
of A's eigenvalues. See SLICOT routines AB09MD and AB09ND for more
information.
Returns
-------
rsys: StateSpace
A reduced order model or a list of reduced order models if orders is a list
Raises
------
ValueError
* if `method` is not ``'truncate'`` or ``'matchdc'``
ImportError
if slycot routine ab09ad, ab09md, or ab09nd is not found
ValueError
if there are more unstable modes than any value in orders
Examples
--------
>>> rsys = balred(sys, orders, method='truncate')
"""
if method != 'truncate' and method != 'matchdc':
raise ValueError("supported methods are 'truncate' or 'matchdc'")
elif method == 'truncate':
try:
from slycot import ab09md, ab09ad
except ImportError:
raise ControlSlycot(
"can't find slycot subroutine ab09md or ab09ad")
elif method == 'matchdc':
try:
from slycot import ab09nd
except ImportError:
raise ControlSlycot("can't find slycot subroutine ab09nd")
#Check for ss system object, need a utility for this?
#TODO: Check for continous or discrete, only continuous supported right now
# if isCont():
# dico = 'C'
# elif isDisc():
# dico = 'D'
# else:
dico = 'C'
job = 'B' # balanced (B) or not (N)
equil = 'N' # scale (S) or not (N)
if alpha is None:
if dico == 'C':
alpha = 0.
elif dico == 'D':
alpha = 1.
rsys = [] #empty list for reduced systems
#check if orders is a list or a scalar
try:
order = iter(orders)
except TypeError: #if orders is a scalar
orders = [orders]
for i in orders:
n = np.size(sys.A, 0)
m = np.size(sys.B, 1)
p = np.size(sys.C, 0)
if method == 'truncate':
#check system stability
if np.any(np.linalg.eigvals(sys.A).real >= 0.0):
#unstable branch
Nr, Ar, Br, Cr, Ns, hsv = ab09md(dico,
job,
equil,
n,
m,
p,
sys.A,
sys.B,
sys.C,
alpha=alpha,
nr=i,
tol=0.0)
else:
#stable branch
Nr, Ar, Br, Cr, hsv = ab09ad(dico,
job,
equil,
n,
m,
p,
sys.A,
sys.B,
sys.C,
nr=i,
tol=0.0)
rsys.append(StateSpace(Ar, Br, Cr, sys.D))
elif method == 'matchdc':
Nr, Ar, Br, Cr, Dr, Ns, hsv = ab09nd(dico,
job,
equil,
n,
m,
p,
sys.A,
sys.B,
sys.C,
sys.D,
alpha=alpha,
nr=i,
tol1=0.0,
tol2=0.0)
rsys.append(StateSpace(Ar, Br, Cr, Dr))
#if orders was a scalar, just return the single reduced model, not a list
if len(orders) == 1:
return rsys[0]
#if orders was a list/vector, return a list/vector of systems
else:
return rsys
def balred(sys, orders, method='truncate', alpha=None):
"""
Balanced reduced order model of sys of a given order.
States are eliminated based on Hankel singular value.
If sys has unstable modes, they are removed, the
balanced realization is done on the stable part, then
reinserted in accordance with the reference below.
Reference: Hsu,C.S., and Hou,D., 1991,
Reducing unstable linear control systems via real Schur transformation.
Electronics Letters, 27, 984-986.
Parameters
----------
sys: StateSpace
Original system to reduce
orders: integer or array of integer
Desired order of reduced order model (if a vector, returns a vector
of systems)
method: string
Method of removing states, either ``'truncate'`` or ``'matchdc'``.
alpha: float
Redefines the stability boundary for eigenvalues of the system matrix A.
By default for continuous-time systems, alpha <= 0 defines the stability
boundary for the real part of A's eigenvalues and for discrete-time
systems, 0 <= alpha <= 1 defines the stability boundary for the modulus
of A's eigenvalues. See SLICOT routines AB09MD and AB09ND for more
information.
Returns
-------
rsys: StateSpace
A reduced order model or a list of reduced order models if orders is a list
Raises
------
ValueError
* if `method` is not ``'truncate'`` or ``'matchdc'``
ImportError
if slycot routine ab09ad, ab09md, or ab09nd is not found
ValueError
if there are more unstable modes than any value in orders
Examples
--------
>>> rsys = balred(sys, orders, method='truncate')
"""
if method!='truncate' and method!='matchdc':
raise ValueError("supported methods are 'truncate' or 'matchdc'")
elif method=='truncate':
try:
from slycot import ab09md, ab09ad
except ImportError:
raise ControlSlycot("can't find slycot subroutine ab09md or ab09ad")
elif method=='matchdc':
try:
from slycot import ab09nd
except ImportError:
raise ControlSlycot("can't find slycot subroutine ab09nd")
#Check for ss system object, need a utility for this?
#TODO: Check for continous or discrete, only continuous supported right now
# if isCont():
# dico = 'C'
# elif isDisc():
# dico = 'D'
# else:
dico = 'C'
job = 'B' # balanced (B) or not (N)
equil = 'N' # scale (S) or not (N)
if alpha is None:
if dico == 'C':
alpha = 0.
elif dico == 'D':
alpha = 1.
rsys = [] #empty list for reduced systems
#check if orders is a list or a scalar
try:
order = iter(orders)
except TypeError: #if orders is a scalar
orders = [orders]
for i in orders:
n = np.size(sys.A,0)
m = np.size(sys.B,1)
p = np.size(sys.C,0)
if method == 'truncate':
#check system stability
if np.any(np.linalg.eigvals(sys.A).real >= 0.0):
#unstable branch
Nr, Ar, Br, Cr, Ns, hsv = ab09md(dico,job,equil,n,m,p,sys.A,sys.B,sys.C,alpha=alpha,nr=i,tol=0.0)
else:
#stable branch
Nr, Ar, Br, Cr, hsv = ab09ad(dico,job,equil,n,m,p,sys.A,sys.B,sys.C,nr=i,tol=0.0)
rsys.append(StateSpace(Ar, Br, Cr, sys.D))
elif method == 'matchdc':
Nr, Ar, Br, Cr, Dr, Ns, hsv = ab09nd(dico,job,equil,n,m,p,sys.A,sys.B,sys.C,sys.D,alpha=alpha,nr=i,tol1=0.0,tol2=0.0)
rsys.append(StateSpace(Ar, Br, Cr, Dr))
#if orders was a scalar, just return the single reduced model, not a list
if len(orders) == 1:
return rsys[0]
#if orders was a list/vector, return a list/vector of systems
else:
return rsys