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Updates to balred() and gram() #118

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Merged
slivingston merged 2 commits into from
Jan 20, 2017
Merged

Updates to balred() and gram() #118

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9d840b8
balred() now has 'matchdc' option and may handle unstable systems and…
mdclemen Jan 6, 2017
4815cf0
Updated docstring for balred to remove abbreviations and better descr…
mdclemen Jan 19, 2017
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28 changes: 17 additions & 11 deletions control/modelsimp.py
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Original file line number Diff line number Diff line change
Expand Up @@ -203,7 +203,7 @@ def balred(sys, orders, method='truncate', alpha=None):
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 IAW reference below.
reinserted in accordance with the reference below.

Reference: Hsu,C.S., and Hou,D., 1991,
Reducing unstable linear control systems via real Schur transformation.
Expand All @@ -219,12 +219,12 @@ def balred(sys, orders, method='truncate', alpha=None):
method: string
Method of removing states, either ``'truncate'`` or ``'matchdc'``.
alpha: float
Specifies the alpha-stability boundary for the eigenvalues
of the state dynamics matrix A. For a continuous-time
system, alpha <= 0 is the boundary value for the real parts
of eigenvalues, while for a discrete-time system, 0 <= alpha <= 1
represents the boundary value for the moduli of eigenvalues.
The alpha-stability domain does not include the boundary.
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

@slivingston slivingston Jan 20, 2017

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While resolving the merge conflict, I added a space here after the .. So, now it reads "...eigenvalues. See SLICOT...".

information.

Returns
-------
Expand All @@ -250,14 +250,14 @@ def balred(sys, orders, method='truncate', alpha=None):
raise ValueError("supported methods are 'truncate' or 'matchdc'")
elif method=='truncate':
try:
from slycot import ab09md
from slycot import ab09md, ab09ad
except ImportError:
raise ControlSlycot("can't find slycot subroutine ab09md")
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")
raise ControlSlycot("can't find slycot subroutine ab09nd")

#Check for ss system object, need a utility for this?

Expand Down Expand Up @@ -289,7 +289,13 @@ def balred(sys, orders, method='truncate', alpha=None):
m = np.size(sys.B,1)
p = np.size(sys.C,0)
if method == 'truncate':
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)
#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':
Expand Down