[Octave-cvsupdate] SF.net SVN: octave:[9470] trunk/octave-forge/extra/control-devel/inst

[<par...@us...>]

Revision: 9470
          http://octave.svn.sourceforge.net/octave/?rev=9470&view=rev
Author:   paramaniac
Date:     2011-12-27 20:41:54 +0000 (Tue, 27 Dec 2011)
Log Message:
-----------
control-devel: doc fixes

Modified Paths:
--------------
    trunk/octave-forge/extra/control-devel/inst/bstmodred.m
    trunk/octave-forge/extra/control-devel/inst/btamodred.m
    trunk/octave-forge/extra/control-devel/inst/cfconred.m
    trunk/octave-forge/extra/control-devel/inst/fwcfconred.m
    trunk/octave-forge/extra/control-devel/inst/hnamodred.m
    trunk/octave-forge/extra/control-devel/inst/spamodred.m

Modified: trunk/octave-forge/extra/control-devel/inst/bstmodred.m
===================================================================
--- trunk/octave-forge/extra/control-devel/inst/bstmodred.m	2011-12-26 21:00:43 UTC (rev 9469)
+++ trunk/octave-forge/extra/control-devel/inst/bstmodred.m	2011-12-27 20:41:54 UTC (rev 9470)
@@ -23,89 +23,25 @@
 ##
 ## Model order reduction by Balanced Stochastic Truncation (BST) method.
 ## The aim of model reduction is to find an LTI system @var{Gr} of order
-## @var{nr} (nr << n) such that the input-output behaviour of @var{Gr}
+## @var{nr} (nr < n) such that the input-output behaviour of @var{Gr}
 ## approximates the one from original system @var{G}.
-## This is motivated by the relation
+##
+## BST is a relative error method which tries to minimize
 ## @iftex
 ## @tex
-## $$ || y - y_r ||_2 = || G - G_r ||_{\\infty} \\ || u ||_2 $$
+## $$ || G^{-1} (G-G_r) ||_{\\infty} = min $$
 ## @end tex
 ## @end iftex
 ## @ifnottex
 ## @example
-## ||y-yr||  = ||G-Gr||    ||u||
-##         2           inf      2
+##    -1
+## ||G  (G-Gr)||    = min
+##              inf
 ## @end example
 ## @end ifnottex
 ##
-## BST is a relative error method which tries to minimize
-## @iftex
-## @math{|| \\Delta_r ||,}
-## @end iftex
-## @ifnottex
-## Deltar,
-## @end ifnottex
-## where
-## @iftex
-## @math{\\Delta_r}
-## @end iftex
-## @ifnottex
-## Deltar
-## @end ifnottex
-## is implicitly defined by
-## @iftex
-## @math{G - G_r = \\Delta_r \\ G.}
-## @end iftex
-## @ifnottex
-## G-Gr = Deltar*G.
-## @end ifnottex
-## For the H-infinity norm, the best approximation problem is
-## unsolved so far.  Nevertheless, balanced truncation and related
-## methods can be used to obtain good approximations using this measure.
 ##
-## Available approximation methods are the accuracy-enhancing square-root (SR)
-## or the balancing-free square-root (BFSR) versions of
-## the Balance & Truncate (BTA) or Singular Perturbation Approximation (SPA) 
-## model reduction methods for the ALPHA-stable part of the system.
 ##
-## Unstable models are handled by separating the stable and unstable
-## parts additively, applying the model reduction only to the stable
-## part and by joining the reduced stable with the original unstable part.
-## The order of the reduced system can be selected by the user or
-## can be determined automatically on the basis of the computed
-## Hankel singular values.
-##
-## For MIMO models, proper scaling of input-output channels is of
-## utmost importance.  This can @strong{not} be done by the equilibration
-## option or the @command{prescale} command because these perform state
-## transformations only.  While enhancing numerics, state transformations
-## have no influence on the input-output behaviour and the magnitude of
-## the corresponding signals.  Since the algorithm calculates the
-## H-infinity norm of these signals, important behaviour of @var{G}
-## could be neglected just because the corresponding signals have smaller
-## numbers than those of other, less important effects of @var{G}.
-##
-## BST is often suitable to perform model reduction in order to obtain
-## low order design models for controller synthesis.
-##
-## Approximation Properties:
-## @itemize @bullet
-## @item
-## Guaranteed stability of reduced models
-## @item
-## Approximates simultaneously gain and phase
-## @item
-## Preserves non-minimum phase zeros
-## @item
-## Guaranteed a priori error bound
-## @iftex
-## @tex
-## $$ || G^{-1} (G-G_r) ||_{\\infty} \\leq 2 \\sum_{j=r+1}^{n} \\frac{1+\\sigma_j}{1-\\sigma_j} - 1 $$
-## @end tex
-## @end iftex
-## @end itemize
-## 
-##
 ## @strong{Inputs}
 ## @table @var
 ## @item G
@@ -218,6 +154,53 @@
 ## false if @code{G.scaled == true}.
 ## @end table
 ##
+##
+## For the H-infinity norm, the best approximation problem is
+## unsolved so far.  Nevertheless, balanced truncation and related
+## methods can be used to obtain good approximations using this measure.
+##
+## Available approximation methods are the accuracy-enhancing square-root (SR)
+## or the balancing-free square-root (BFSR) versions of
+## the Balance & Truncate (BTA) or Singular Perturbation Approximation (SPA) 
+## model reduction methods for the ALPHA-stable part of the system.
+##
+## Unstable models are handled by separating the stable and unstable
+## parts additively, applying the model reduction only to the stable
+## part and by joining the reduced stable with the original unstable part.
+## The order of the reduced system can be selected by the user or
+## can be determined automatically on the basis of the computed
+## Hankel singular values.
+##
+## For MIMO models, proper scaling of input-output channels is of
+## utmost importance.  This can @strong{not} be done by the equilibration
+## option or the @command{prescale} command because these perform state
+## transformations only.  While enhancing numerics, state transformations
+## have no influence on the input-output behaviour and the magnitude of
+## the corresponding signals.  Since the algorithm calculates the
+## H-infinity norm of these signals, important behaviour of @var{G}
+## could be neglected just because the corresponding signals have smaller
+## numbers than those of other, less important effects of @var{G}.
+##
+## BST is often suitable to perform model reduction in order to obtain
+## low order design models for controller synthesis.
+##
+## Approximation Properties:
+## @itemize @bullet
+## @item
+## Guaranteed stability of reduced models
+## @item
+## Approximates simultaneously gain and phase
+## @item
+## Preserves non-minimum phase zeros
+## @item
+## Guaranteed a priori error bound
+## @iftex
+## @tex
+## $$ || G^{-1} (G-G_r) ||_{\\infty} \\leq 2 \\sum_{j=r+1}^{n} \\frac{1+\\sigma_j}{1-\\sigma_j} - 1 $$
+## @end tex
+## @end iftex
+## @end itemize
+## 
 ## @strong{Algorithm}@*
 ## Uses SLICOT AB09HD by courtesy of
 ## @uref{http://www.slicot.org, NICONET e.V.}

Modified: trunk/octave-forge/extra/control-devel/inst/btamodred.m
===================================================================
--- trunk/octave-forge/extra/control-devel/inst/btamodred.m	2011-12-26 21:00:43 UTC (rev 9469)
+++ trunk/octave-forge/extra/control-devel/inst/btamodred.m	2011-12-27 20:41:54 UTC (rev 9470)
@@ -23,14 +23,14 @@
 ##
 ## Model order reduction by frequency weighted Balanced Truncation Approximation (BTA) method.
 ## The aim of model reduction is to find an LTI system @var{Gr} of order
-## @var{nr} (nr << n) such that the input-output behaviour of @var{Gr}
+## @var{nr} (nr < n) such that the input-output behaviour of @var{Gr}
 ## approximates the one from original system @var{G}.
 ##
 ## BTA is an absolute error method which tries to minimize
 ## @iftex
 ## @tex
 ## $$ || G - G_r ||_{\\infty} = min $$
-## $$ || W_o \\ (G - G_r) \\ W_i ||_{\\infty} = min $$
+## $$ || V \\ (G - G_r) \\ W ||_{\\infty} = min $$
 ## @end tex
 ## @end iftex
 ## @ifnottex
@@ -38,31 +38,13 @@
 ## ||G-Gr||    = min
 ##         inf
 ##
-## ||Wo (G-Gr) Wi||    = min
-##                 inf
+## ||V (G-Gr) W||    = min
+##               inf
 ## @end example
 ## @end ifnottex
-## where @var{Wo} and @var{Wi} denote output and input weightings.
+## where @var{V} and @var{W} denote output and input weightings.
 ##
-## UNSTABLE (from bstmodred)
 ##
-## MIMO (from bstmodred)
-##
-## Approximation Properties:
-## @itemize @bullet
-## @item
-## Guaranteed stability of reduced models
-## @item
-## Lower guaranteed error bound
-## @item
-## Guaranteed a priori error bound
-## @iftex
-## @tex
-## $$ \\sigma_{r+1} \\leq || (G-G_r) ||_{\\infty} \\leq 2 \\sum_{j=r+1}^{n} \\sigma_j $$
-## @end tex
-## @end iftex
-## @end itemize
-##
 ## @strong{Inputs}
 ## @table @var
 ## @item G
@@ -110,15 +92,15 @@
 ## Hankel singular values @var{info.hsv} > @var{tol1} are retained.
 ##
 ## @item 'left', 'output'
-## LTI model of the left/output frequency weighting.
+## LTI model of the left/output frequency weighting @var{V}.
 ## Default value is an identity matrix.
 ##
 ## @item 'right', 'input'
-## LTI model of the right/input frequency weighting.
+## LTI model of the right/input frequency weighting @var{W}.
 ## Default value is an identity matrix.
 ##
 ## @item 'method'
-## Order reduction approach to be used as follows:
+## Approximation method for the L-infinity norm to be used as follows:
 ## @table @var
 ## @item 'sr', 'b'
 ## Use the square-root Balance & Truncate method.
@@ -202,6 +184,26 @@
 ## false if @code{G.scaled == true}.
 ## @end table
 ##
+##
+## UNSTABLE (from bstmodred)
+##
+## MIMO (from bstmodred)
+##
+## Approximation Properties:
+## @itemize @bullet
+## @item
+## Guaranteed stability of reduced models
+## @item
+## Lower guaranteed error bound
+## @item
+## Guaranteed a priori error bound
+## @iftex
+## @tex
+## $$ \\sigma_{r+1} \\leq || (G-G_r) ||_{\\infty} \\leq 2 \\sum_{j=r+1}^{n} \\sigma_j $$
+## @end tex
+## @end iftex
+## @end itemize
+##
 ## @strong{Algorithm}@*
 ## Uses SLICOT AB09ID by courtesy of
 ## @uref{http://www.slicot.org, NICONET e.V.}

Modified: trunk/octave-forge/extra/control-devel/inst/cfconred.m
===================================================================
--- trunk/octave-forge/extra/control-devel/inst/cfconred.m	2011-12-26 21:00:43 UTC (rev 9469)
+++ trunk/octave-forge/extra/control-devel/inst/cfconred.m	2011-12-27 20:41:54 UTC (rev 9470)
@@ -22,6 +22,8 @@
 ## @deftypefnx{Function File} {[@var{Kr}, @var{info}] =} cfconred (@var{G}, @var{F}, @var{L}, @var{ncr}, @var{opt}, @dots{})
 ##
 ## Reduction of state-feedback-observer based controller by coprime factorization (CF). 
+## Given a plant @var{G}, state feedback gain @var{F} and full observer gain @var{L},
+## determine a reduced order controller @var{Kr}.
 ##
 ## @strong{Inputs}
 ## @table @var

Modified: trunk/octave-forge/extra/control-devel/inst/fwcfconred.m
===================================================================
--- trunk/octave-forge/extra/control-devel/inst/fwcfconred.m	2011-12-26 21:00:43 UTC (rev 9469)
+++ trunk/octave-forge/extra/control-devel/inst/fwcfconred.m	2011-12-27 20:41:54 UTC (rev 9470)
@@ -22,6 +22,8 @@
 ## @deftypefnx{Function File} {[@var{Kr}, @var{info}] =} fwcfconred (@var{G}, @var{F}, @var{L}, @var{ncr}, @var{opt}, @dots{})
 ##
 ## Reduction of state-feedback-observer based controller by frequency-weighted coprime factorization (FW CF). 
+## Given a plant @var{G}, state feedback gain @var{F} and full observer gain @var{L},
+## determine a reduced order controller @var{Kr} by using stability enforcing frequency weights.
 ##
 ## @strong{Inputs}
 ## @table @var

Modified: trunk/octave-forge/extra/control-devel/inst/hnamodred.m
===================================================================
--- trunk/octave-forge/extra/control-devel/inst/hnamodred.m	2011-12-26 21:00:43 UTC (rev 9469)
+++ trunk/octave-forge/extra/control-devel/inst/hnamodred.m	2011-12-27 20:41:54 UTC (rev 9470)
@@ -23,14 +23,14 @@
 ##
 ## Model order reduction by frequency weighted optimal Hankel-norm (HNA) method.
 ## The aim of model reduction is to find an LTI system @var{Gr} of order
-## @var{nr} (nr << n) such that the input-output behaviour of @var{Gr}
+## @var{nr} (nr < n) such that the input-output behaviour of @var{Gr}
 ## approximates the one from original system @var{G}.
 ##
 ## HNA is an absolute error method which tries to minimize
 ## @iftex
 ## @tex
 ## $$ || G - G_r ||_H = min $$
-## $$ || W_o \\ (G - G_r) \\ W_i ||_H = min $$
+## $$ || V \\ (G - G_r) \\ W ||_H = min $$
 ## @end tex
 ## @end iftex
 ## @ifnottex
@@ -38,32 +38,13 @@
 ## ||G-Gr||  = min
 ##         H
 ##
-## ||Wo (G-Gr) Wi||  = min
-##                 H
+## ||V (G-Gr) W||  = min
+##               H
 ## @end example
 ## @end ifnottex
-## where @var{Wo} and @var{Wi} denote output and input weightings.
+## where @var{V} and @var{W} denote output and input weightings.
 ##
-## UNSTABLE (from bstmodred)
 ##
-## MIMO (from bstmodred)
-##
-## Approximation Properties:
-## @itemize @bullet
-## @item
-## Guaranteed stability of reduced models
-## @item
-## Lower guaranteed error bound
-## @item
-## Guaranteed a priori error bound
-## @iftex
-## @tex
-## $$ \\sigma_{r+1} \\leq || (G-G_r) ||_{\\infty} \\leq 2 \\sum_{j=r+1}^{n} \\sigma_j $$
-## @end tex
-## @end iftex
-## @end itemize
-##
-##
 ## @strong{Inputs}
 ## @table @var
 ## @item G
@@ -266,6 +247,26 @@
 ## false if @code{G.scaled == true}.
 ## @end table
 ##
+##
+## UNSTABLE (from bstmodred)
+##
+## MIMO (from bstmodred)
+##
+## Approximation Properties:
+## @itemize @bullet
+## @item
+## Guaranteed stability of reduced models
+## @item
+## Lower guaranteed error bound
+## @item
+## Guaranteed a priori error bound
+## @iftex
+## @tex
+## $$ \\sigma_{r+1} \\leq || (G-G_r) ||_{\\infty} \\leq 2 \\sum_{j=r+1}^{n} \\sigma_j $$
+## @end tex
+## @end iftex
+## @end itemize
+##
 ## @strong{Algorithm}@*
 ## Uses SLICOT AB09JD by courtesy of
 ## @uref{http://www.slicot.org, NICONET e.V.}

Modified: trunk/octave-forge/extra/control-devel/inst/spamodred.m
===================================================================
--- trunk/octave-forge/extra/control-devel/inst/spamodred.m	2011-12-26 21:00:43 UTC (rev 9469)
+++ trunk/octave-forge/extra/control-devel/inst/spamodred.m	2011-12-27 20:41:54 UTC (rev 9470)
@@ -22,7 +22,29 @@
 ## @deftypefnx{Function File} {[@var{Gr}, @var{info}] =} spamodred (@var{G}, @var{nr}, @var{opt}, @dots{})
 ##
 ## Model order reduction by frequency weighted Singular Perturbation Approximation (SPA).
+## The aim of model reduction is to find an LTI system @var{Gr} of order
+## @var{nr} (nr < n) such that the input-output behaviour of @var{Gr}
+## approximates the one from original system @var{G}.
 ##
+## SPA is an absolute error method which tries to minimize
+## @iftex
+## @tex
+## $$ || G - G_r ||_{\\infty} = min $$
+## $$ || V \\ (G - G_r) \\ W ||_{\\infty} = min $$
+## @end tex
+## @end iftex
+## @ifnottex
+## @example
+## ||G-Gr||    = min
+##         inf
+##
+## ||V (G-Gr) W||    = min
+##               inf
+## @end example
+## @end ifnottex
+## where @var{V} and @var{W} denote output and input weightings.
+##
+##
 ## @strong{Inputs}
 ## @table @var
 ## @item G
@@ -70,15 +92,15 @@
 ## Hankel singular values @var{info.hsv} > @var{tol1} are retained.
 ##
 ## @item 'left', 'output'
-## LTI model of the left/output frequency weighting.
+## LTI model of the left/output frequency weighting @var{V}.
 ## Default value is an identity matrix.
 ##
 ## @item 'right', 'input'
-## LTI model of the right/input frequency weighting.
+## LTI model of the right/input frequency weighting @var{W}.
 ## Default value is an identity matrix.
 ##
 ## @item 'method'
-## Order reduction approach to be used as follows:
+## Approximation method for the L-infinity norm to be used as follows:
 ## @table @var
 ## @item 'sr', 's'
 ## Use the square-root Singular Perturbation Approximation method.

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