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[Octave-cvsupdate] SF.net SVN: octave:[8429] trunk/octave-forge/main/control/devel
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From: <par...@us...> - 2011-08-02 15:28:26
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Revision: 8429
http://octave.svn.sourceforge.net/octave/?rev=8429&view=rev
Author: paramaniac
Date: 2011-08-02 15:28:20 +0000 (Tue, 02 Aug 2011)
Log Message:
-----------
control: touch up ncfsyn and example
Modified Paths:
--------------
trunk/octave-forge/main/control/devel/MDSSystem.m
trunk/octave-forge/main/control/devel/ncfsyn/ncfsyn.m
Modified: trunk/octave-forge/main/control/devel/MDSSystem.m
===================================================================
--- trunk/octave-forge/main/control/devel/MDSSystem.m 2011-08-01 21:45:22 UTC (rev 8428)
+++ trunk/octave-forge/main/control/devel/MDSSystem.m 2011-08-02 15:28:20 UTC (rev 8429)
@@ -1,16 +1,16 @@
+% ===============================================================================
+% Robust Control of a Mass-Damper-Spring System
+% ===============================================================================
+% Reference: Gu, D.W., Petkov, P.Hr. and Konstantinov, M.M.
+% Robust Control Design with Matlab, Springer 2005
+% ===============================================================================
+
% Tabula Rasa
clear all, close all, clc
-% Nominal Values
-m_nom = 3; % Mass
-c_nom = 1; % Damping Coefficient
-k_nom = 2; % Spring Stiffness
-
-% Perturbations
-p_m = 0.4; % 40% uncertainty in the mass
-p_c = 0.2; % 20% uncertainty in the damping coefficient
-p_k = 0.3; % 30% uncertainty in the spring stiffness
-
+% ===============================================================================
+% System Model
+% ===============================================================================
% +---------------+
% | d_m 0 0 |
% +-----| 0 d_c 0 |<----+
@@ -23,6 +23,16 @@
% u ----->| |-----> y
% +---------------+
+% Nominal Values
+m_nom = 3; % Mass
+c_nom = 1; % Damping Coefficient
+k_nom = 2; % Spring Stiffness
+
+% Perturbations
+p_m = 0.4; % 40% uncertainty in the mass
+p_c = 0.2; % 20% uncertainty in the damping coefficient
+p_k = 0.3; % 30% uncertainty in the spring stiffness
+
% State-Space Representation
A = [ 0, 1
-k_nom/m_nom, -c_nom/m_nom ];
@@ -51,12 +61,36 @@
D22 = [ 0 ];
-inname = {"u_m", "u_c", "u_k", "u"}; % Input Names
-outname = {"y_m", "y_c", "y_k", "y"}; % Output Names
+inname = {'u_m', 'u_c', 'u_k', 'u'}; % Input Names
+outname = {'y_m', 'y_c', 'y_k', 'y'}; % Output Names
G_nom = ss (A, [B1, B2], [C1; C2], [D11, D12; D21, D22], \
- "inname", inname, "outname", outname);
+ 'inputname', inname, 'outputname', outname);
+
+% ===============================================================================
+% Frequency Analysis of Uncertain System
+% ===============================================================================
+
+% Uncertainties: -1 <= delta_m, delta_c, delta_k <= 1
+[delta_m, delta_c, delta_k] = ndgrid ([-1, 0, 1], [-1, 0, 1], [-1, 0, 1]);
+w = logspace (-1, 1, 100); % Frequency Vector
+figure (1)
+
+for k = 1 : numel (delta_m)
+ Delta = diag ([delta_m(k), delta_c(k), delta_k(k)]);
+ G_per = lft (Delta, G_nom);
+ bode (G_per, w)
+ subplot (2, 1, 1)
+ hold on
+ subplot (2, 1, 2)
+ hold on
+endfor
+
+
+% ===============================================================================
+% Mixed Sensitivity H-infinity Controller Design
+% ===============================================================================
% +-------+
% +--------------------->| W_p |----------> e_p
% | +-------+
@@ -72,11 +106,11 @@
% +-----------------------------------------+
% Weighting Functions
-s = tf ("s");
+s = tf ('s');
W_p = 0.95 * (s^2 + 1.8*s + 10) / (s^2 + 8.0*s + 0.01);
W_u = 10^-2;
-% Suboptimal H-infinity Controller Design
+% Mixed Sensitivity H-infinity Controller Design
G = G_nom(4, 4); % Extract output y and input u
%K = mixsyn (G, W_p, W_u);
%[K, ~, gamma] = mixsyn (G, W_p, W_u)
@@ -91,33 +125,38 @@
% Closed Loop
T = feedback (L);
-figure (1)
+figure (2)
sigma (T)
-figure (2)
+figure (3)
sigma (N)
norm (N, inf)
-figure (3)
+figure (4)
step (T)
-figure (4)
+% ===============================================================================
+% H-infinity Loop-Shaping Design
+% ===============================================================================
-w = logspace (-1, 1, 100);
+W1 = 8 * (2*s + 1) / (0.9*s); % Precompensator
+W2 = 1; % Postcompensator
+factor = 1.1 % Suboptimal Controller
-% Uncertainties
-% -1 <= delta_m, delta_c, delta_k <= 1
-[delta_m, delta_c, delta_k] = ndgrid ([-1, 0, 1], [-1, 0, 1], [-1, 0, 1]);
+% Compute the suboptimal positive feedback controller
+K = ncfsyn (G, W1, W2, factor)
-for k = 1 : numel (delta_1)
- Delta = diag ([delta_m(k), delta_c(k), delta_k(k)]);
- G_per = lft (Delta, G_nom);
- %figure (4)
- bode (G_per, w)
- subplot (2, 1, 1)
- hold on
- subplot (2, 1, 2)
- hold on
-endfor
\ No newline at end of file
+K = -K; % negative feedback controller
+
+% Open Loop
+L = G * K;
+
+% Closed Loop
+T = feedback (L);
+
+figure (5)
+step (T)
+
+% ===============================================================================
Modified: trunk/octave-forge/main/control/devel/ncfsyn/ncfsyn.m
===================================================================
--- trunk/octave-forge/main/control/devel/ncfsyn/ncfsyn.m 2011-08-01 21:45:22 UTC (rev 8428)
+++ trunk/octave-forge/main/control/devel/ncfsyn/ncfsyn.m 2011-08-02 15:28:20 UTC (rev 8429)
@@ -21,13 +21,42 @@
## Compute positive feedback controller using the McFarlane/Glover Loop Shaping Design Procedure.
## Uses SLICOT SB10ID, SB10KD and SB10ZD by courtesy of
## @uref{http://www.slicot.org, NICONET e.V.}
+##
+## @strong{Inputs}
+## @table @var
+## @item G
+## LTI model of plant.
+## @item W1
+## LTI model of precompensator. Model must be SISO or of appropriate size.
+## An identity matrix is taken if @var{W1} is not specified or if an empty model
+## @code{[]} is passed.
+## @item W2
+## LTI model of postcompensator. Model must be SISO or of appropriate size.
+## An identity matrix is taken if @var{W2} is not specified or if an empty model
+## @code{[]} is passed.
+## @item factor
+## @code{factor = 1} implies that an optimal controller is required.
+## @code{factor > 1} implies that a suboptimal controller is required,
+## achieving a performance taht is @var{factor} times less than optimal.
+## Default value is 1.
+## @end table
+##
+## @strong{Outputs}
+## @table @var
+## @item K
+## State-space model of the H-infinity loop-shaping controller.
+## @item N
+## State-space model of the lower LFT of @var{P} and @var{K}.
+## @item gamma
+## L-infinity norm of @var{N}.
+## @end table
## @end deftypefn
## Author: Lukas Reichlin <luk...@gm...>
## Created: July 2011
## Version: 0.1
-% function [K, N, gamma] = ncfsyn (G, W1 = [], W2 = [], factor = 1.0)
+% function [K, N, gamma, info] = ncfsyn (G, W1 = [], W2 = [], factor = 1.0)
function K = ncfsyn (G, W1 = [], W2 = [], factor = 1.0)
if (nargin == 0 || nargin > 4)
@@ -65,7 +94,7 @@
K = W1 * Ks * W2;
- %struct ("Gs", Gs, "Ks", Ks);
+ %struct ("Gs", Gs, "Ks", Ks, "rcond", rcond);
endfunction
@@ -76,12 +105,12 @@
W = ss (eye (s));
else
W = ss (W);
- if (! isstable (W))
- error ("ncfsyn: %s must be stable", inputname (1));
- endif
- if (! isminimumphase (W))
- error ("ncfsyn: %s must be minimum-phase", inputname (1));
- endif
+ %if (! isstable (W))
+ % error ("ncfsyn: %s must be stable", inputname (1));
+ %endif
+ %if (! isminimumphase (W))
+ % error ("ncfsyn: %s must be minimum-phase", inputname (1));
+ %endif
[p, m] = size (W);
if (m == s && p == s) # model is of correct size
return;
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