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[Octave-cvsupdate] SF.net SVN: octave:[11015] trunk/octave-forge/main/control
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From: <par...@us...> - 2012-09-14 14:31:31
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Revision: 11015
http://octave.svn.sourceforge.net/octave/?rev=11015&view=rev
Author: paramaniac
Date: 2012-09-14 14:31:20 +0000 (Fri, 14 Sep 2012)
Log Message:
-----------
control: quicksave work on further multiplot features
Modified Paths:
--------------
trunk/octave-forge/main/control/inst/__frequency_response__.m
trunk/octave-forge/main/control/inst/bode.m
trunk/octave-forge/main/control/inst/sigma.m
Added Paths:
-----------
trunk/octave-forge/main/control/devel/MDSSystem2.m
Added: trunk/octave-forge/main/control/devel/MDSSystem2.m
===================================================================
--- trunk/octave-forge/main/control/devel/MDSSystem2.m (rev 0)
+++ trunk/octave-forge/main/control/devel/MDSSystem2.m 2012-09-14 14:31:20 UTC (rev 11015)
@@ -0,0 +1,154 @@
+%% -*- texinfo -*-
+%% Robust control of a mass-damper-spring system.
+%% Type @code{which MDSSystem} to locate,
+%% @code{edit MDSSystem} to open and simply
+%% @code{MDSSystem} to run the example file.
+
+% ===============================================================================
+% Robust Control of a Mass-Damper-Spring System Lukas Reichlin August 2011
+% ===============================================================================
+% 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
+
+% ===============================================================================
+% System Model
+% ===============================================================================
+% +---------------+
+% | d_m 0 0 |
+% +-----| 0 d_c 0 |<----+
+% u_m | | 0 0 d_k | | y_m
+% u_c | +---------------+ | y_c
+% u_k | | y_k
+% | +---------------+ |
+% +---->| |-----+
+% | G_nom |
+% 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 ];
+
+B1 = [ 0, 0, 0
+ -p_m, -p_c/m_nom, -p_k/m_nom ];
+
+B2 = [ 0
+ 1/m_nom ];
+
+C1 = [ -k_nom/m_nom, -c_nom/m_nom
+ 0, c_nom
+ k_nom, 0 ];
+
+C2 = [ 1, 0 ];
+
+D11 = [ -p_m, -p_c/m_nom, -p_k/m_nom
+ 0, 0, 0
+ 0, 0, 0 ];
+
+D12 = [ 1/m_nom
+ 0
+ 0 ];
+
+D21 = [ 0, 0, 0 ];
+
+D22 = [ 0 ];
+
+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], ...
+ 'inputname', inname, 'outputname', outname);
+
+G = G_nom(4, 4); % extract output y and input u
+
+
+% ===============================================================================
+% 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]);
+
+% Bode Plots of Perturbed Plants
+w = logspace (-1, 1, 100); % frequency vector
+Delta = arrayfun (@(m, c, k) diag ([m, c, k]), delta_m(:), delta_c(:), delta_k(:), 'uniformoutput', false);
+G_per = cellfun (@lft, Delta, {G_nom}, 'uniformoutput', false);
+
+figure (1)
+bode (G_per{:}, w);
+
+
+% ===============================================================================
+% Mixed Sensitivity H-infinity Controller Design (S over KS Method)
+% ===============================================================================
+% +-------+
+% +--------------------->| W_p |----------> e_p
+% | +-------+
+% | +-------+
+% | +---->| W_u |----------> e_u
+% | | +-------+
+% | | +---------+
+% | | ->| |->
+% r + e | +-------+ u | | G_nom |
+% ----->(+)---+-->| K |----+--->| |----+----> y
+% ^ - +-------+ +---------+ |
+% | |
+% +-----------------------------------------+
+
+% Weighting Functions
+s = tf ('s'); % transfer function variable
+W_p = 0.95 * (s^2 + 1.8*s + 10) / (s^2 + 8.0*s + 0.01); % performance weighting
+W_u = 10^-2; % control weighting
+
+% Synthesis
+K_mix = mixsyn (G, W_p, W_u); % mixed-sensitivity H-infinity synthesis
+
+% Interconnections
+L_mix = G * K_mix; % open loop
+T_mix = feedback (L_mix); % closed loop
+
+
+% ===============================================================================
+% H-infinity Loop-Shaping Design (Normalized Coprime Factor Perturbations)
+% ===============================================================================
+
+% Settings
+W1 = 8 * (2*s + 1) / (0.9*s); % precompensator
+W2 = 1; % postcompensator
+factor = 1.1; % suboptimal controller
+
+% Synthesis
+K_ncf = ncfsyn (G, W1, W2, factor); % positive feedback controller
+
+% Interconnections
+K_ncf = -K_ncf; % negative feedback controller
+L_ncf = G * K_ncf; % open loop
+T_ncf = feedback (L_ncf); % closed loop
+
+% ===============================================================================
+
+% Plotting
+figure (2)
+bode (K_mix, K_ncf) % bode plot
+
+figure (3)
+step (T_mix, 10) % step response for 10 seconds
+
+figure (4)
+step (T_ncf, 10) % step response for 10 seconds
+
+% ===============================================================================
Modified: trunk/octave-forge/main/control/inst/__frequency_response__.m
===================================================================
--- trunk/octave-forge/main/control/inst/__frequency_response__.m 2012-09-14 12:02:15 UTC (rev 11014)
+++ trunk/octave-forge/main/control/inst/__frequency_response__.m 2012-09-14 14:31:20 UTC (rev 11015)
@@ -30,7 +30,7 @@
%endif
sys_idx = cellfun (@isa, args, {"lti"}); # look for LTI models
- w_idx = cellfun (@is_real_vector, args); # look for frequency vectors
+ w_idx = cellfun (@(x) is_real_vector (x) && length (x) > 1, args); # look for frequency vectors
r_idx = cellfun (@iscell, args); # look for frequency ranges {wmin, wmax}
sys_cell = args(sys_idx); # extract LTI models
@@ -50,7 +50,8 @@
error ("frequency_response: invalid cell");
endif
elseif (any (w_idx)) # are there any frequency vectors?
- w = args(w_idx)(end);
+ w = args(w_idx){end};
+ w = repmat ({w}, 1, numel (sys_cell));
else # there are neither frequency ranges nor vectors
w = __frequency_vector__ (sys_cell, wbounds);
endif
Modified: trunk/octave-forge/main/control/inst/bode.m
===================================================================
--- trunk/octave-forge/main/control/inst/bode.m 2012-09-14 12:02:15 UTC (rev 11014)
+++ trunk/octave-forge/main/control/inst/bode.m 2012-09-14 14:31:20 UTC (rev 11015)
@@ -84,7 +84,7 @@
style = varargin(style_idx(style_idx > sys_idx(k) & style_idx <= lim));
mag_args = cat (2, mag_args, w(k), mag_db(k), style);
pha_args = cat (2, pha_args, w(k), pha(k), style);
- legend_args{k} = inputname(sys_idx(k));
+ legend_args{k} = inputname(sys_idx(k)); # watch out for bode (lticell{:})
endfor
subplot (2, 1, 1)
Modified: trunk/octave-forge/main/control/inst/sigma.m
===================================================================
--- trunk/octave-forge/main/control/inst/sigma.m 2012-09-14 12:02:15 UTC (rev 11014)
+++ trunk/octave-forge/main/control/inst/sigma.m 2012-09-14 14:31:20 UTC (rev 11015)
@@ -60,44 +60,56 @@
## Author: Lukas Reichlin <luk...@gm...>
## Created: May 2009
-## Version: 0.6
+## Version: 0.7
-function [sv_r, w_r] = sigma (sys, w = [], resptype = 0)
+function [sv_r, w_r] = sigma (varargin)
- ## TODO: multiplot feature: sigma (sys1, "b", sys2, "r", ...)
-
- if (nargin == 0 || nargin > 3)
+ if (nargin == 0)
print_usage ();
endif
+resptype = 0;
+ [H, w] = __frequency_response__ (varargin, true, resptype, "std", true);
- [H, w] = __frequency_response__ (sys, w, true, resptype, "std", true);
+ sv = cellfun (@(H) cellfun (@svd, H, "uniformoutput", false), H, "uniformoutput", false);
+ sv = cellfun (@(sv) horzcat (sv{:}), sv, "uniformoutput", false);
- sv = cellfun (@svd, H, "uniformoutput", false);
- sv = horzcat (sv{:});
-
if (! nargout) # plot the information
## convert to dB for plotting
- sv_db = 20 * log10 (sv);
+ sv_db = cellfun (@(sv) 20 * log10 (sv), sv, "uniformoutput", false);
- ## determine xlabel
- if (isct (sys))
- xl_str = "Frequency [rad/s]";
- else
- xl_str = sprintf ("Frequency [rad/s] w_N = %g", pi / get (sys, "tsam"));
- endif
+ tmp = cellfun (@isa, varargin, {"lti"});
+ sys_idx = find (tmp);
+ tmp = cellfun (@ischar, varargin);
+ style_idx = find (tmp);
+ len = numel (H);
+ plot_args = {};
+ legend_args = cell (len, 1);
+
+ for k = 1:len
+ if (k == len)
+ lim = nargin;
+ else
+ lim = sys_idx(k+1);
+ endif
+ style = varargin(style_idx(style_idx > sys_idx(k) & style_idx <= lim));
+ plot_args = cat (2, plot_args, w(k), sv_db(k), style);
+ legend_args{k} = inputname(sys_idx(k)); # watch out for sigma (lticell{:})
+ endfor
+
## plot results
- semilogx (w, sv_db, "b")
+ semilogx (plot_args{:})
axis ("tight")
ylim (__axis_margin__ (ylim))
grid ("on")
- title (["Singular Values of ", inputname(1)])
- xlabel (xl_str)
+ title ("Singular Values")
+ xlabel ("Frequency [rad/s]")
ylabel ("Singular Values [dB]")
+ legend (legend_args)
else # return values
- sv_r = sv;
- w_r = reshape (w, [], 1);
+ sv_r = sv{1};
+ w_r = reshape (w{1}, [], 1);
endif
endfunction
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