qftex3.m

机器人控制仿真程序一书的所有源代码

% QFTEX3 Non-parametric uncertainty.

% Author: Y. Chait
% 10/10/94
% Copyright (c) 1995-98 by The MathWorks, Inc.
%       $Revision: 1.4 $

clc
clear
echo on

% Example #3 (non-parametric uncertainty) describes the application of
% QFT to a feedback design problem with a non-parametrically uncertain
% plant and several robust performance specifications.

% Please refer to manual for more details....

% Strike any key to advance from one plot to another....
pause % Strike any key to continue
clc

%	Consider a continuous-time, siso, negative unity feedback system

%                                   |V(s)            |D(s)
%                         ----      |      ----      |
%             ---->x---->|G(s)|---->x---->|P(s)|---->x---->
%             R(s) |      ----             ----        | Y(s)
%                  |               --                  |
%                  ---------------|-1|------------------
%                                  --

%       The plant P(s) has a non-parametric uncertainty model:
%	           |   10                   delta(s) stable                |
%      P(s) = {--------- (1+delta(s)): |delta(jw)|<a(w)               }
%	           |s(0.1s+1)               a(w)=.9(jw/.91+1)/((jw/1.001+1)|

pause % Strike any key to continue
clc

%	The performance specifications are: design a controller
%  G(s) such that it achieves

%  1) Robust stability

%  2) Robust margins (via closed-loop magnitude peaks)
%         | P(jw)G(jw) |
%         |------------| < 1.2,  w>0
%         |1+P(jw)G(jw)|

%  3) Robust sensitivity reduction
%         |     1      |
%         |------------| < 0.089w^2,  w<5
%         |1+P(jw)G(jw)|

pause % Strike any key to continue
echo off
clc

% PROBLEM DATA

%  plant templates
nump=10; denp=conv([1,0],[.1,1]); % nominal plant
w = [0.05,0.5,2,5,90];
P=freqcp(nump,denp,w);
R = abs(freqcp(.9*[1/.91,1],[1/1.001,1],w)); % magnitude of uncertainty circle

% BOUNDS
disp(' ')
disp('Computing bounds...')
disp(' ')
disp('bdb1=sisobnds(1,w,wbd1,W1,P,R); %stability')
drawnow
wbd1 = w; % the frequency array
W1 = 1.2;  % define weight
bdb1 = sisobnds(1,w,wbd1,W1,P,R);
disp('plotbnds(bdb1); %show bounds')
plotbnds(bdb1),title('Robust Stability Bounds');
qpause;close(gcf);
%
disp(' ')
disp('bdb2=sisobnds(2,w,wbd2,W2,P,R); %sensitivity')
drawnow
wbd2=[0.05,0.5,2,5]; % the frequency array
W2=freqcp(0.089*[1,0,0],1,w); % computing weight at frequencies in w
W2=abs(W2);
bdb2 = sisobnds(2,w,wbd2,W2,P,R);
disp('plotbnds(bdb2); %show bounds')
drawnow
plotbnds(bdb2),title('Robust Sensitivity Bounds');
qpause;close(gcf);

disp(' ')
disp('bdb=grpbnds(bdb1,bdb2); %grouping bounds')
drawnow
bdb=grpbnds(bdb1,bdb2);
disp('plotbnds(bdb); %show all bounds')
drawnow
plotbnds(bdb),title('All Bounds');
qpause;close(gcf);

disp(' ')
disp('ubdb=sectbnds(bdb); %intersect bounds')
drawnow
ubdb=sectbnds(bdb);
disp('plotbnds(ubdb); %show bounds')
plotbnds(ubdb),title('Intersection of Bounds');
qpause;close(gcf);

% DESIGN
disp(' ')
disp('Design')
disp('lpshape(wl,ubdb,nL0,dL0,del0,nc0,dc0); %loop shaping')
drawnow
wl = logspace(-2,8,300);  % define a frequency array for loop shaping
nL0=nump;dL0=denp; % nominal loop
del0=0; % no delay
nc0=[ 5.032245193701399e+015
    1.047651224010599e+021
    2.783298073926963e+025
    2.091612032833357e+029
    3.180392975934304e+032
    8.265557006790552e+034
    2.627506261665202e+036
    4.929810064633756e+036
    2.260724023982798e+036]';
dc0=[1.000000000000000e+000
    1.123537042440132e+006
    2.734200460173087e+012
    7.574140703600440e+017
    4.919207207185055e+022
    7.266655789062400e+026
    2.669203151502317e+030
    1.910241138970628e+033
    1.932735079737017e+035
                         0]';
lpshape(wl,ubdb,nL0,dL0,del0,nc0,dc0);  qpause;
numC=nc0; denC=dc0;

% ANALYSIS
disp(' ')
disp('Analysis....')

R = freqcp(.9*[1/.91,1],[1/1.001,1],wl); % magnitude of uncertainty circle
R=abs(R);
P=freqcp(nump,denp,wl);
G=freqcp(numC,denC,wl);

disp(' ')
disp('chksiso(1,wl,W1,P,R,G); %stability spec')
drawnow
ind=find(wl<=5*10^6);
chksiso(1,wl(ind),W1,P(ind),R(ind),G(ind));
qpause;close(gcf);
%
disp(' ')
disp('chksiso(2,wl,W2,P,R,G); %sensitivity spec')
drawnow
ind=find(wl<=5);
W2=[];
W2=freqcp(0.089*[1,0,0],1,wl);
W2=abs(W2);
chksiso(2,wl(ind),W2(ind),P(ind),R(ind),G(ind));
qpause;close(gcf);