www.gusucode.com > rctobsolete 工具箱 matlab源码程序 > rctobsolete/lmi/radardem.m
%RADARDEM Loop-shaping design of the velocity loop of a
% radar antenna (demo)
%
%See also LMIDEM, SATELDEM, MISLDEM
% Author: P. Gahinet
% Copyright 1995-2004 The MathWorks, Inc.
echo off
clc
disp(' ');
disp(' ');
disp(' ');
disp(' ');
disp(' DEMO "RADAR" ');
disp(' ************* ');
disp(' ');
disp(' ');
disp(' LOOP-SHAPING DESIGN OF THE VELOCITY LOOP OF A RADAR ANTENNA ');
disp(' ');
disp(' ');
disp(' ');
disp(' ');
disp(' (see user''s manual for further detail)');
disp(' ');
disp(' ');
disp(' ');
echo on
pause % Strike any key to continue...
clc
% BODE PLOT OF THE NOMINAL SYSTEM G0
% -----------------------------------
% plant transfer function
n=3e4;
d=conv([1 .02],[1 .99 3.03e4]);
G0=ltisys('tf',n,d);
fig1 = figure;
splot(G0,'bo',logspace(0,3,100))
pause % Strike any key to continue...
clc
%
% TRACKING LOOP:
%
% d
% _______ _______ |
% r e | | u | | V
% ----->O----->| K |------->| G |------+---> y
% |- |_____| |_____| |
% | |
% +----------------------------------+
%
% Specifications:
% * performance: integral control
% | GK | > 30 dB at 1 rd/s
% * 99% rejection of the disturbance d with frequency
% band [0,1] rd/s
% * robustness to a relative model uncertainty with
% frequency-dependent bound b(s) = s/100
%
% Loop-shaping criterion:
%
% || w1 S ||
% || || < 1 , S = 1/(1+GK) , T = GK*S
% || w2 T ||oo
pause % Strike any key to continue...
%
% GRAPHICALLY specify the corresponding shaping filters
% w1(s) (performance) and w2(s) (robustness):
%
% >> magshape
%
% Each filter is specified by its name, order, and
% magnitude profile ...
echo off
magshape
echo on
pause % Strike any key to continue...
echo off
clc
if any([exist('w1') exist('w2') input(['Enter 1 to continue with your filters, ' ...
'0 to load pre-computed ones: '])]~=1), load radardem, end
echo on,clc
%
% H-INFINITY SYNTHESE :
%
% Specify the control structure with SCONNECT:
inputs='r';
outputs='e=r-G0 ; G0';
[P,r]=sconnect(inputs,outputs,'K:e','G0:K',G0);
Paug=smult(P,sdiag(w1,w2,1));
pause % Strike any key to continue...
% Closing the augmented plant PAUG on the controller K
% yields the closed-loop transfer function (w1 S ; w2 T)
%
% Call HINFRIC to test whether the design specifications
% are feasible, i.e., whether || (w1 S ; w2 T) ||oo < 1 :
[gopt,K]=hinfric(Paug,r,1,1);
pause % Strike any key to continue...
clc, clf
%
% VALIDATION OF THE CONTROLLER K(s):
%
% Plot the open-loop response GK
GK=smult(G0,K);
splot(GK,'bo',logspace(-2,2,50));
title('open loop GK')
pause % Strike any key to continue...
% Form the closed-loop system (w/o the filters!)
% Its input is r and its outputs are e,y
Pcl=slft(P,K);
sinfo(Pcl)
pause % Strike any key to continue...
% Plot the singular value of S,T
S=ssub(Pcl,1,1);
T=ssub(Pcl,1,2);
clf
splot(S,'sv',logspace(0,3,100)); hold
splot(T,'sv',logspace(0,3,100)); title('S and T');
pause % Strike any key to continue...
clf, clc
%
% Step response:
subplot(211);
splot(T,'st'); title('step response r -> y');
% Rejection of a disturbance at the plant input
subplot(212);
splot(smult(S,G0),'im');
title('rejection of an impulse disturbance on u');
pause % Strike any key to continue...
clc
%
% H-INFINITY SYNTHESIS WITH POLE PLACEMENT
%
%
% Chosen region:
%
% disk with center (-1e3,0) and radius R=1e3
%
% The (closed-loop) modes of (w1 S; w2 T) always
% include the shaping filter dynamics!! To prevent
% interference with the pole placement objective,
% we use the loop-shaping structure:
%
% +----+ +----+
% | w1 |----> | w2 |---->
% +----+ +----+
% | |
% _______ e | _______ _______ |
% r | | | | | | | |
% ----->O--->| 1/s |---+-->| K0 |----->| G |--+---> y
% |- |_____| |_____| |_____| |
% | |
% +----------------------------------------+
%
%
% with
% s^2 + 16s + 200 s
% w1(s) = ---------------- w2(s) = 0.9 + ---
% s^2 + 1.2s + 0.8 200
%
%
pause % Strike any key to continue...
clc
%
% Specify the control structure with SCONNECT:
% integrator 1/s
i0=ltisys('tf',1,[1 0]);
inputs='r';
outputs='I0; G';
[P,r]=sconnect(inputs,outputs,'K:I0','G:K',G0,'I0:e=r-G',i0);
pause % Strike any key to continue...
% Add the shaping filters:
% W1
w1=ltisys('tf',[1 16 200],[1 1.2 0.8]);
Paug=smult(P,sdiag(w1,1,1));
% W2=0.9+s/200
Paug=sderiv(Paug,2,[1/200 0.9]);
% Closing the augmented plant PAUG on K0 yields
% the desired criterion (w1/s * S ; w2 * T)
pause % Strike any key to continue...
clc
%
% Perform an H-infinity synthesis with pole placement in
% the disk of center (-1000,0) and radius R = 1000 :
% specify this LMI region with LMIREG
% (type q to skip this step) :
region=lmireg;
pause % Strike any key to continue...
echo off
if isempty(region), region=[-1000+2*sqrt(-1) 1000 0 0;1000 -1000 1 0]; end
echo on
% perform the synthesis with HINFMIX :
[gopt,xx,K0]=hinfmix(Paug,[0 r],[0 0 1 0],region);
pause % Strike any key to continue...
echo off
if isempty(K0),
disp('Your choice of region is infeasible. Aborting demo...')
return
end
echo on
clc
%
% VALIDATION OF THE CONTROLLER K(s):
%
% Open-loop response GK
GK=smult(i0,K0,G0);
figure(fig1+1); clf;
splot(GK,'bo',logspace(-1,3,100)); title('open loop GK');
pause % Strike any key to continue...
% Form the closed-loop system (w/o the filters!)
% The input is r and the outputs are e and y
Pcl=sconnect('r','e;y=GK','','GK:e=r-y',GK);
pause % Strike any key to continue...
clc
%
% Plot the singular values of S and T
S=ssub(Pcl,1,1);
T=ssub(Pcl,1,2);
clf
splot(S,'sv',logspace(0,3,100)); hold
splot(T,'sv',logspace(0,3,100)); title('S and T');
pause % Strike any key to continue...
figure(fig1+1), clf, clc
%
% Step response:
subplot(211);
splot(T,'st',[0:.001:.5]); title('Response to a step r');
% Impulse response
subplot(212);
splot(smult(S,G0),'im',[0:.001:.5]);
title('Response to an impulse disturbance on u');
pause % Strike any key to continue...
% Closed-loop poles
figure(fig1+2),clf
plot(spol(Pcl),'+');
title('Closed-loop poles');
% The flexible modes of the system have been damped
% and the rejection of a disturbance at the plant input
% is now satisfactory
pause % Strike any key to continue...
echo off
close all
return