robust control: a simple pid controller is better then every hinf! Why?

Hi folks. I currently experiments with a PT2 uncertrain plant. For
that system i'll create a controller which has a specific robust
performance. For that i'll use Matlab 7.3 with Robust Control Toolbox
3.1.1. Cause of the robust performance i need mu-synthesis with d-k
iteration. The mentioned toolbox contains the dksyn function. The
weighting function envelopes sensitivity of the closed loop of the PID
controller with the uncertain plant. I understand the h-inf. norm,
that it'll find out of a set of controllers a specific one, which can
achieve my requierements. So if i argue, that the PID controller
contains to this set of controllers, why isn't a similar structure
found?

Thx for every comments and ideas. Best greets Eggi


% nominelle Parameter
nm = 3;
nc = 1;
nk = 2;

% relative Fehler
pm = .4;
pc = .2;
pk = .3;

% erzeuge "unsichere Parameter"
um = ureal('m',nm,'Percentage',[-1 1]*100*pm);
uc = ureal('c',nc,'Percentage',[-1 1]*100*pc);
uk = ureal('k',nk,'Percentage',[-1 1]*100*pk);

% normale Matrizen
A0 = [    0        1;
        -nk/nm    -nc/nm];
B0 = [    0;        1/nm];
C0 = [    1        0];
D0 = [    0]; %#ok<NBRAK>

% Matrizen mit unsicheren Parametern
A = [    0        1;
        -uk/um    -uc/um];
B = [    0;        1/um];

% nominelle Strecke
G0 = ss(A0,B0,C0,D0);

% Zusammenbinden des Zustandsraumsystems (unsicheres strukturiertes
SS)
Gus = ss(A, B, C0, D0);

% Erzeugen eines Vergleichsreglers (PID)
k    = 15;
ti    = 1;
td    = 1;

Kpidtf = k*tf([ti*td ti 1],[0.01 ti 0]);
[a,b,c,d] = tf2ss(Kpidtf.num,Kpidtf.den);
Kpid = ss(a,b,c,d);

figure;
CLpid = feedback((Gus.NominalValue*Kpid),1);
step(CLpid),grid;

%% Wichtungsfunktionen
% Wichtungsfunktion zur Bewertung des Stellgliedes
nWu = 1;
dWu = 1;
gWu = 10^(-2);
Wr = tf(nWu, dWu)*gWu;

Wt = ss([15.05 -15.06; 16.58 -16.56],[0.5211; -0.5211],[0.7307
-0.7589],1.312);
Ws = ss([-0.02859 0.05684; 0.5143 -1.028],[3.237; -1.618],[1.116 1.59],
0.9393);

% Zusammenbinden des Systems mit "unsicheren" Parametern und den
% Wichtungsfunktionen
systemnames        = ' Gus Ws Wr ';
inputvar        = '[ dist; control ]';
outputvar        = '[ Ws; -Wr; -Gus-dist ]';
input_to_Gus    = '[ control ]';
input_to_Ws        = '[ Gus+dist ]';
input_to_Wr        = '[ control ]';
sysoutname        = 'Pus';
cleanupsysic    = 'yes';
sysic;

% Reglersynthese
[Khinfs, clps, GAMhinfs,DKINFOhinfs]    = dksyn(Pus, 1, 1);

disp(['Hinfs: ' num2str(GAMhinfs)]);

% Binden des geschlossenen Systems
CLhinfs    = feedback((Gus*Khinfs),1);
CLpid    = feedback((Gus*Kpid),1);

% Empfindlichkeitsfunktion
Shinfs    = 1/(1+Khinfs*Gus);
Spid    = 1/(1+Kpid*Gus);

%%

figure;
bode(Khinfs,Kpid),grid;
figure;
step(CLhinfs,CLpid),grid,legend('H-unendlich strukturiert','PID');
figure;
bode(Shinfs,Spid,'c',1/Ws,'r'),grid,legend('H-unendlich
strukturiert','PID','1/Ws');