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% Aufgabe 4
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 A=[   0 1    0;
     980 0 -2.8;
       0 0 -100]
 b=[0 0 100]'
 c=[1 0 0]
 d=0

 % (a)
 eig(A)

 % (b)
 t=0:0.005:2;
 u=0*t;
 x0 = [0.005 0 0]
 figure
 lsim(A,b,c,d,u,t,x0)

 % (c)
 rank(ctrb(A, b))

 % (d)
 p1=-10+10i;
 p2=-10-10i;
 p3=-50;
 k=place(A,b,[p1 p2 p3])

 % (e)
 figure
 lsim(A-b*k,b,c,d,u,t,x0)

 % (f) Realteil der Pole nach links verschieben
 p1=-20+10i;
 p2=-20-10i;
 p3=-100;
 k=place(A,b,[p1 p2 p3])
 figure
 lsim(A-b*k,b,c,d,u,t,x0)

 % (g)
 rank(obsv(A, c))

 % (h)
 op1=-100;
 op2=-101;
 op3=-102;
 f=place(A',c',[op1 op2 op3])';

 % (i)
 At = [A-b*k          b*k;
       zeros(size(A)) A-f*c]
 bt = [b; zeros(size(b))]
 ct = [c  zeros(size(c))]
 figure
 lsim(At,bt,ct,0,zeros(size(t)),t,[x0 x0])  %e0=x0-[0 0 0]

 % (j) (Separationstheorem gilt!)
 eig(At)

 % (k)
 [num,den]=ss2tf(A-b*k-f*c,f,-k,0)
 BR=tf(num,den)
 
 % (l) (Zusatzaufgabe)
 k2=polvorgabe(A,b,[p1 p2 p3])
 max(abs(k - k2))