Subversion Repositories svnkaklik

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Rev Author Line No. Line
1058 kaklik 1 
%% ukol 9
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%% pr 1
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clc, clear;
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A = [-0.01 0;0 -0.02];
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B=[1 1;-0.25 0.75];
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C1 = [1 0];
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C2 = [0 1];
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D = 0;
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F1 = [-1.1 -3.7;0 0];
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F2=[0 0;-1.1 1.233];
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F3=[-0.1 0;0 -0.1];
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sys11 = ss(A+B*F1,B,C1,D);
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sys21 = ss(A+B*F2,B,C1,D);
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sys31 = ss(A+B*F3,B,C1,D);
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sys12 = ss(A+B*F1,B,C2,D);
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sys22 = ss(A+B*F2,B,C2,D);
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sys32 = ss(A+B*F3,B,C2,D);
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plot(initial(sys11,'b',[0;1]), initial(sys21,'r',[0;1]), initial(sys31,'k',[0;1]));
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xlabel('time'), ylabel('x_1'), grid on, legend('F1','F2','F3');
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plot(initial(sys12,'b',[0;1]), initial(sys22,'r',[0;1]), initial(sys32,'k',[0;1]));
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xlabel('time');
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ylabel('x_2');
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legend('F1','F2','F3'),grid on;
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%% pr 2
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clc,clear;
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A = [0 1 0 0;0 0 1 0;0 0 0 1;1 1 -3 4]
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B = [1 0;1 0;1 0;0 1]
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B1 = [1 1 1 0]'
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B2 = [0 0 0 1]'
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Con = ctrb(A,B)
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rank(Con)
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Con1 = ctrb(A,B1)
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rank(Con1)
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Con2 = ctrb(A,B2)
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rank(Con2)
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ad = ((s+1+i)*(s+1-i)*(s+2+i)*(s+2-i))
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syms a b c d
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Fc = [a b c d]
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ac = det(sym(s*eye(4))-(A+B2*Fc))
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F = [0 0 0 0;-11 -19 -12 -10]
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Fj=[0 0 0 0;-11 -29 -22 -20]
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Bj = [0 0;0 0;0 0;0 1]
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roots(det((s*eye(4))-(A+B*Fj)))
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%% pr 3
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clc, clear;
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A = [0 1;1 0]
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B = [1;0]
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Q = [1 0;0 0]
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R = 1
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syms a b c
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Pc = [a b;b c]
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rica = A'*Pc+Pc*A-Pc*B*inv(R)*B'*Pc+Q
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[x y z]=solve('2*b-a^2+1=0','a+c-a*b=0','2*b-b^2=0')
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Pcc = [x(3),y(3);y(3) z(3)]
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u = -inv(R)*B'*Pcc
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%% pr 4
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clc,clear;
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A = [0 1;0 0]
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B = [0;1]
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C = [1 0]
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D = 1
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syms a b
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F = [a b]
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Af = A+B*F
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Cf = C+D*F
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O = [Cf;Cf*Af]
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Ff = [-1 0]
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Aff = A+B*Ff
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Cff = C+D*Ff
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Hf=Cff*(sym(s*eye(2))-Aff)^-1*B+D
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%% pr 5
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clc,clear;
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A = [0 1;0 -1]
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B = [0;1]
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Con = ctrb(A,B)
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rank(Con)