| 0,0 → 1,89 |
|---|
| %% ukol 9 |
| %% pr 1 |
| clc, clear; |
| A = [-0.01 0;0 -0.02]; |
| B=[1 1;-0.25 0.75]; |
| C1 = [1 0]; |
| C2 = [0 1]; |
| D = 0; |
| F1 = [-1.1 -3.7;0 0]; |
| F2=[0 0;-1.1 1.233]; |
| F3=[-0.1 0;0 -0.1]; |
| |
| sys11 = ss(A+B*F1,B,C1,D); |
| sys21 = ss(A+B*F2,B,C1,D); |
| sys31 = ss(A+B*F3,B,C1,D); |
| sys12 = ss(A+B*F1,B,C2,D); |
| sys22 = ss(A+B*F2,B,C2,D); |
| sys32 = ss(A+B*F3,B,C2,D); |
| |
| subplot(211) |
| hold on |
| initial(sys11,'b',[0;1]); |
| initial(sys21,'r',[0;1]); |
| initial(sys31,'k',[0;1]); |
| xlabel('time'); |
| ylabel('x_1'); |
| grid on; |
| legend('F1','F2','F3'); |
| |
| subplot(212),hold on; |
| initial(sys12,'b',[0;1]); |
| initial(sys22,'r',[0;1]); |
| initial(sys32,'k',[0;1]); |
| xlabel('time'); |
| ylabel('x_2'); |
| legend('F1','F2','F3'),grid on; |
| %% pr 2 |
| clc,clear; |
| A = [0 1 0 0;0 0 1 0;0 0 0 1;1 1 -3 4] |
| B = [1 0;1 0;1 0;0 1] |
| B1 = [1 1 1 0]' |
| B2 = [0 0 0 1]' |
| Con = ctrb(A,B) |
| rank(Con) |
| Con1 = ctrb(A,B1) |
| rank(Con1) |
| Con2 = ctrb(A,B2) |
| rank(Con2) |
| ad = ((s+1+i)*(s+1-i)*(s+2+i)*(s+2-i)) |
| syms a b c d |
| Fc = [a b c d] |
| ac = det(sym(s*eye(4))-(A+B2*Fc)) |
| F = [0 0 0 0;-11 -19 -12 -10] |
| Fj=[0 0 0 0;-11 -29 -22 -20] |
| Bj = [0 0;0 0;0 0;0 1] |
| roots(det((s*eye(4))-(A+B*Fj))) |
| %% pr 3 |
| clc, clear; |
| A = [0 1;1 0] |
| B = [1;0] |
| Q = [1 0;0 0] |
| R = 1 |
| syms a b c |
| Pc = [a b;b c] |
| rica = A'*Pc+Pc*A-Pc*B*inv(R)*B'*Pc+Q |
| [x y z]=solve('2*b-a^2+1=0','a+c-a*b=0','2*b-b^2=0') |
| Pcc = [x(3),y(3);y(3) z(3)] |
| u = -inv(R)*B'*Pcc |
| %% pr 4 |
| clc,clear; |
| A = [0 1;0 0] |
| B = [0;1] |
| C = [1 0] |
| D = 1 |
| syms a b |
| F = [a b] |
| Af = A+B*F |
| Cf = C+D*F |
| O = [Cf;Cf*Af] |
| Ff = [-1 0] |
| Aff = A+B*Ff |
| Cff = C+D*Ff |
| Hf=Cff*(sym(s*eye(2))-Aff)^-1*B+D |
| %% pr 5 |
| clc,clear; |
| A = [0 1;0 -1] |
| B = [0;1] |
| Con = ctrb(A,B) |
| rank(Con) |
