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  1. close all; clear all;
  2. TS_lab_04
  3. function TS_lab_04
  4. tspan1 =[0 0.25];
  5. tspan2 =[0.251 0.50];
  6. tspan3 =[0.501 0.75];
  7. tspan4 =[0.751 1];
  8. x0_1 =[1 0 0];
  9. a1 =0; b1 =2; c1 = -3;
  10. a2 =5; b2 = -3; c2 =1;
  11. a3 = -1; b3 =1; c3 =7;
  12. a4 =0; b4 =3; c4 = -2;
  13. [ tsol , xsol ] = ode45 ( @ (t , x ) odefcn (t ,x , a1 , b1 , c1 ) , tspan1 , x0_1 );
  14. x3 =1 - xsol (: ,1) - xsol (: ,2);
  15. z1 =[0.25 ,0.25];
  16. z2 =[0.5 ,0.5];
  17. z3 =[0.75 ,0.75];
  18. y =[0 ,1];
  19. figure (1); hold on ; grid on ;
  20. plot ( tsol , xsol (: ,1) , ’r ’ , tsol , xsol (: ,2) , ’b ’ , tsol , x3 , ’g ’ );
  21. title ( ’ Wykres ␣ x ( t ));
  22. xlabel ( ’t ’ );
  23. ylabel ( ’x ( t ));
  24. % legend ( ’x1 ’ , ’x2 ’ , ’x3 ’);
  25. x0_2 =[ xsol (end ,1) xsol (end ,2) x3 (end )];
  26. [ tsol , xsol ] = ode45 ( @ (t , x ) odefcn (t ,x , a2 , b2 , c2 ) , tspan2 , x0_2 );
  27. x3 =1 - xsol (: ,1) - xsol (: ,2);
  28. plot ( tsol , xsol (: ,1) , ’r ’ , tsol , xsol (: ,2) , ’b ’ , tsol , x3 , ’g ’ );
  29. x0_3 =[ xsol (end ,1) xsol (end ,2) x3 (end )];
  30. [ tsol , xsol ] = ode45 ( @ (t , x ) odefcn (t ,x , a3 , b3 , c3 ) , tspan3 , x0_3 );
  31. x3 =1 - xsol (: ,1) - xsol (: ,2);
  32. plot ( tsol , xsol (: ,1) , ’r ’ , tsol , xsol (: ,2) , ’b ’ , tsol , x3 , ’g ’ );
  33. x0_4 =[ xsol (end ,1) xsol (end ,2) x3 (end )];
  34. [ tsol , xsol ] = ode45 ( @ (t , x ) odefcn (t ,x , a4 , b4 , c4 ) , tspan4 , x0_4 );
  35. x3 =1 - xsol (: ,1) - xsol (: ,2);
  36. plot ( tsol , xsol (: ,1) , ’r ’ , tsol , xsol (: ,2) , ’b ’ , tsol , x3 , ’g ’ );
  37. plot ( z1 ,y , ’k - - ’ );
  38. plot ( z2 ,y , ’k - - ’ );
  39. plot ( z3 ,y , ’k - - ’ );
  40. t1 =0:0.001:0.25;
  41. t2 = t1 +0.25;
  42. t3 = t2 +0.25;
  43. t4 = t3 +0.25;
  44. u1 = @ ( t ) min (max ( a1 .* t  + b1 , 0) , 1);
  45. u2 = @ ( t ) min (max ( a2 .* t .* t + b2 .* t + c2 , 0) , 1);
  46. 4
  47. u3 = @ ( t ) min (max ( a3 .* t .* t + b3 .* t + c3 , 0) , 1);
  48. u4 = @ ( t ) min (max ( a4 .* t + b4, 0) , 1);
  49. figure (2); hold on ; grid on ;
  50. title ( ’ Wykres ␣ czterech ␣ funkcji ␣ u ( t ) ␣ zmiennych ␣ na ␣ p r z e d z i a a c h ’ );
  51. xlabel ( ’t ’ );
  52. ylabel ( ’u ( t ));
  53. plot ( t1 , u1 ( t1 ));
  54. plot ( t2 , u2 ( t2 ));
  55. plot ( t3 , u3 ( t3 ));
  56. plot ( t4 , u4 ( t4 ));
  57. plot ( z1 ,y , ’k - - ’ );
  58. plot ( z2 ,y , ’k - - ’ );
  59. plot ( z3 ,y , ’k - - ’ );
  60. end
  61. function dxdt = odefcn (t ,x ,a ,b , c )
  62. u = a * t * t + b * t + c ;
  63. if u >1
  64. u =1;
  65. end
  66. if u <0
  67. u =0;
  68. end
  69. dxdt = zeros (3 ,1);
  70. dxdt (1) = u *(10* x (2) - x (1));
  71. dxdt (2) = u *( x (1) -10* x (2)) -(1 - u )* x (2);
  72. end
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