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ÏßÐÔϵͳdx/dt=Ax+Bu, y=Cx, A,B,CÕóÈçÏÂËùʾ£¬
A=[0 0 1 0 0;0 -0.154 -0.0042 1.54 0;0 0.249 -1 -5.2 0;0.0386 -0.996 -0.0003 -0.117 0;0 0.5 0 0 -0.5];
B=[0 0;-0.744 -0.032;0.337 -1.12;0.02 0;0 0];C=[0 1 0 0 -1;0 0 1 0 0;0 0 0 1 0;1 0 0 0 0];ÆäÖÐA,B¿É¿Ø£¬A,C¿É¹Û£¬ÏÖÔÚÈÃÕò¶¨ÏµÍ³£¬Ñ¡Ôñ״̬·´À¡u=-Kx£¬´Ó¶øÏµÍ³»¯Îªdx/dt=(A-BK)x,¿É¿Ø£¬ËùÒÔ¿ÉÒÔÅäÖü«µã¡£ÎÒÑ¡ÔñµÄ¼«µãÊÇP=[-3,-0.5,-3,-9,-7]£¬Êä³öy1=x2-x5,y2=x3,y3=x4,y4=x1£¬·ÂÕæ²½³¤0.001s,·ÂÕæÊ±¼ä5s.¿ÉÊǵõ½µÄÊä³öÇúÏßÓÐ2¸öСÎÊÌ⣬µÚÒ»¸öÊÇy1=x2-x5ÊÕÁ²Ì«ÂýÁË£¨ÆäÖÐx1ÊÕÁ²Í¦¿ìµÄ£¬¾ÍÊÇÓÉÓÚx5ÊÕÁ²Âýµ¼ÖÂy1ÊÕÁ²Âý£©£¬µÚ¶þ¸öÊÇy2=x3·ÂÕæÒ»¿ªÊ¼ºóµÄÖµÅܵÄÉÔ΢ÓеãÔ¶µ½-0.8×óÓÒÁË£¬Ï£Íû¸úÆäËû״̬һÑù£¬ÔÚ[-0.5,0.5]·¶Î§ÄÚ²¨¶¯¡£ÎÒ×Ô¼ºµ÷°ëÌ켫µãPÒ²µ÷Õû²»ºÃ£¬¸Ð¾õµÚ2¸ö¼«µã-0.5»ù±¾²»Äܶ¯ÁË£¬µÚ4¸ö¼«µã¸úµÚ5¸ö¼«µãµ¥¶À±ä»¯¶¼Êä³öÓ°Ïì²»´ó£¬»ù±¾¾ÍÊǵ÷ÕûµÚ1¸ö¸úµÚ3¸ö£¬ÅäºÏµÚ4¸ö¸úµÚ5¸öÀ´µÃµ½±È½ÏºÃµÄÊÕÁ²ÇúÏߣºÒ»·½Ãæy1,y2,y3,y4ÊÕÁ²µÄ¿ìµã£¬2s×óÓÒÊÕÁ²µ½0¶¼ÄܽÓÊÜ£»¶þ·½Ãæ²»Òª¿ªÊ¼ÕðµÄÄÇôÀ÷º¦¡£Èç¹ûÕðµ´ÊµÔÚ½â¾ö²»ÁË£¬Ö»ÒªÃ»ÎÒÏÂÃæµÄͼÕðµÄÀ÷º¦Ò²ÐУ¬µ«ÊÇÊÕÁ²Ëٶȵýâ¾ö°¡¡£ÎÒÓõÄPÕóµ÷ÕûµÄͼ³ýÁËy1,ÆäËû3¸öÊÕÁ²Ê±¼ä»¹´ÕºÏ¡£ÎÒ¼òµ¥¸½Ï³ÌÐò£¬ÕÒÈ˰ïдµÄ£¬´ó¼Ò´ÕºÏ¿´°É¡£
K=place(A,B,P);h=0.001;
t_end=5;
t_inter=h;
t=0:t_inter:t_end;
t=t';
nps=length(t);
x(1, =[0.4328 0.0657 0.5233 0.0698 0.3489];
for i=2:nps
x(i, =x(i-1, +h*((A-B*K)*x(i-1, ')';
end
figure(1);
plot(t,x(:,2)-x(:,5),'y-',t,x(:,3),'g-',t,x(:,4),'r-',t,x(:,1),'k-');
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[ Last edited by everfx on 2013-11-9 at 16:47 ] |