¡¶¼ÆËã»ú¿ØÖƼ¼Êõ¼°ÆäÓ¦Óá· µÚ3Õ Êý×Ö¿ØÖÆÆ÷µÄÉè¼ÆÓëʵÏÖ Ë¼¿¼ÌâÓëÏ°Ìâ Ö¸µ¼ÐÅÏ¢
y(k): 0.000 0.000 1.484 2.999 3.999 4.998 5.998 6.998
(3)ÔÚ½×Ô¾Ðźż¤ÀøÏÂ:
12?z?1(1?1.5z?1)(1?0.1z?1)R(z)? G(z)?1?z?1(1?z?1)(1?0.6z?1)(1?0.2z?1)-1-1
ÓÉG(z)¿ÉÖª¦µ(z) Ó¦°üÀ¨z?1ºÍ(1+1.5z)ºÍ(1+0.1z)Òò×Ó£»ÓÉG(z)ºÍR(z¿ÉÖªGe(z)Ó¦°üº¬(1?z?1)Òò×Ó£»¦µ(z)ºÍGe(z)Ó¦¸ÃÊÇz?1ͬ½×´ÎµÄ¶àÏîʽ£¬ËùÒÔÓУº
?1?1?1?1???(z)?1?Ge(z)?az(1?1.5z)(1?0.1z)(1?bz) ??1?1?2??Ge(z)?(1?z)(1?cz?dz)?1?1?1???(z)?1?Ge(z)?az(1?1.5z)(1?0.1z) ??1?1?2??Ge(z)?(1?z)(1?bz?cz)
Á½Ê½ÖеÄa,b,c,dΪ´ý¶¨ÏµÊý¡£a =4/11;b =7/11;c =3/55;
(²Î¿¼MATLABÃüÁ[a,b,c]=solve('3/20*a=c','(8/5*a)=-(c-b)','a=-(b-1)')) ÇóµÃ£ºa =4/11,b =7/11,c =3/55,ÔòÓУº
?1?1?1???(z)?1?Ge(z)?4/11?z(1?1.5z)(1?0.1z) ??1?1?2??Ge(z)?(1?z)(1?7/11z?3/55z)½«ÉÏÃæÁ½Ê½´úÈ룬¿ÉÇó³öÊý×Ö¿ØÖÆÆ÷µÄÂö³å´«µÝº¯Êý
D(z)?¦µ(z)G(z)?Ge(z)4/11?z?1(1?1.5z?1)(1?0.1z?1)?
2?z?1(1?1.5z?1)(1?0.1z?1)?(1?z?1)(1?7/11z?1?3/55z?2)?1?1?1(1?z)(1?0.6z)(1?0.2z)2/11?(1?0.6z?1)(1?0.2z?1)?(1?7/11z?1?3/55z?2)¸÷µã²¨ÐΣº
10.810.80.40.20024k6810e(k)r(k)0.60.60.40.20024k6810
- 3-11 -
¡¶¼ÆËã»ú¿ØÖƼ¼Êõ¼°ÆäÓ¦Óá· µÚ3Õ Êý×Ö¿ØÖÆÆ÷µÄÉè¼ÆÓëʵÏÖ Ë¼¿¼ÌâÓëÏ°Ìâ Ö¸µ¼ÐÅÏ¢
10.10.8p(k)0-0.1024k6810y(k)0.60.40.20024k6810
ÐòÁÐÊý¾Ý:
k: 0 1 2 3 4 5 6 7 r(k): 1 1 1 1 1 1 1 1 e(k): 1.000 0.636 0.055 0.000 0.000 0.000 0.000 0.000 p(k): 0.182 -0.145 0.022 -0.000 0.000 -0.000 0.000 -0.000 y(k): 0.000 0.364 0.945 1.000 1.000 1.000 1.000 1.000
(4)ÔÚµ¥Î»ËÙ¶ÈÐźż¤ÀøÏÂ:
T?z?12?z?1(1?1.5z?1)(1?0.1z?1)R(z)?G(z)??12?1?1?1(1?z)(1?z)(1?0.6z)(1?0.2z) ,
-1-1
ÓÉG(z)¿ÉÖª¦µ(z) Ó¦°üÀ¨z?1ºÍ(1+1.5z)ºÍ(1+0.1z)Òò×Ó£»ÓÉG(z)ºÍR(z¿ÉÖªGe(z)Ó¦°üº¬(1?z?1)Òò×Ó£»¦µ(z)ºÍGe(z)Ó¦¸ÃÊÇz?1ͬ½×´ÎµÄ¶àÏîʽ£¬ËùÒÔÓУº
?1?1?1?1???(z)?1?Ge(z)?az(1?1.5z)(1?0.1z)(1?bz) ??12?1??Ge(z)?(1?z)(1?cz)(²Î¿¼MATLABÃüÁ[a,b,c,d]= solve('3/20*a*b=-d','(8/5*a*b+3/20*a)=(2*d-c)', '(a*b+8/5*a)= (-d+2*c-1)' , 'a=(-c+2)' ) )
ÇóµÃ£ºa =592/605,b =-93/148,c =618/605,d =279/3025.,ÒÔ¼°£º
?1?1?1?z?1)??(z)?1?Ge(z)?592/605?z(1?1.5z)(1?0.1z)(1?93/148 ??12?1?2?z?279/3025z)?Ge(z)?(1?z)(1?618/605½«ÉÏÃæÁ½Ê½´úÈ룬¿ÉÇó³öÊý×Ö¿ØÖÆÆ÷µÄÂö³å´«µÝº¯Êý
D(z)?¦µ(z)G(z)?Ge(z)592/605?z?1(1?1.5z?1)(1?0.1z?1)(1?93/148z?1)?
2?z?1(1?1.5z?1)(1?0.1z?1)?(1?z?1)2(1?618/605z?1?279/3025z?2)?1?1?1(1?z)(1?0.6z)(1?0.2z)296/605?(1?93/148z?1)(1?0.6z?1)(1?0.2z?1)?(1?z?1)(1?618/605z?1?279/3025z?2)¸÷µã²¨ÐΣº
- 3-12 -
¡¶¼ÆËã»ú¿ØÖƼ¼Êõ¼°ÆäÓ¦Óá· µÚ3Õ Êý×Ö¿ØÖÆÆ÷µÄÉè¼ÆÓëʵÏÖ Ë¼¿¼ÌâÓëÏ°Ìâ Ö¸µ¼ÐÅÏ¢
10810.8420024k6810e(k)r(k)60.60.40.20024k6810
108
0.4p(k)y(k)024k68100.20-0.26420024k6810ÐòÁÐÊý¾Ý£º
k: 0 1 2 3 4 5 6 7 r(k): 0 1 2 3 4 5 6 7 e(k): 0.000 1.000 1.021 0.092 0.000 0.000 0.000 0.000 p(k): 0.000 0.489 -0.210 0.095 0.058 0.058 0.058 0.058 y(k): 0.000 0.000 0.979 2.908 4.000 5.000 6.000 7.000
¸½£º²»Í¬ÊäÈëÐźÅϵĸ÷µã²¨ÐΣº (1)ÔÚÈý¸ö½×Ô¾Ðźż¤ÀøÏÂ:
0.5z?1(1?0.6z?1)¦µ(z)1.25?(1?0.4z?1)1G(z)?D(z)??R(z)??1?1?1(1?z)(1?0.4z)£¬G(z)?Ge(z)(1?0.375?z?1) 1?z,
3210.8e(k)0510k152025r(k)0.60.40.21000510k152025
- 3-13 -
¡¶¼ÆËã»ú¿ØÖƼ¼Êõ¼°ÆäÓ¦Óá· µÚ3Õ Êý×Ö¿ØÖÆÆ÷µÄÉè¼ÆÓëʵÏÖ Ë¼¿¼ÌâÓëÏ°Ìâ Ö¸µ¼ÐÅÏ¢
1.513210p(k)0.50-0.50510k152025y(k)0510k152025Èç¹ûÊäÈëÊÇËٶȺ¯Êý£¬Ôò»á´æÔÚÎó²î£¬ÈçÏÂËùʾ£º
61e(k)0510k152025r(k)4200-10510k152025
10.56p(k)y(k)0510k1520250-0.5-14200510k152025
(2)ÔÚÈý¸öµ¥Î»ËÙ¶ÈÐźż¤ÀøÏÂ:
T?z?10.5z?1(1?0.6z?1),G(z)? R(z)??12?1?1(1?z)(1?z)(1?0.4z)¦µ(z)2.968?(1?0.4z?1)(1-0.578z?1)D(z)??G(z)?Ge(z)(1?z?1)(1?0.516z?1)
- 3-14 -