[解題] 自控問題

[nictsz (巴斯光年)]

[題目]
        ---     -3   -2  -0.5   0    0    ---           ---  1  ---
        |        2    0    0    0    0       |          |    0    |
x'=     |        0    2    0    0    0       |   x+     |    0    |   u
        |        0    0    1    0    0       |          |    0    |
        ---      0    0    0    2    0    ---           ---  0  ---
y=[ 0  0  0  0  1.25] x

Giving the initial state x(0)= [ 2  3.25  1.78  4  5.12]T  ,
show that the final state x(0)=0 can be achieved in a finite time using
 a controller  u=k(t)x(0)




[答案]






[請板友解題or對答案提供詳解]




請板有幫忙解題...謝謝!!
--
好人有好報
你會考上好學校

--
※ 發信站: 批踢踢實業坊(ptt.cc) 
◆ From: 210.85.135.25
推 ethan7201:這不是東華最後ㄧ提嗎?我也不會...請好心人提ꠠ
> -------------------------------------------------------------------------- <

作者: eai (hahaha) 看板: graduate
標題: Re: [解題] 自控問題
時間: Wed Apr  6 15:29:25 2005

※ 引述《nictsz (巴斯光年)》之銘言：
: [題目]
:         ---     -3   -2  -0.5   0    0    ---           ---  1  ---
:         |        2    0    0    0    0       |          |    0    |
: x'=     |        0    2    0    0    0       |   x+     |    0    |   u
:         |        0    0    1    0    0       |          |    0    |
:         ---      0    0    0    2    0    ---           ---  0  ---
: y=[ 0  0  0  0  1.25] x
: Giving the initial state x(0)= [ 2  3.25  1.78  4  5.12]T  ,
: show that the final state x(0)=0 can be achieved in a finite time using
:  a controller  u=k(t)x(0)
: [答案]
: [請板友解題or對答案提供詳解]
: 請板有幫忙解題...謝謝!!
這題的意思應該是只要證證明
Qc矩陣滿秩即可
雖然是五乘五....但他的物理結構其實已經很接近controller form
所以Qc會很好算

令x'=Ax +B U

Qc=[B AB A^2B A^3B  A^4B ]

可以輕鬆解得這是個上三角矩陣...滿秩...controllerable

所以the final state x(0)=0 can be achieved in a finite time using
 a controller  u=k(t)x(0)


--
※ 發信站: 批踢踢實業坊(ptt.cc) 
◆ From: 61.56.235.142
推 ethan7201:為什麼只要可控制就可以呢...還是不懂...
推 eai:你有張碩的書嗎??CT. Chen的也行
→ eai:你會發現題目的要求就是可控制的定義
推 ethan7201:有阿但是上面有寫嗎??
→ ethan7201:->我有張碩的書