Linux命令、编辑器与Shell编程02.pdf

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1、12Ù"5zÙÄعkØ(½5üÑXÚ§Ù3²ï:xU⊂RnSÄ£exeãx˙=f(x)+g(x)u,x∈Rn,u∈R(2.1)Ù¥x´éAuÑu=0²ï:§=f(x)=0¶bfÚg½Â3Rnþ1wþee

2、§g(xe)6=0"32.2!Ú2.3!¥©OÑü(ا±²XÚ(2.1)=ÏL5IC(2.3!)§½ÏL5"IC(2.2!)§C5XÚ¿^"ùü¯K©O¡G5zÚ"5z""5zÀ5XÚ4:í2§2.1!£5XÚ4:"ÙØãÊH¯K§XÜ©"5z(2.4!)9Ù3½¯K¥A^(2.5!)§Û

3、"5z(2.6!)±93õCþXÚ¥í2(2.7!)"2.8!?Ø¢~"2.15XÚ4:Äk§·£5XÚnØ¥¯¤±(ص4:½n§¿ÑÙy²§±Bí25XÚ(2.1)¥"½n2.1.14:(PolePlacement)ÄüÑ5XÚx˙=Fx+gu,x∈Rn,u∈R(2.2)éu½ν6n/2§é?¿
ÝEêγi±jωi,16i6νÚn−2ν?¿¢êλj,2ν+16j6n§=Kalman5^(Kalmancontrollabilitycondition)span{g,Fg,···,Fn−1g}=Rn(2.3)¤á§3

4、5G"C(linearstatefeedbacktransformation)§=5IC(T´ÛÉ)z=Tx,z∈Rn±9G"(v∈R)u=kx+v¦4XÚx˙=(F+gk)x+gv2.15XÚ4:293zIXez˙=T(F+gk)T−1z+TgvÙ¥010···0001···0T(F+gk)T−1=...........,A....000···1−a0−a1−a2···−an−10...Tg=,b01det(sI−A)=sn+asn−1+···+as+an−110Yν

5、Yn=(s−γi−jωi)(s−γi+jωi)(s−λk)i=1k=2ν+1y²:¿©5"d5bª(2.3)§n×n5Ý(controllabilitymatrix)R=[g,Fg,···,Fn−1g]´ÛɧÏd31þh÷v5§hR=h[g,Fg,···,Fn−1g]=[hg,hFg,···,hFn−1g]=[0,···,0,1](2.4)=h=[0,···,0,1]R−1(2.5)-det(sI−F)=sn+αsn−1+···+αs+αn−110ÝFAõª"KdCayley-Hamilton½nFn=−αFn−1−···−α

6、F−αI(2.6)n−110½Ân×nÛÉÝT§hhFT=...hFn−130"5zÝTÛÉ5ÏL*Xen×nToeplitzÝÛÉ5yµhhFhiN=TR=.gFg···Fn−1g..hFn−1hghFg···hFn−1g2nhFghFg···hFg=....(2.7)........hFn−1ghFng···hF2n−2g¢Sþ§d½Â(2.4)hFig=0,06i6n−2hFn−1g=1(2.8)dubRÛɧ¤±T=NR−1´Ûɧz=Tx´5IC"

7、3zIXe§5XÚx˙=Fx+guCz˙=TFT−1z+Tgu"O(/`§âª(2.8)±Oz˙1=hx˙=hFx+hgu=hFx=z2...z˙=hFn−2x˙=hFn−1x+hFn−2gu=hFn−1x=zn−1nz˙=hFnx+hFn−1gu=hFnx+u(2.9)n2A^ª(2.6)§khFnx=−αhFn−1x−···−αhFx−αhxn−110=−α0z1−α1z2−···−αn−1znòÙª(2.9)§010···00001···00z˙=...........z+..u..

8、...000···10−α0−α1−α2···−αn−11=TFT−1z+Tgu(2.10)=5XÚìIO.(controllerform)"y3½ÂG"u=[α0−a0,···,αn−1−an−1]z+v=[α0−a0,···,αn−1−an−1]Tx+v,(α−a)TTx+v,kx+v(2.11)2.15XÚ4:31¿òÙª(2.10)§010···00001···00z˙=...........z+..v=Az+bv.....000·

9、··10−a0−a1−a2···−an−11l¿©5y"75"^y{y²"b^(2.3)ؤá§=rank[g,Fg,···,Fn−1g]=r