2状态过渡矩阵 令F(s)=0,则X(s)=(s)X(0) zi,r:x(t)=(0)x(0) p(t=li adj(s/-a) ,9(t)=L[(s) x(t)=(t)x(o, p (t)=e 3倒:令R=0;则本侧的状态 方程如下: Eu(t)
2.状态过渡矩阵 } , ( ) [ ( )] ( ) ( ) { . . : ( ) ( ) (0) ( ) 0, ( ) ( ) (0) 1 1 t L s sI A adj sI A t L zi r x t t x F s X s s X − − = − − = = 令 = 则 = At x(t) = (t)x(0),(t) = e 3.例:令R=0;则本例的状态 方程如下： Eu(t)
(m,D).(L)=(mm) LFm 0 1/L L 1/L E() 1/ 0 0 「101「s-1/Ll「s1/L S-4 011c0 1/c S 9()=(1-4)+1=a(s1-4) S 1/ s2+∞2L1/c
m L Ln = m n ( m , L).( L.n ) = ( m.n ) ( ) 01/ 1/ 0 0 1/ '' Eu t L vi c L vi cL cL + − = − = − − − = c s s L cs L sI A s 1/ 1/ 1/ 01/ 0 1 1 0 c s Lc s L s sI A adj sI A s sI A 1 , 1/ 1 1 / ( ) ( ) ( ) 2 2 0 0 2 1 = − + = − − = − = −
1/L 2 2 s+O s+O (s) C S 2 S+00S+00 若x(0)=0,则二.r的拉氏变换(s)=0(s)F(S) 1/L E/L 2 2 2 2 x(S)= s+0, s+O E S+O C 1/c 2 2 2 OSEG s-+0 s-+0 2 sS+O
+ − + = + + + − + = = = + + + − + = ) 1 ( / 0 1 1/ 1/ 1/ ( ) (0) 0, . . ( ) ( ) ( ) 1/ 1/ ( ) 2 0 2 2 0 2 2 0 2 2 0 2 2 0 2 2 0 2 2 0 2 2 0 2 2 0 2 2 0 2 s s s E s E L s E L s c s c s L s s x s x z s r x s s F s s s s c s L s s s 若 则 的拉氏变换为
E sin oot x(t)=L[X(S=OL E(-coS @ot 二輪出方程的解和多輪入多输出条统的转移 函数 y(t)=cx(t)+Dy(t)>Y(s)=cX(s)+ DF(s) V(S=C(S)X(O)+[C(s)B+D]F(S) y(t)=LiLcp(s)X(O]+L [Cp(SB+ DF(S)
− = = − (1 cos ) sin ( ) [ ( )] 0 0 0 1 E t t L E x t L X s 二.输出方程的解和多输入多输出系统的转移 函数 y(t) = Cx(t) + Dy(t) → Y(s) = CX(s) + DF(s) ( ) {[ ( ) (0)] [ ( ) ] ( )} ( ) ( ) (0) [ ( ) ] ( ) 1 1 y t L c s X L C s B D F s y s c s X C s B D F s = + + = + + − − z.i.r z.s.r
1.转移函数矩阵(多输入多輪出糸统) y(s)=[co(s)b+ d]f(sy (s)=h(s)F(s) Hs=C(S-A)B+D 若糸统有r个輪出,m个输入,k阶则 nkxl'(t)=Akxknkxi(t)+ Bkxmemxi(t) (t)=C r×kk×1 (t)+D × (t) Hxm(s)=crxk(sl-a) Bkxm+ D Hx(s). Hxm(s
1.转移函数矩阵(多输入多输出系统) H s C sI A B D y s c s B D F s y s H s F s f f = − + = + = −1 ( ) ( ) ( ) [ ( ) ] ( )而 ( ) ( ) ( ) 若系统有 r个输出,m个输入,k阶则 ( ) ( ) ( ) '( ) ( ) ( ) 1 1 1 1 1 1 ' r t C t D e t t A t B e t r r k k r m m k k k k k m m = + = + r m r k A Bk m Dr m H s C sI − = − + 1 ( ) ( ) = ( ) . ( ) . . . ( ) . ( ) 1 11 1 H s H s H s H s r r m m