3.5由状态方程求传递函数 )状态方程的传递函数的导出 X=Ax+Bu Cx sX(S)=AX(S)+BU(S Y(S)=CX(S) (SI-A)X(S)=BU(S) MODERN CONTROL SYSTEM
MODERN CONTROL SYSTEM 0 3.5 由状态方程求传递函数 一）状态方程的传递函数的导出 x = Ax +Bu y = Cx sX(s) = AX(s) + BU(s) Y(s) = CX(s) (sI − A)X(s) = BU(s)
[sI-A]=(s) X(S=qSBU(S Y(S=Cq()BU(S) G(S)=Y(S)/U(S) G(s)=CΦ(s)B MODERN CONTROL SYSTEM
MODERN CONTROL SYSTEM 1 [ ] ( ) 1 sI − A =Φ s − X(s) =Φ(s)BU(s) Y(s) = CΦ(s)BU(s) G(s) = Y(s)/U(s) G(s) = CΦ(s)B
二)实例 例6:RLC网络的传递函数 X x+ 0 R 1-R LL 解 R (S+ R S S MODERN CONTROL SYSTEM
MODERN CONTROL SYSTEM 2 二）实例 例6：RLC网络的传递函数 x x u + − − = 0 1 1 1 0 C L R L C y = 0 Rx 解： + − − = ( ) 1 1 L R s L C s sI A − + = − = − s L L C R s s s s 1 1 ( ) ( ) 1 ( ) 1 Φ I A
R S)=[SIAJ= △(s) S 其中 R △(s) S十 LC MODERN CONTROL SYSTEM
MODERN CONTROL SYSTEM 3 − + = − = − s L L C R s s s s 1 1 ( ) ( ) 1 ( ) 1 Φ I A LC s L R s s 1 ( ) 2 = + + 其中:
于是RLC网络的传递函数为 R S G(s)=pA(s)C△(s)lc L△(S)△(s) R/LC R/LC △(S R S-+—S LO MODERN CONTROL SYSTEM
MODERN CONTROL SYSTEM 4 于是RLC网络的传递函数为： LC s L R s R LC s R LC C s s L s s C s L R s G s R 1 / ( ) / 0 1 ( ) ( ) 1 ( ) 1 ( ) ( ) ( ) 0 2 + + = = − + =