基于 matlab 的控制系统与仿真 2- 传递函数模型

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发布于: 2021 年 02 月 23 日

Author：AXYZdong

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传递函数模型

2.4 已知控制系统的传递函数

\frac{Y ( s )}{U ( s )} = \frac{2 s ^{2} + 1 8 s + 4 0}{s ^{3} + 6 s ^{2} + 1 1 s + 6}

试求其零极点模型和状态空间模型。

>> sys1=tf([2 18 40],[1 6 11 6 ])
sys1 =     2 s^2 + 18 s + 40  ----------------------  s^3 + 6 s^2 + 11 s + 6 Continuous-time transfer function.
>> sys2=zpk(sys1)
sys2 =     2 (s+5) (s+4)  -----------------  (s+3) (s+2) (s+1) Continuous-time zero/pole/gain model. >> sys3=ss(sys1)
sys3 =   A =           x1     x2     x3   x1     -6  -2.75   -1.5   x2      4      0      0   x3      0      1      0   B =        u1   x1   4   x2   0   x3   0   C =           x1     x2     x3   y1    0.5  1.125    2.5   D =        u1   y1   0 Continuous-time state-space model.

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2.5 已知控制系统的零极点模型

G (s) = \frac{2 ( s + 4 ) ( s + 5 )}{( s + 1 ) ( s + 2 ) ( s + 3 )}

试求其传递函数模型和状态空间模型。

>>  z=[-4;-5];p=[-1;-2;-3];k=2;>>  [num,den]=zp2tf(z,p,k);G=tf(num,den)
G =     2 s^2 + 18 s + 40  ----------------------  s^3 + 6 s^2 + 11 s + 6 Continuous-time transfer function.
>> [a,b,c,d]=zp2ss(z,p,k)
a =
   -1.0000         0         0    1.0000   -5.0000   -2.4495         0    2.4495         0

b =
     1     0     0

c =
    2.0000    8.0000   11.4310

d =
     0

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2.7 已知一串联系统的三个传递函数

G 1 = \frac{2 s ^{2} + 6 s + 5}{s ^{3} + 4 s ^{2} + 5 s + 2}, G 2 = \frac{s ^{2} + 4 s + 1}{s ^{3} + 9 s ^{2} + 8 s}, G_{3} = \frac{5 ( s + 3 ) ( s + 7 )}{( s + 1 ) ( s + 4 ) ( s + 6 )}

求此系统的传递函数。

>> g1=tf([2 6 5],[1 4 5 2])
g1 =      2 s^2 + 6 s + 5  ---------------------  s^3 + 4 s^2 + 5 s + 2 Continuous-time transfer function.
>> g2=tf([1 4 1],[1 9 8 0])
g2 =     s^2 + 4 s + 1  -----------------  s^3 + 9 s^2 + 8 s Continuous-time transfer function.
>> g3=zpk([-3,-7],[-1,-4,-6],5)
g3 =     5 (s+3) (s+7)  -----------------  (s+1) (s+4) (s+6) Continuous-time zero/pole/gain model.
 >> g=series(g1,g2)
g =         2 s^4 + 14 s^3 + 31 s^2 + 26 s + 5  ----------------------------------------------  s^6 + 13 s^5 + 49 s^4 + 79 s^3 + 58 s^2 + 16 s Continuous-time transfer function.
>> g4=series(g,g3)
g4 =   10 (s+3) (s+3.732) (s+7) (s+0.2679) (s^2 + 3s + 2.5)  ----------------------------------------------------           s (s+1)^4 (s+2) (s+4) (s+6) (s+8) Continuous-time zero/pole/gain model.

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2.8 已知一并联系统，其中，

G 1 = \frac{s + 3}{( s + 1 ) ^{2} ( s + 2 )}, G 2 = \frac{3 s ^{2} + s + 4}{5 s ^{2} + 1 2 s + 3}

求此并联系统的传递函数。

>> G1=zpk([-3],[-1,-1,-2],1)
G1 =       (s+3)  -------------  (s+1)^2 (s+2) Continuous-time zero/pole/gain model.
>> G2=tf([3 1 4],[5 12 3])
G2 =    3 s^2 + s + 4  ----------------  5 s^2 + 12 s + 3 Continuous-time transfer function.
>> G=parallel(G1,G2)
G =   0.6 (s+0.3913) (s^2 + 3.896s + 3.819) (s^2 + 0.04608s + 3.793)  --------------------------------------------------------------                (s+1)^2 (s+2) (s+2.117) (s+0.2835) Continuous-time zero/pole/gain model.
>>