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.
>> 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
>> 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.
>> 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.
>>