LAB1控制系统的模型建立实验记录

1

(1)传递函数模型

>> num=[2 18 40];

>> den=[1 5 8 6];

>> Gtf=tf(num,den) //生成空间状态方程Transfer function:

2 s^2 + 18 s + 40

---------------------

s^3 + 5 s^2 + 8 s + 6

(2)零极点增益模型

>> Gzpk=zpk(Gtf)

Zero/pole/gain:

2 (s+5) (s+4)

--------------------

(s+3) (s^2 + 2s + 2)

//存在两个零点和三个极点

（3）状态空间方程

>> tf2ss(num,den)

ans =

-5 -8 -6

1 0 0

0 1 0

(4)零极点坐标图

>> pzmap(G)

>> pzmap(Gzpk);

>> grid on

2.

(1)空间状态方程模型

>> A=[0 1 0 0;0 0 1 0;0 0 0 1;-1 -2 -3 -4]; >> B=[0;0;0;1];

>> C=[10 2 0 0];

>> D=[0];

>> Gss=ss(A,B,C,D) //生成空间状态方程a =

x1 x2 x3 x4

x1 0 1 0 0

x2 0 0 1 0

x3 0 0 0 1

x4 -1 -2 -3 -4

b =

u1

x1 0

x2 0

x3 0

x4 1

c =

x1 x2 x3 x4

y1 10 2 0 0

d =

u1

y1 0

（2）传递函数模型

>> T=tf(Gss) //转换成传递函数Transfer function:

2 s + 10

-----------------------------

s^4 + 4 s^3 + 3 s^2 + 2 s + 1

（3）零极点增益模型

>> Z=zpk(Gss)

Zero/pole/gain:

2 (s+5)

---------------------------------------------

(s+3.234) (s+0.6724) (s^2 + 0.0936s + 0.4599) （4）零极点坐标图

>> pzmap(Gss)

>> grid on

3.

>> num1=[2 6 5]; >> den1=[1 4 5 2]; >> G1=tf(num1,den1)

Transfer function:

2 s^2 + 6 s + 5

---------------------

s^3 + 4 s^2 + 5 s + 2

>> num2=[1 4 1]; >> den2=[1 9 1 0]; >> G2=tf(num2,den2)

Transfer function:

s^2 + 4 s + 1

---------------

s^3 + 9 s^2 + s

>> z=[-3 -7];

>> p=[-1 -4 -6];

>> k=[5];

>> G3=zpk(z,p,k)

Zero/pole/gain:

5 (s+3) (s+7)

-----------------

(s+1) (s+4) (s+6) //生成G1\G2\G3

>> H=G1*G2*G3

Zero/pole/gain:

10 (s+3.732) (s+3) (s+7) (s+0.2679) (s^2 + 3s + 2.5)

----------------------------------------------------

s (s+8.887) (s+6) (s+4) (s+2) (s+1)^3 (s+0.1125)

//得到了零极点增益模型

>> G=tf(H)

Transfer function:

10 s^6 + 170 s^5 + 1065 s^4 + 3150 s^3 + 4580 s^2 + 2980 s + 525

--------------------------------------------------------------------------------

s^9 + 24 s^8 + 219 s^7 + 979 s^6 + 2324 s^5 + 2997 s^4 + 2028 s^3 + 620 s^2+ 48 s // 转换成传递函数模型

4.

>> num1=[1];

>> den1=[1 1];

>> G1=tf(num1,den1)

Transfer function:

1

-----

s + 1

>> num2=[1];

den2=[0.5 1];

G2=tf(num2,den2)

Transfer function:

1

---------

0.5 s + 1

>> num3=[3];

den3=[1 0];

G3=tf(num3,den3)

Transfer function:

3

S

>> G=(G1*G2)+G3

Transfer function:

1.5 s^2 + 5.5 s + 3

---------------------

0.5 s^3 + 1.5 s^2 + s //生成总的传递函数

>> num4=[1];

>> den4=[0.5 1]；

>> H=tf(num4,den4)

Transfer function:

1

---------

0.5 s + 1 //生成反馈回路

>> H1=G/(1+G*H)

Transfer function:

0.375 s^6 + 3.25 s^5 + 10.63 s^4 + 16.25 s^3 + 11.5 s^2 + 3 s -----------------------------------------------------------------

0.125 s^7 + s^6 + 3.875 s^5 + 9.75 s^4 + 14.75 s^3 + 11 s^2 + 3 s //得到闭环传递函数

5.

>> num1=[10];

>> den1=[1 1];

>> G1=tf(num1,den1)

Transfer function:

10

-----

s + 1

>> num2=[2];

den2=[1 1 0];

G2=tf(num2,den2)

Transfer function:

2

-------

s^2 + s

>> num3=[1 3];

den3=[1 2];

G3=tf(num3,den3)

Transfer function:

s + 3

-----

s + 2

>> num4=[5 0];

den4=[1 6 8];

H=tf(num4,den4)

Transfer function:

5 s

-------------

s^2 + 6 s + 8

>> H2=G3/G1

Transfer function:

s^2 + 4 s + 3

-------------

10 s + 20 //将G3前移一个节点

>> H0=H+H2

Transfer function:

s^4 + 10 s^3 + 85 s^2 + 150 s + 24

----------------------------------

10 s^3 + 80 s^2 + 200 s + 160 //总反馈传递函数>> G0=G1*G2

Transfer function:

20

---------------

s^3 + 2 s^2 + s //总传递函数

>> G0/(1+G0*H0)

//得到闭环传递函数

Transfer function:

200 s^6 + 2000 s^5 + 7400 s^4 + 12800 s^3 + 10400 s^2 + 3200 s

--------------------------------------------------------------------------------

10 s^9 + 120 s^8 + 600 s^7 + 1720 s^6 + 4290 s^5 + 8440 s^4 + 9020 s^3 + 4120 s^2 + 480 s