MATLAB语言与控制系统仿真参考答案及解析第4章.docx
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MATLAB语言与控制系统仿真参考答案及解析第4章
4.5控制系统的数学模型MATLAB实训
4.5.1实训目的
1.练习并掌握TF模型、ZPK模型、SS模型的建立方法。
2.练习并掌握TF模型、ZPK模型、SS模型间的转换方法。
3.练习并掌握求取多个模块串联、并联、反馈后总的模型的方法。
4.练习并掌握模型数据的还原方法。
4.5.2实训内容
1.写出以下系统的多项式模型,并将其转换为零极点模型；
〔1
>>n1=[91,-52,3.5,-11,52];
d1=[1,15,26,73,31,215];
sys1=tf
[z1,p1,k1]=tf2zp
sys1zp=zpk
运行结果如下：
Transferfunction:
91s^4-52s^3+3.5s^2-11s+52
-------------------------------------------
s^5+15s^4+26s^3+73s^2+31s+215
z1=
0.7705+0.5468i
0.7705-0.5468i
-0.4848+0.6364i
-0.4848-0.6364i
p1=
-13.4656
-1.3473+1.9525i
-1.3473-1.9525i
0.5801+1.5814i
0.5801-1.5814i
k1=
91
Zero/pole/gain:
91
--------------------------------------------------------------------------
〔2
>>n2=[1,-38.7,101,-71.5,63.1,562.39];
d2=[1,2,5,-31,51,-22.5,39,311.21];
sys2=tf
[z2,p2,k2]=tf2zp
sys2zpkmx=zpk
Transferfunction:
s^5-38.7s^4+101s^3-71.5s^2+63.1s+562.4
---------------------------------------------------------------------------
s^7+2s^6+5s^5-31s^4+51s^3-22.5s^2+39s+311.2
z2=
35.9437
2.9589
0.5590+1.9214i
0.5590-1.9214i
-1.3206
p2=
-2.5015+3.1531i
-2.5015-3.1531i
1.9492+1.0027i
1.9492-1.0027i
0.2072+1.7349i
0.2072-1.7349i
-1.3097
k2=
1
Zero/pole/gain:
--------------------------------------------------------------------------------------------------
2.写出以下系统的零极点模型,并将其转换为多项式模型,并将其展开成为部分分式形式；
〔1
>>z=[-0.5;-6.02];
>>p=[0;-1.3;-2.6;-3.5;-4.9;-5.11];
>>k=36;
>>sys=zpk
Zero/pole/gain:
36
--------------------------------------------------
s
>>[n,d]=zp2tf
n=
000036.0000234.7200108.3600
d=
1.000017.4100116.1430367.5889544.8325296.21140
>>systfxs=tf
Transferfunction:
36s^2+234.7s+108.4
-------------------------------------------------------------------------------
s^6+17.41s^5+116.1s^4+367.6s^3+544.8s^2+296.2s
>>[r,p,k]=residue;
>>[r';p']
ans=
9.1407-14.873017.4236-14.72272.66560.3658
-5.1100-4.9000-3.5000-2.6000-1.30000
即部分分式分解结果为
〔2
>>z=[-1;-3;3.5];
>>p=[0;0;-2;-4;5;6];
>>k=9.15;
>>sys=zpk
Zero/pole/gain:
9.15
-------------------------------
s^2
>>[n,d]=zp2tf
n=
0009.15004.5750-100.6500-96.0750
d=
1-5-289224000
>>systfxs=tf
Transferfunction:
9.15s^3+4.575s^2-100.7s-96.08
---------------------------------------------------
s^6-5s^5-28s^4+92s^3+240s^2
>>[r,p,k]=residue;
>>[r';p']
ans=
0.5004-0.41830.07150.1123-0.2659-0.4003
6.00005.0000-4.0000-2.000000
即部分分式分解结果为
3.已知系统的状态空间表达式,写出其SS模型,并求其传递函数矩阵<传递函数模型>,若状态空间表达式为
则传递函数矩阵表达式为：
。
〔1
>>a1=[-1,0;0,-3];
>>b1=[1;1];
>>c1=[0,5];
>>d1=6;
>>sys1=ss
a=
x1x2
x1-10
x20-3
b=
u1
x11
x21
c=
x1x2
y105
d=
u1
y16
>>tf
Transferfunction:
6s+23
-----------%传递函数矩阵<传递函数模型>
s+3
〔2
>>a2=[0,1,0;0,0,1;-7,-13,-6];
>>b2=[0;0;1];
>>c2=[7.5,4,0.6];
>>d2=0;
>>sys2=ss
a=
x1x2x3
x1010
x2001
x3-7-13-6
b=
u1
x10
x20
x31
c=
x1x2x3
y17.540.6
d=
u1
y10
Continuous-timemodel.
>>tf
Transferfunction:
0.6s^2+4s+7.5
----------------------------
s^3+6s^2+13s+7
〔3
>>a3=[0,1,0;0,-5,4;-1,-1,-3];
>>b3=[0,0;2,0;0,1];
>>c3=[1,0,0;0,0,1];
>>d3=0;
>>sys3=ss
a=
x1x2x3
x1010
x20-54
x3-1-1-3
b=
u1u2
x100
x220
x301
c=
x1x2x3
y1100
y2001
d=
u1u2
y100
y200
Continuous-timemodel.
>>tf
Transferfunctionfrominput1tooutput...
2s+6
#1:
------------------------------
s^3+8s^2+19s+4
-2s-2
#2:
------------------------------
s^3+8s^2+19s+4
Transferfunctionfrominput2tooutput...
4
#1:
------------------------------
s^3+8s^2+19s+4
s^2+5s
#2:
------------------------------
s^3+8s^2+19s+4
〔4
>>a4=[0.5,2,1.3,6;10,-1.7,0,4.5;12,0.8,-3,1.6;3,5,-6.5,11];
>>b4=[2,2;3,0;4,-3;0,8];
>>c4=[0,1,0.5,0.9;0.7,1.6,0.8,2.9;0.3,0.1,0,5.11];
>>d4=[0.2,0.31;0.9,0.27;0.6,0.15];
>>sys4=ss
a=
x1x2x3x4
x10.521.36
x210-1.704.5
x3120.8-31.6
x435-6.511
b=
u1u2
x122
x230
x34-3
x408
c=
x1x2x3x4
y1010.50.9
y20.71.60.82.9
y30.30.105.11
d=
u1u2
y10.20.31
y20.90.27
y30.60.15
Continuous-timemodel.
>>tf
Transferfunctionfrominput1tooutput...
0.2s^4+3.64s^3-38.23s^2-513.1s-1390
#1:
-----------------------------------------------------------------
s^4-6.8s^3-109.2s^2+291.7s+1859
0.9s^4+3.28s^3-132.8s^2-850.6s-1534
#2:
-----------------------------------------------------------------
s^4-6.8s^3-109.2s^2+291.7s+1859
0.6s^4-3.18s^3-92.01s^2+38.67s+1431
#3:
-----------------------------------------------------------------
s^4-6.8s^3-109.2s^2+291.7s+1859
Transferfunctionfrominput2tooutput...
0.31s^4+3.592s^3+108.5s^2+648.3s+1351
#1:
-------------------------------------------------------------------
s^4-6.8s^3-109.2s^2+291.7s+1859
0.27s^4+20.36s^3+306.5s^2+809.2s+244
#2:
------------------------------------------------------------------
s^4-6.8s^3-109.2s^2+291.7s+1859
0.15s^4+40.46s^3+300.7s^2-1228s-6749
#3:
------------------------------------------------------------------
s^4-6.8s^3-109.2s^2+291.7s+1859
4.已知各环节〔模块的传递函数如下,各系统的组成如以下各小题所描述,编程求取各系统总的传递函数。
〔1模块1、模块2串联,串联后总的系统记为sys12c；
〔2模块3、模块4并联,并联后总的系统记为sys34b；
〔3模块1、模块3、模块5串联,串联后总的系统记为sys135c；
〔4模块1、模块2、模块5并联,并联后总的系统记为sys125b；
〔5前向通道：
模块1、模块2串联；反馈通道：
模块4；正反馈；闭环传递函数记为sys12cf4z;
〔6前向通道：
模块1、模块3、模块5串联；反馈通道：
模块2、模块4并联；负反馈;闭环传递函数记为sys135cf24bf;
>>n1=[5,-12,33];
>>d1=[1,6,3,5,15];
>>sys1=tf
Transferfunction:
5s^2-12s+33
-----------------------------------------
s^4+6s^3+3s^2+5s+15
>>n2=[1,-6.5,32,35];
>>d2=[6,7,26,-11,17,51];
>>sys2=tf
Transferfunction:
s^3-6.5s^2+32s+35
------------------------------------------------------
6s^5+7s^4+26s^3-11s^2+17s+51
>>z3=[-5;-6];p3=[0;-3;-2;-8];k3=20;
>>sys3=zpk
Zero/pole/gain:
20
------------------------------
s
>>sys4=zpk<[-11;-13;7.5],[0;0;-14;25;-6],[3]>
Zero/pole/gain:
3
----------------------------------
s^2
>>sys5=zpk<[-11;-13],[-14;25],[3]>*tf<[1,2.56,1],[3,9,5,6]>
Zero/pole/gain:
----------------------------------------------------------
>>sys12c=sys1*sys2
Transferfunction:
5s^5-44.5s^4+271s^3-423.5s^2+636s+1155
------------------------------------------------------------------------------------------------------------
6s^9+43s^8+86s^7+196s^6+154s^5+355s^4+692s^3+73s^2+510s+765
>>zpk
Zero/pole/gain:
0.83333
---------------------------------------------------------------------------------------------------------------------------------------
>>sys34b=sys3+sys4
Zero/pole/gain:
23s
---------------------------------------------------------------------------------------
s^3
>>sys135c=sys1*sys3*sys5
Zero/pole/gain:
100
------------------------------------------------------------------------------------------------------------------------------------------
s
>>sys125b=sys1+sys2+sys5
Zero/pole/gain:
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
>>sys12cf4z=/<1-sys1*sys2*sys4>
Zero/pole/gain:
0.83333s^2
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
>>sys135cf24bf=/<1+sys1*sys3*sys5*>
Zero/pole/gain:
100s^3^2^2<
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