实验4数学模型建立与转换Word文档格式.docx
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实验4数学模型建立与转换Word文档格式.docx
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[z,p,k]=zpkdata(G,'
v'
);
6(s+2.312)(s^2-0.3118s+0.7209)
-------------------------------------------------
(s^2+0.08663s+0.413)(s^2+1.913s+2.421)
2)用MATLAB将下列零极点形式的传递函数模型转换为分子、分母多项式形式的传递函数模型:
z=[0;
-6;
-5];
-2;
-3-4*j;
-3+4*j];
[num,den]=zp2tf(z,p,k);
G=tf(num,den)
Transferfunction:
s^3+11s^2+30s
--------------------------------
s^4+9s^3+45s^2+87s+50
3.用MATLAB命令求如下图所示控制系统的闭环传递函数
G1=tf(1,[5000]);
G2=tf([12],[14]);
G3=tf([11],[12]);
G4=G1*G2;
GP=G4/(1+G3*G4);
GP1=minreal(GP)
0.002s+0.004
---------------------
s^2+4.002s+0.002
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)
(2)
A=[010;
001;
-7-13-6];
B=[0;
0;
1];
C=[7.540.6];
D=0;
G=ss(A,B,C,D)
a=
x1x2x3
x1010
x2001
x3-7-13-6
b=
u1
x10
x20
x31
c=
y17.540.6
d=
y10
Continuous-timemodel.
(3)
0-54;
-1-1-3];
B=[00;
20;
0,1];
C=[100;
001];
x20-54
x3-1-1-3
u1u2
x100
x220
x301
y1100
y2001
y100
y200
(4)
A=[0.521.36;
10-1.704.5;
120.8-31.6;
35-6.511];
B=[22;
30;
4,-3;
08];
C=[010.50.9;
0.71.60.82.9;
0.30.105.11];
D=[0.20.31;
0.90.27;
0.60.15];
x1x2x3x4
x10.521.36
x210-1.704.5
x3120.8-31.6
x435-6.511
x122
x230
x34-3
x408
y1010.50.9
y20.71.60.82.9
y30.30.105.11
y10.20.31
y20.90.27
y30.60.15
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。
G1=tf([5-1233],[163515]);
G2=tf([1-6.53235],[6726-111751]);
G3=tf(20*conv([15],[16]),conv(conv(conv([10],[13]),[12]),[18]));
G4=tf(3*conv(conv([111],[113]),[1-7.5]),conv(conv(conv([100],[114]),[1-25]),[16]));
G5=tf(3*conv(conv([111],[113]),[12.561]),conv(conv([1-25],[114]),[3956]));
(1)模块1、模块2串联,串联后总的系统记为sys12c;
sys12c=series(G1,G2)
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
(2)模块3、模块4并联,并联后总的系统记为sys34b;
Sys34c=parallel(G3,G4)
23s^7+208.5s^6-8150s^5-1.388e005s^4-7.562e005s^3-1.413e006s^2-154440s
----------------------------------------------------------------------------------------
s^9+8s^8-435s^7-7690s^6-46676s^5-116568s^4-100800s^3
(3)模块1、模块3、模块5串联,串联后总的系统记为sys135c;
sys135c=series(series(G1,G3),G5)
300s^8+10548s^7+1.332e005s^6+7.285e005s^5+1.742e006s^4+3.177e006s^3+1.271e007s^2
+2.32e007s+8.494e006
----------------------------------------------------------------------------------------------------
3s^13+33s^12-1219s^11-26879s^10-215199s^9-874306s^8-2.037e006s^7-3.225e006s^6
-4.593e006s^5-5.895e006s^4-5.187e006s^3-3.261e006s^2-1.512e006s
(4)模块1、模块2、模块5并联,并联后总的系统记为sys125b;
>
sys125b=parallel(parallel(G1,G2),G5)
18s^13+700.1s^12+6526s^11+7120s^10+6.018e004s^9+4.458e004s^8-4.939e005s^7
-1.618e006s^6-3.932e006s^5-1.868e006s^4-6.302e006s^3-6.757e006s^2-4.164e006s
-4.309e006
------------------------------------------------------------------------------------------------------
18s^14-15s^13-7638s^12-69862s^11-251079s^10-592657s^9-1.056e006s^8-1.452e006s^7
-2.619e006s^6-3.275e006s^5-2.837e006s^4-4.092e006s^3-3.527e006s^2-2.46e006s
-1.607e006
(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;
Ga=series(G1,G2);
sys12cf4z=feedback(Ga,G4)
5s^10-69.5s^9-1587s^8+6234s^7-1.653e004s^6-394949s^5+618999s^4-1.816e006s^3
-2.426e006s^2
6s^14+13s^13-2625s^12-30722s^11-126902s^10-262551s^9-476732s^8-474353s^7
-1.035e006s^6-1.484e006s^5-2.752e005s^4-2.179e006s^3-2.573e005s^2-2.175e006s
-3.716e006
(6)前向通道:
模块1、模块3、模块5串联;
模块2、模块4并联;
负反馈;
闭环传递函数记为sys135cf24bf;
Gb=series(series(G1,G3),G5);
Gc=parallel(G2,G4);
sys135cf24bf=feedback(Gb,Gc,-1)
1800s^18+56388s^17-1.948e005s^16-2.981e007s^15-5.128e008s^14-4.215e009s^13
-1.968e010s^12-6.044e010s^11-1.614e011s^10-4.225e011s^9-8.951e011s^8
-1.487e012s^7-1.544e012s^6-1.123e012s^5-2.548e012s^4-2.968e012s^3-9.097e011s^2
-------------------------------------------------------------------------------------------------------
18s^23+129s^22-15588s^21-262861s^20+1.788e006s^19+8.513e007s^18+9.971e008s^17
+6.331e009s^16+2.564e010s^15+7.271e010s^14+1.56e011s^13+2.721e011s^12
+4.217e011s^11+6.097e011s^10+7.408e011s^9+6.521e011s^8+2.997e011s^7
-4.567e011s^6-2.454e012s^5-4.523e012s^4-3.382e012s^3-3.804e012s^2-4.319e012s
-1.394e012
5.飞机俯仰角控制系统结构图如下,设K=0.25,编程解决以下问题
(1)求取系统闭环传递函数的多项式模型;
k=0.25;
G1=tf(-0.4,[21]);
G2=feedback(G1,0.5);
G3=0.4*G2;
G4=tf(1,[10.31]);
G5=feedback(G4,G3);
Gs=feedback(0.7*G5,k,-1)
1.4s+0.56
-------------------------------
2s^3+1.4s^2+2.59s+0.78
(2)将其转换为ZPK模型;
zsys=zpk(Gs)
0.7(s+0.4)
-----------------------------------
(s+0.3325)(s^2+0.3675s+1.173)
(3)求取系统的特征根;
[z,p,k]=zpkdata(Gs,'
)
z=
-0.4000
p=
-0.1837+1.0673i
-0.1837-1.0673i
-0.3325
k=
0.7000
6.发动机速度控制系统的结构图结构图如图4-12所示,编程解决以下问题。
(1)求取系统闭环传递函数的多项式模型
,此时令
G1=tf(100^2,[1140100^2]);
G2=tf(10,[0.11]);
G3=tf(10,[21]);
Ga=G1*G2*G3;
Gs=feedback(Ga,1,-1)
1e006
--------------------------------------------------
0.2s^4+30.1s^3+2295s^2+21140s+1.01e006
(2)求多项式模型
Gb=G1*G2;
Gn=feedback(G3,Gb)
s^3+150s^2+11400s+100000
(3)求取系统的特征根。
Gc=Gs+Gn;
[z,p,k]=zpkdata(Gc,'
1.0e+002*
-1.2806
-0.7359+0.7134i
-0.7359-0.7134i
-0.1097+0.9203i
-0.1097-0.9203i
-0.0166+0.2186i
-0.0166-0.2186i
-73.5865+71.3418i
-73.5865-71.3418i
-1.6635+21.8626i
-1.6635-21.8626i
5.0000
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