东北大学 自动化 控制系统计算机辅助设计实验docx.docx
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东北大学 自动化 控制系统计算机辅助设计实验docx.docx
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东北大学自动化控制系统计算机辅助设计实验docx
控制系统计算机辅助设计
第一部分
1
functiondx=lorenzeq(t,x)
dx=[-x
(2)-x(3);
x
(1)+0.2*x
(2);
0.2+(x
(1)-5.7)*x(3);]
>>x0=[0;0;0];
>>[t,y]=ode45('lorenzeq',[0,100],x0);
>>plot(t,y)
>>figure;plot3(y(:
1),y(:
2),y(:
3)),grid,
2
function[y,yeq]=f2a(x)
yeq=[];
y=4*x
(1)^2+x
(2)^2-4;
>>Aeq=[];Beq=[];A=[];B=[];
>>xm=[0;0];xM=[];x0=[0;0];
>>f1=inline('x
(1)^2-2*x
(1)+x
(2)');
>>[x,f]=fmincon(f1,x0,A,B,Aeq,Beq,xm,xM,'f2a');x',f
ans=
1.00000
f=
-1
3
(a)
>>s=tf('s');G=(s^3+4*s+2)/s^3/(s^2+2)/[(s^2+1)^3+2*s+5]
Transferfunction:
s^3+4s+2
------------------------------------------------------
s^11+5s^9+9s^7+2s^6+12s^5+4s^4+12s^3
(b)
>>z=tf('z',0.1);
>>H=(z^2+0.568)/(z-1)/(z^2-0.2*z+0.99)
Transferfunction:
z^2+0.568
-----------------------------
z^3-1.2z^2+1.19z-0.99
Samplingtime:
0.1
4
>>A=[010;001;-5-4-13];
>>B=[0;0;2];
>>C=[100;000;000];
>>D=[0];
>>G=ss(A,B,C,D);
>>G
a=
x1x2x3
x1010
x2001
x3-5-4-13
b=
u1
x10
x20
x32
c=
x1x2x3
y1100
y2000
y3000
d=
u1
y10
y20
y30
Continuous-timemodel.
>>G=tf(G)
Transferfunctionfrominputtooutput...
2
#1:
----------------------
s^3+13s^2+4s+5
#2:
0
#3:
0
>>GG=zpk(G)
Zero/pole/gainfrominputtooutput...
2
#1:
----------------------------------
(s+12.72)(s^2+0.2836s+0.3932)
#2:
0
#3:
0
根据微分方程也可以直接写出传递函数模型:
>>num=[2];
>>den=[1,13,4,5];
>>G=tf(num,den);
>>G
Transferfunction:
2
----------------------
s^3+13s^2+4s+5
>>GG=zpk(G)
Zero/pole/gain:
2
----------------------------------
(s+12.72)(s^2+0.2836s+0.3932)
5
>>num=[1,2];
>>den=[1,1,0.16];
>>H=tf(num,den,'Ts',1);
>>H
Transferfunction:
z+2
--------------
z^2+z+0.16
Samplingtime:
1
6
functionH=feedback(G1,G2,key)
ifnargin==2;key=-1;end,H=G1/(sym
(1)-key*G1*G2);H=simple(H);
>>symsJKpKis;
>>gc=(Kp*s+Ki)/s;
>>g=(s+1)/(J*s^2+2*s+5);
>>gg=feedback(g*gc,1)
>>gg=feedback(g*gc,1)
gg=
((Ki+Kp*s)*(s+1))/(J*s^3+(Kp+2)*s^2+(Ki+Kp+5)*s+Ki)
7
(a)
>>s=tf('s');
>>G=(211.87*s+317.64)/(s+20)/(s+94.34)/(s+0.1684);
>>Gc=(169.6*s+400)/s/(s+4);
>>Hs=1/(0.01*s+1);
>>GG=feedback(G*Gc,Hs)
Transferfunction:
359.3s^3+3.732e004s^2+1.399e005s+127056
-----------------------------------------------------------------
0.01s^6+2.185s^5+142.1s^4+2444s^3+4.389e004s^2
+1.399e005s+127056
>>zpk(GG)
Zero/pole/gain:
35933.152(s+100)(s+2.358)(s+1.499)
--------------------------------------------------------------------------
(s^2+3.667s+3.501)(s^2+11.73s+339.1)(s^2+203.1s+1.07e004)
(b)
>>z=tf('z');
>>G=(35786.7*z^-1+108444)/[(z^-1+4)*(z^-1+20)*(z^-1+74.04)];
>>Gc=1/(z^-1-1);
>>H=1/(0.5*z^-1-1);
>>GG=feedback(G*Gc,H)
Transferfunction:
-108444z^6+1.844e004z^5+1.789e004z^4
------------------------------------------------------------------
1.144e005z^6+2.876e004z^5+274.2z^4+782.4z^3+47.52z^2
+0.5z
Samplingtime:
unspecified
>>zpk(GG)
Zero/pole/gain:
-0.94821z^4(z-0.5)(z+0.33)
-------------------------------------------------------------
z(z+0.3035)(z+0.04438)(z+0.01355)(z^2-0.11z+0.02396)
Samplingtime:
unspecified
8
>>s=tf('s');
c1=feedback(1/(s+1)*s/(s^2+2),(4*s+2)/(s+1)^2);
c2=feedback(1/s^2,50);
G=feedback(c1*c2,(s^2+2)/(s^3+14))
Transferfunction:
s^6+2s^5+s^4+14s^3+28s^2+14s
---------------------------------------------------------------------------------
s^10+3s^9+55s^8+175s^7+300s^6+1323s^5+2656s^4+3715s^3
+7732s^2+5602s+1400
9
>>s=tf('s');
>>G=(s+1)^2*(s^2+2*s+400)/(s+5)^2/(s^2+3*s+100)/(s^2+3*s+2500);
>>G1=c2d(G,0.01)
Transferfunction:
4.716e-005z^5-0.0001396z^4+9.596e-005z^3+8.18e
-005z^2-0.0001289z+4.355e-005
-----------------------------------------------------------------
z^6-5.592z^5+13.26z^4-17.06z^3+12.58z^2-5.032z
+0.8521
Samplingtime:
0.01
>>step(G1)
>>G2=c2d(G,0.1)
Transferfunction:
0.0003982z^5-0.0003919z^4-0.000336z^3+0.0007842z^2
-0.000766z+0.0003214
-----------------------------------------------------------------
z^6-2.644z^5+4.044z^4-3.94z^3+2.549z^2-1.056z
+0.2019
Samplingtime:
0.1
>>step(G2)
>>G3=c2d(G,1)
Transferfunction:
8.625e-005z^5-4.48e-005z^4+6.545e-006z^3+1.211e-005z^2
-3.299e-006z+1.011e-007
-----------------------------------------------------------------
z^6-0.0419z^5-0.07092z^4-0.0004549z^3+0.002495z^2
-3.347e-005z+1.125e-007
Samplingtime:
1
>>step(G3)
10
(a)
>>G=1/(s^3+2*s^2+s+2);
>>pzmap(G)
系统极点均在虚轴左侧,系统稳定
(b)
>>G=1/(6*s^4+3*s^3+2*s^2+s+1);
>>pzmap(G)
系统极点在虚轴右侧侧,系统不稳定
(c)
>>G=1/(s^4+s^3-3*s^2-s+2);
>>pzmap(G)
系统极点在虚轴右侧侧,系统不稳定
11
(a)
>>z
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