控制系统计算及辅助设计实验Word下载.docx
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控制系统计算及辅助设计实验Word下载.docx
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[x,a,b]=fmincon(@c3exmobj,x,A,B,Aeq,Beq,xm,xM,@c3exmcon,ff);
ifb>
0,break;
end
i=i+1;
3.
(a)>
symss,G=(s^3+4*s+2)/(s^3*(s^2+2)*((s^2+1)^3+2*s+5))
结果:
G=
(s^3+4*s+2)/s^3/(s^2+2)/((s^2+1)^3+2*s+5)
(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=[0,1,0;
0,0,1;
-5,-4,-13];
B=[0;
0;
2];
C=[1,0,0];
D=0;
G=ss(A,B,C,D)
a=
x1x2x3
x1010
x2001
x3-5-4-13
b=
u1
x10
x20
x32
c=
y1100
d=
y10
Continuous-timemodel.
G1=tf(G)%系统传递函数
Transferfunction:
2
----------------------
s^3+13s^2+4s+5
GG=zpk(G1)%零极点模型
Zero/pole/gain:
(s+12.72)(s^2+0.2836s+0.3932)
5.
6.
functionH=feedback(G1,G2,key)
ifnargin==2;
key=-1;
end,H=G1/(sym
(1)-key*G1*G2);
H=simple(H)
%使feedback函数能处理符号运算
>
G1=(s+1)/(j*s^2+2*s+5)
G1=
(s+1)/(j*s^2+2*s+5)
Gc=(kp*s+ki)/s
Gc=
(kp*s+ki)/s
G=feedback(G1*Gc,1)
(s+1)*(kp*s+ki)/(j*s^3+2*s^2+5*s+kp*s^2+s*ki+kp*s+ki)
7.
(a)>
s=tf('
s'
);
G1=(211.87*s+317.64)/((s+20)*(s+94.34)*(s+0.1684))
Gc1=(169.6*s+400)/(s*(s+4));
H1=1/(0.01*s+1);
GG1=feedback(G1*Gc1,H1)
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
>
GG10=zpk(GG1)
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)>
G2=(35786.7*z^-1+108444)/((z^-1+4)*(z^-1+20)*(z^-1+74.04));
Gc2=1/(z^-1-1);
H2=1/(0.5*z^-1-1);
GG2=feedback(G2*Gc2,H2)
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
G20=zpk(GG2)
-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:
8.
G1=1/(s+1);
G2=s/(s^2+2);
G3=1/s^2;
H1=50;
H2=(4*s+2)/(s+1)^2;
H3=(s^2+2)/(s^3+14);
c1=feedback(G3,H1);
c2=feedback(G1*G2,H2);
c3=feedback(c1*c2,H3);
G3=3*c3
3s^6+6s^5+3s^4+42s^3+84s^2+42s
-----------------------------------------------------------------------------------------
s^10+3s^9+55s^8+175s^7+300s^6+1323s^5+2656s^4+3715s^3+7732s^2+5602s+1400
9.
(1)连续:
G=((s+1)^2*(s^2+2*s+400))/((s+5)^2*(s^2+3*s+100)*(s^2+3*s+2500));
step(G,7)
(2)T=1
G1=c2d(G,1)
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
1
step(G1,10)
(3)T=0.1
G2=c2d(G,0.1)
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
step(G2,7)
(4)T=0.01
G3=c2d(G,0.01)
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
0.01
step(G3,7)
10.
(1)>
G1=1/(s^3+2*s^2+s+2)
-------------------
s^3+2s^2+s+2
pzmap(G1)
eig(G1),isstable(G1)
ans=
-2.0000
-0.0000+1.0000i
-0.0000-1.0000i
ans=
1
系统临界稳定。
(2)>
G2=1/(6*s^4+3*s^3+2*s^2+1);
eig(G2),isstable(G2)
-0.5099+0.5585i
-0.5099-0.5585i
0.2599+0.4732i
0.2599-0.4732i
0
系统不稳定。
(3)>
G3=1/(s^4+s^3-3*s^2-s+2);
eig(G3),isstable(G3)
-2.0000
-1.0000
1.0000
11.
(1)
num=[-32];
den=[10.2-0.250.05];
H1=tf(num,den,'
Ts'
0.1)
-3z+2
-----------------------------
z^3+0.2z^2-0.25z+0.05
v=abs(eig(H1)),isstable(H1)
v=
0.6777
0.2716
系统是稳定的。
(2)
num=[3-0.39-0.09];
den=[11.71.040.2680.024];
H2=tf(num,den,'
3z^2-0.39z-0.09
------------------------------------------
z^4+1.7z^3+1.04z^2+0.268z+0.024
v=abs(eig(H2)),isstable(H2)
0.6000
0.5000
0.4000
0.2000
12.
A=[-0.2,0.5,0,0,0;
0,-0.5,1.6,0,0;
0,0,-14.3,85.8,0;
0,0,0,-33.3,100;
0,0,0,0,-10];
B=[0;
30];
C=zeros(5,1);
D=0;
G=ss(A,B,C,D);
eig(G),pzmap(G),isstable(G)
-0.2000
-0.5000
-14.3000
-33.3000
-10.0000
13.
(1)数值解:
f=@(t,x)[-5*x
(1)+2*x
(2);
-4*x
(2);
-3*x
(1)+2*x
(2)-4*x(3)-x(4);
-3*x
(1)+2*x
(2)-4*x(4)];
t_final=10;
x0=[1200];
[t,x]=ode45(f,[0,t_final],x0);
plot(t,x)
(2)解析解:
function[Ga,Xa]=ss_augment(G,cc,dd,X)
G=ss(G);
Aa=G.a;
Ca=G.c;
Xa=X;
Ba=G.b;
D=G.d;
if(length(dd)>
0&
sum(abs(dd)>
1e-5)),
if(abs(dd(4))>
1e-5),
Aa=[Aadd
(2)*Ba,dd(3)*Ba;
...
zeros(2,length(Aa)),[dd
(1),-dd(4);
dd(4),dd
(1)]];
Ca=[Cadd
(2)*Ddd(3)*D];
Xa=[Xa;
1;
Ba=[Ba;
else,
Aa=[Aadd
(2)*B;
zeros(1,length(Aa))dd
(1)];
Ca=[Cadd
(2)*D];
1];
Ba=[B;
end
if(length(cc)>
sum(abs(cc))>
1e-5),M=length(cc);
Aa=[AaBazeros(length(Aa),M-1);
zeros(M-1,length(Aa)+1)...
eye(M-1);
zeros(1,length(Aa)+M)];
Ca=[CaDzeros(1,M-1)];
cc
(1)];
ii=1;
fori=2:
M,ii=ii*i;
Xa(length(Aa)+i)=cc(i)*ii;
end,end
Ga=ss(Aa,zeros(size(Ca'
)),Ca,D);
c=0;
d=[0,0,0,0];
x0=[1;
2;
A=[-5,2,0,0;
0,-4,0,0;
-3,2,-4,-1;
-3,2,0,-4];
B=zeros(4,1);
C=zeros(1,4);
Ga.a,xx0'
symst;
y=Ga.c*expm(Ga.a*t)*xx0
y=
14.
(a)>
G1=((s+6)*(s-6))/(s*(s+3)*(s+4+4i)*(s+4-4i))
s^2-36
----------------------------
s^4+11s^3+56s^2+96s
rlocus(G1)
增益K>
0。
(b)>
num=[1,2,2];
den=[1,1,14,8,0];
G2=tf(num,den)
s^2+2s+2
------------------------
s^4+s^3+14s^2+8s
rlocus(G2)
根据图像知,增益K>
15.
G=(s-1)/(s+1)^5;
G.ioDelay=2;
rlocus(pade(G,2))
所以K值范围是0-1.15。
16.
(a)
G=(8*(s+1))/(s^2*(s+15)*(s^2+6*s+10));
bode(G)
nyquist(G),grid
set(gca,'
Xlim'
[-61])
nichols(G),grid
[gm,pm,wg,wp]=margin(G)
gm=%幅值裕量
30.4686
pm=
4.2340
wg=%相位裕量
1.5811
wp=
0.2336
G1=feedback(G,1)
8s+8
s^5+21s^4+100s^3+150s^2+8s+8
所以系统是稳定的。
step(G1,1000)
(b)
'
H=0.45*((z+1.31)*(z+0.054)*(z-0.957))/(z*(z-1)*(z-0.368)*(z-0.99))
0.45z^3+0.1832z^2-0.5556z-0.03046
z^4-2.358z^3+1.722z^2-0.3643z
bode(H)
nyquist(H),grid
nichols(H),grid
H1=feedback(H,1)
0.45z^3+0.1832z^2-0.5556z-0.03046
------------------------------------------------
z^4-1.908z^3+1.905z^2-0.9199z-0.03046
pzmap(H1)
系统是不稳定的。
step(H1,1000)
17.
z=[-2.5];
p=[0;
-0.5;
-50];
G=zpk(z,p,100/2.5*0.5*50);
z=[-1;
-2.5];
p=[-0.5;
Gc=zpk(z,p,1000);
G1=feedback(G*Gc,1)
1000000(s+1)(s+2.5)^2
------------------------------------------------------
(s+1)(s^2+4.99s+6.239)(s^2+95.01s+1.002e006)
bode(G1)
step(G1)
第二部分:
y的仿真结果曲线:
阶跃响应曲线:
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