最优控制实验Word格式.docx
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0.5;
0;
-1];
C=[1
0
0;
1
0];
D=0;
Q=diag([1,0,1,0]);
R=[1];
[K,P,e]=lqr(A,B,Q,R);
Ac=A-B*K;
Bc=B;
Cc=C;
Dc=D;
T=0:
0.02:
6;
U=ones(size(T));
[Y,X]=lsim(Ac,Bc,Cc,Dc,U,T);
plot(T,Y(:
1),'
.-'
T,Y(:
2));
xlabel('
Time(sec)'
);
ylabel('
Response'
grid;
legend('
cart'
'
pendulum'
)
disp('
K='
),disp(K);
P='
),disp(P);
Q='
),disp(Q);
A=[0100;
C=[1000;
0010];
Q=diag([1,1,1,1]);
R=[0.1];
[K,P,e]=lqr(A,B,Q,R);
Ac=A-B*K;
Bc=B;
Cc=C;
T=0:
xlabel('
ylabel('
grid;
e='
),disp(e);
K=
-3.1623-6.6417-82.2581-16.5062
P=
2.10031.70565.21971.1690
1.70563.04979.79402.1890
5.21979.794065.796313.1228
1.16902.189013.12282.7451
e=
-7.3085+0.0000i
-4.0976+0.0000i
-0.8897+0.4933i
-0.8897-0.4933i
将r改为10的图像:
-0.3162-1.5313-64.1858-12.0873
1.0e+03*
0.00480.01120.03820.0088
0.01120.05050.17630.0405
0.03820.17633.80740.7300
0.00880.04050.73000.1411
-5.5827+0.0000i
-5.2675+0.0000i
-0.2357+0.2232i
-0.2357-0.2232i
实验二:
(1)
代码:
A=[0,1;
-1,-1];
B=[1;
1];
C=[01];
Q1=[0,1];
Q=diag(Q1);
N=[0;
2];
K=dlqr(A,B,Q,R,N)
Ac=(A-B*K);
Bc=B;
Cc=C;
Dc=D;
T=0:
0.01:
15;
U=ones(size(T));
sys_c=ss(Ac,Bc,Cc,Dc);
[Y,T,X]=lsim(sys_c,U,T);
figure
(1)%½
¨
Á
¢
Í
¼
Ð
Î
plot(T,Y)%Ö
Æ
£
¬
Ò
Ô
TÎ
ª
º
á
×
ø
±
ê
YÎ
Ý
time(s)'
%º
move(m)'
½
Ç
¶
È
'
u'
dlb2'
K值:
K=
-0.19640.0906
图标:
(2)
Q1=[1,1];
N=[1;
-0.28170.0000
图像:
(1)Q=[1000;
01];
A=[01;
-11];
KX=dlqr(A,B,Q,R);
[K,S]=[-0.0188,0.9904]
用上述方法进行迭代