현대제어 control law , estimation , output feedback 시뮬레이션

소개글

현대제어 control law , estimation , output feedback 시뮬레이션에 대한 보고서 자료입니다.

목차

[1] MatLab exercise of the p.18 example

[2] MatLab exercise of the p.19 example

[3] MatLab exercise of the p.20 example

[4] Design the output feedback control for the DC motor problem.

[5] MatLab exercise of the p.26 example

[6] MatLab exercise of the p.29 example

본문내용

poles1 = roots([1 2*zeta*wn wn^2]);
K = acker(A,B,poles1);
poles2 = [-8 -8];
Lt = acker(A',C',poles2);
L=Lt';
Anew = [A -B*K;L*C A-B*K-L*C];
Bnew = [0;0;0;0];
Cnew = [C zeros(size(C))];
x0=[1 -2 0 0];
t = 0: 0.01 : 5;
u = 0*t;
[y,x] = lsim(Anew,Bnew,Cnew,0,u,t,x0);
plot(t,x);
grid
legend('x1 (=y)','x2', 'x1 hat','x2 hat');
[5] MatLab exercise of the p.26 example
A=[0 1;0 -1];
B=[0;1];
C=[1 0];
D=0;
Q=[1 0;0 0];
r=1;
[P,E,K]=care(A,B,Q,r);
Anew = A -B*K;
x0=[1;1];
t = 0: 0.01 : 10;
u = 0*t;
[y,x] = lsim(Anew,B,C,D,u,t,x0);
P
K
for i=1:1:1001,
u(i)=-K(1)*x(i,1);
end
plot(t,x,t,u);
grid
legend('x1','x2','u');
-실행결과-
1)q=1, r=0.1
P =
0.8558 0.3162
0.3162 0.1706
K =
3.1623 1.7064
2)q=1, r=1
P =
1.7321 1.0000
1.0000 0.7321
K =
1.0000 0.7321
[6] MatLab exercise of the p.29 example
A=[0 1;0 -1];
B=[0;1];
C=[1 0];
D=0;
I=[1 0;0 1];
Q=[1 0;0 0];
r=1;
a=0;
[P,E,K]=care(A+a*I,B,Q,r);
Anew = A -B*K;
x0=[1;1];
t = 0: 0.01 : 10;
u = 0*t;
[y,x] = lsim(Anew,B,C,D,u,t,x0);
P
K
poles=eig(Anew)
for i=1:1:1001,
u(i)=-K(1)*exp(-a*i)*x(i,1);
x(i,1)=exp(-a*i)*x(i,1);
x(i,2)=exp(-a*i)*x(i,2);
end
plot(t,x,t,u);
grid
legend('x1','x2','u');
-실행결과-
1. q=1, r=1
1) a=0
P =
1.7321 1.0000
1.0000 0.7321
K =
1.0000 0.7321
poles =
-0.8660 + 0.5000i
-0.8660 - 0.5000i
2) a=1
P =
6.4641 3.7321
3.7321 2.7321
K =
3.7321 2.7321
poles =
-1.8660 + 0.5000i
-1.8660 - 0.5000i
3) a=10
P =
1.0e+003 *
7.2203 0.3800
0.3800 0.0380
K =
380.0085 38.0003
poles =
-19.0029
-19.9974
2. q=1, r=0.1
1)a=0
P =
0.8558 0.3162
0.3162 0.1706
K =
3.1623 1.7064
poles =
-1.3532 + 1.1537i
-1.3532 - 1.1537i
2) a=1
P =
1.8589 0.6869
0.6869 0.3706
K =
6.8687 3.7064
poles =
-2.3532 + 1.1537i
-2.3532 - 1.1537i
3) a=10
P =
722.2722 38.0085
38.0085 3.8003
K =
380.0848 38.0029
poles =
-19.0300
-19.9729
a=10일때는 transient response가 상당히 짧아졌습니다.

키워드

현대제어,   control law,   estimation,   output feedback,   제어공학,   선형시스템