자동제어 | 가관측성표준형 |
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작성자 cemtool 작성일14-04-22 12:27 조회15,145회 댓글1건본문
상태방정식의 계수행렬이 다음과 같다.
«풀이»
상태방정식을 가관측성표준형으로 변환하려면, 먼저 행렬 Q을 구한 후 공식을 이용하여 를 구한다. 행렬 Q는
을 사용하여 구한다.
- ex3_7.cem
A = [1 2 1; 0 1 3; 1 1 1]; B = [1; 0; 1]; C = [1 1 0]; D = [0]; coeff = poly(A); a1 = coeff(3); a2 = coeff(2); M = [a1 a2 1; a2 1 0; 1 0 0]
M = -1.0000 -3.0000 1.0000 -3.0000 1.0000 0.0000 1.0000 0.0000 0.0000
- ex3_7.cem
V = [C; C*A; C*A^2]
V = 1 1 0 1 3 4 5 9 14
Q = 0.3333 -0.1667 0.3333 -0.3333 0.1667 0.6667 0.1667 0.1667 0.1667
Abar = 0.0000 0.0000 3.0000 1.0000 0.0000 1.0000 0.0000 1.0000 3.0000
Bbar = 3.0000 2.0000 1.0000
- ex3_7.cem
Cbar = C*Q
Cbar = 0 0 1
앞의 예제와 마찬가지로 tr2ocf 라는 함수를 만들어 사용할 수 있다.
- ex3_7.cem
function; Q, Abar, Bbar, Cbar<>A, B, C, D a = poly(A); if( a != 1 ) a = a/a(1); order = length(a)-1; V = C; M = a(order); for(i=1;i<order;i=i+1) M = [M; a(order-i)]; for(i=1;i<order;i=i+1){ V = [V; C*A^i]; vec = a(order-i); for(j=1;j<order-i;j=j+1) vec = [vec; a(order-i-j)]; for(j=order-i;j<order;j=j+1) vec = [vec; 0]; M = [M vec]; }Q = inv(M*V); Abar = inv(Q)*A*Q; Bbar = inv(Q)*B; Cbar = C*Q; Dbar = []; if(nargin == 4) Dbar = D;
tr2ocf를 사용하여 가관측성표준형을 구해보자.
- ex3_7.cem
A = [1 2 1; 0 1 3; 1 1 1]; B = [1; 0; 1]; C = [1 1 0]; D = [0]; [Q, Abar, Bbar, Cbar] = tr2ocf(A,B,C)
Q = 0.3333 -0.1667 0.3333 -0.3333 0.1667 0.6667 0.1667 0.1667 0.1667 Abar = 0.0000 0.0000 3.0000 1.0000 0.0000 1.0000 0.0000 1.0000 3.0000 Bbar = 3.0000 2.0000 1.0000 Cbar = 0 0 1
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