:
- , ;
- . .
x(t0)
x(tk) ≅0, (2)
.
,
Gk Q(t) - , R(t) - .
, (3), (1) -
.
(7) (1) :
(8), (9)
S(t)
S(tk) = Gk,
.
. .
, Gk, Q(t) R(t) , , :
.
,
tk=∞, Q R
(11)
(13)
,
ζ , .
T u2(t)
u2(t), x1(t), x2(t) v1(t), (22) .
|
|
ζ T q11 q22
q11 q22 . , .
tk ( ) tk.
, , (23)
, , , ..
:
ü
ü
ü
:
, :
:
> W=[tf([16],[0.01 0.08 1]) tf([16],[0.01 0.08 1])]
Transfer function from input 1 to output:
---------------------
0.01 s^2 + 0.08 s + 1
Transfer function from input 2 to output:
---------------------
0.01 s^2 + 0.08 s + 1
>> [A,B,C,D]=SSDATA(W)
A = //
0 -12.5000
8.0000 -8.0000
B = //
0 0
0 8.0000
C = // ()
1.0000 0
0 12.5000
Q = //
4.5903 0
0 0.0000
:
:
R -:
lqr (MatLAB)
[K,S,E]=lqr(A,B,Q,R)
sys1=ss(A,B,eye(2),D);
sys2=ss(K);
sys3=ss(C);
Pss1=feedback(sys1,sys2);
Pss1=series(Pss1,sys3);
[A1,B1,C1,D1] = ssdata(Pss1);
:
feedback, , .