4
.
, . - .
, . , . , . , (sampling) , (sampling time) . , .
.
, (1.11)
x[(k+1)h]≈ x(kh)+h∙f(x,u) (1.15)
h - k - ; f(x,u) (1.11). , h .
x1[(k+1)h]=(1+ha11)x1(kh)++ha1nxn(kh)+ hb11u1(kh) ++ hb1rur(kh)
.
. (1.16)
.
xn[(k+1)h]=(1+han1)x1(kh)++hannxn(kh)+ hbn1u1(kh) ++ hbnrur(kh)
, u(t) , .. /.
(1.16) h .
y (kh)= C x (kh)+ D u (kh) (1.17)
.
, (1.16) .
/.
, , w , , , .. . - q (shift operator). z (t) , h (forward shifting).
qz(kh)=z[(k+1)h] (1.18)
, . .
|
|
q-1 (backward shift operator) .
qnz(kh)=qqqz(kh)=z[(k+n)h] (1.19)
q x(kh), .
[ (1.17)], , ,
y[(k+n)h]+a1y[(k+n-1)h]++any(kh)=b0u[(k+n)h]++bnu(kh) (1.20)
q
(qn+a1qn-1++an)y(kh)=(b0qn+b1qn-1++bn)u(kh) (1.21)
, . q . H(q) (discrete operator) (1.21)
H(q)= (1.22)
(1.22) n . , /
H*(q)= (1.23)
, , .