Page 165 - Distributed model predictive control for plant-wide systems

Networked Distributed Predictive Control with Information Structure Constraints 139

⎡ (1) ⋅
s ··· ⎤
⋅ ⋮
⎢ (2) ⎥
A = ⎢ s ⎥
ss
⎢ ⋮ ⋱ ⎥
··· ⋅
⎢ (n s ) ⎥
⎣ s ⎦
⎡(1 − ) I L ··· ⎤
⎢ I L (1 − )I L ⋱ ⋮ ⎥
+
⎢ ⋮ ⋱ ⋱ ⎥
⎢ ⎥
⎣ ··· I L (1 − )I ⎦
L
⎡ (1)
s ⎤
B = ⎢ ⋮ ⎥
ss
⎣
⎢ (n s ) ⎥
s ⎦
[
C = m −1 ⋅ 1×L⋅(n s −1) 1×L ]
ss
[ ]
L×L⋅(n s −1) I
D = L
s,s−1 L(n s −1)×L⋅(n s −1) L⋅(n s −1)×L
( )
(1, j)
⎡ ⎤
a ̆x s ··· 0
(j) = ⎢ ⎥
s ⎢ ⋮ ⋱ ⋮ ⎥
⎢ 0 ··· a(̆x (L, j) ⎥
⎣ s ) ⎦
(1, j) (1, j) (1, j)
⎡ s (̆x s − x ) ⋅ (̆x s )⎤
∞
(j) (L−2)×1
(x )= ⎢ ⎥
s
s
⎢ (L, j) (L, j) (L, j) ⎥
⎣ s (̆x s − x ) ⋅ (̆x s )⎦
∞
−1 1 0 ··· 0
⎡ ⎤
⎢ 1 −2 1 ⋱ ⋮ ⎥
= ⎢ 0 ⋱ ⋱ ⋱ 0 ⎥
⋮ ⋱ 1 −2 1
⎢ ⎥
⎢ ⎥
⎣ 0 ··· 0 1 −1⎦
I ∈ ℝ L×L
L
{
(i, j) (i, j) a
s =(̆x s ∕x) , s ∈ C W
(i, j) (i, j)
s = h (̆x s ), s ∈ C A
air
{ ( ) b
c
u = 2186.7 × 10 −6 × a ⋅ v∕v 0 ×(F ∕F ) , s ∈ C W
0
s
s
u = 1, s ∈ C A
s
(i, j) (i, j) 2 (i, j) (i, j)
a(x s )=−Δt ⋅ (x s )∕(Δz (x s ))c (x s ))
p
(i, j) (i, j) (i, j)
(x s )=Δt ⋅ a(x s )∕ (x s )
=Δt ⋅ v∕Δl, i = 1, 2, … , L, j = 1, 2, … , n
s