Improved Chemical Process Operations through Data-Based Disturbance Models Finding no. of disturbances
Model x + = Ax + Gw
Tr(Q)
w ∼ N(0, Q) 2 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0
min Ψ (Q, Rv )
y = Cx + v
(1)
Q,Rv
v ∼ N(0, R)
subject to
Q, Rv ≥ 0
Ψ (Q, Rv ) = Φ(Q, Rv ) + ρtr(Q)
Theorem A solution (Q, Rv ) to the ALS-SDP in (1) is unique if dim[Null(M)] = 0.
ρ = 0.36
0
2
4 6 Fit to data Φ
J.B. Rawlings (U. Wisconsin)
8
10
M = (C ⊗In )(In2 −A⊗A)−1 (F ⊗F )Dg 2008
1/1
