Page 176 - Distributed model predictive control for plant-wide systems

150 Distributed Model Predictive Control for Plant-Wide Systems

The online optimization of serially connected large-scale systems can be converted to that of
several small-scale systems via distributed computation, thus can significantly reduce the com-
putational complexity. Meanwhile, information exchange among neighboring subsystems in a
distributed structure via communication can improve control performance, which is superior
to traditional decentralized MPC methods. The following two subsections are to analyze the
convergent condition of the proposed networked predictive control algorithm and the nominal
stability for distributed control systems without inequality constraints.
The control and output constraints will not be addressed in these two sections, but can be
incorporated directly into the local optimization problems.

7.3.4 Convergence and Optimality Analysis for Networked

At the sampling time instant k , the output prediction model for each subsystem at iteration l
can be described as
(l) ∑ (l)
Y (k)= G ̂ x (k)+ H ΔU (k)+ H ΔU (k) (i = 1, … , m) (7.54)
̂
i,P i i ii i,M ij j,M
j∈ℕ i , j≠i
(l)
where G , H , and Y (k) are given in Equation (F1) in Appendix F.
̂
i,P
ij
i
The relationship of control decision for the subsystem S between iteration l and iteration
i
l + 1 can be derived by solving the local QP problem (7.52) without inequality constraints
( ) −1
∑
(l+1) T
ΔU (k)= H Q H + R
i,M ji j ji i
j∈P i
(7.55)
⎡ ⎤
∑ T ∑ (l)
H Q R (k) − G ̂ x (k)− H ΔU (k) ⎥
⎢
ji j j,P j j jh h,M
⎢ ⎥
j∈P i h∈P j ,h≠i
⎣ ⎦
The integral control decision of the whole system can be written as
(l+1) −1 (l) −1 T
ΔU (k)=−( + R) Φ ΔU (k)+( + R) H Q[R (k)− Ĝ x(k)] (7.56)
M d nd M d P
where
[ T T ] T
R (k)= R 1,P (k) ··· R m,P (k)
P
[ T T ] T
x(k)= x (k) ··· x (k)
1 m
G = block-diag(G , … , G )
1
m
Q = block-diag(Q , … , Q )
1 m
R = block-diag(R , … , R )
1 m
= block-diag(S , … , S )
d 1 m
∑ T
S = H Q H ji
j
i
ji
j∈ℕ i