Page 255 - Distributed model predictive control for plant-wide systems

Networked Distributed Predictive Control with Inputs and Information Structure Constraints 229

subject to the constraints (10.52)
s
∑
‖ p ‖
‖u (k + l|k) − ̂ u (k + l|k)‖
s−l ‖ i i ‖2
l=0
(1 − )
≤ √ , s = 1, 2, … , N − 1,
2 m(m − 1)
p f
‖x (k + s|k)‖ ≤ ‖x (k + s|k)‖
i P i i P i

+ √ , s = 1, 2, … , N,
N m
p
u (k + s − 1|k)∈ U , s = 1, 2, … , N,
i i
p
x (k + N |k)∈Ω ( ∕2), j ∈ L
j,i j
It can be seen that the optimization problem with C-DMPC is much simpler than Prob-
lem 10.1. The constraints (10.13) in Problem 8.1 have not appeared. It is because that the
assumed state sequences of other subsystems are not used in the predictive model of each
subsystem-based MPC.

10.6 Simulation Results
10.6.1 The System

A distributed system consisting of four interacted subsystems is used to demonstrate the effec-
tiveness of the proposed method. The relationship among these four subsystems is shown in
Figure 10.1, where S is impacted by S , S is impacted by S and S , and S is impacted
1
2
1
3
4
2 [
by S .Let ΔU be defined to reflect both the constraint on the input u ∈ u min u max ] and the
3 i i i i
[ min max ]
constraint on the increment of the input Δu ∈ Δu i Δu i .
i
The models of these four subsystems are respectively given by
S ∶ x (k + 1)= 0.62x (k)+ 0.34u (k)− 0.12x (k)
2
1
1
1
1
S ∶ x (k + 1)= 0.58x (k)+ 0.33u (k)
2
2
2
2
(10.53)
S ∶ x (k + 1)= 0.60x (k)+ 0.34u (k)+ 0.11x (k)− 0.07x (k)
3
1
3
3
3
2
S ∶ x (k + 1)= 0.65x (k)+ 0.35u (k)+ 0.13x (k)
4
4
3
4
4
For the purpose of comparison, both the centralized MPC and the N-DMPC are applied to
this system.
1
4
x 1
x 3
x 2
3
x 2
2
Figure 10.1 The interaction relationship among subsystems