Page 258 - Distributed model predictive control for plant-wide systems

232 Distributed Model Predictive Control for Plant-Wide Systems

u 1
0
u 2
u 3
u 4
–0.5
u i

–1

–1.5
5 10 15 20
Time (s)

Figure 10.3 The evolution of the control inputs under the N-DMPC

are [−2, 2] and [−1,1], respectively. Set the initial presumed inputs and states of each local
cost optimization based DMPC be the solution calculated by a centralized MPC and the cor-
responding predictive state sequences at time k = 0.
0
Figures 10.4 and 10.5 show the state responses and the control inputs of the closed-loop sys-
tem under the control of the centralized MPC. Figures 10.6 and 10.7 show the state responses
and the control inputs of the closed-loop system under the control of the local optimization
based DMPC. The shape of the state response curves under the centralized MPC are sim-
ilar to those under the N-DMPC, all subsystems converge to near zero in 8 sec. Under the
LCO-DMPC control design, all subsystems converge to near zero in about 14 sec. There is no
significant undershooting.
Figures 10.8 and 10.9 show the differences between the absolute value of the states and
control inputs of the closed-loop system under the centralized MPC and those under the
N-DMPC, respectively. The state responses under the N-DMPC are very similar to those

x 1
1
x 2
x 3
x 4
0.5
x i

0

–0.5
5 10 15 20
Time (s)
Figure 10.4 The evolution of the states under the centralized MPC