Page 269 - Distributed model predictive control for plant-wide systems

Hot-Rolled Strip Laminar Cooling Process with Distributed Predictive Control 243

main cooling section N ho is used to adjust the strip temperature at the exit of main cooling
section, and is calculated online according to the feedforward signal of FT at each control
period as follows:
( )
x FT − x cm
N = Int
ho
CR
m
where x is the reference temperature at the exit of main cooling section, x is the finishing
cm FT
rolling temperature, and CR is the reference cooling rate in main cooling section. In the
m
closed-loop part, a PI controller is employed to control the water flux in fine cooling section
according to the feedback measurement of CT.
However, in this method, some inaccurate or unreasonable assumptions are applied addi-
tionally for the simplification of this large-scale system (e.g., the cooling rate in main cooling
section is impossible to be constant if the water flux of every header remains the same), which
makes the system less flexible for various cooling curves and be less precise. On the other
hand, since the major disturbance (the fluctuation of x ) does not feed into PI controller in
cm
closed-loop part, it is also difficult to achieve an accurate CT. Thus, this control method is
difficult to satisfy the increasing quality requirements of steel industry.

11.2.3.2 Why Using DMPC Framework
To obtain productions with better quality, a suitable optimization method is required for mak-
ing the average temperature of strip in thickness direction consistent with the desired temper-
ature profile at any position of the water-cooling section. To realize it, we should consider the
water flux of each header group as an individual manipulated variable rather than consider all
of them as one or two manipulated variables simply. That means the control method should be
suitable for large-scale, nonlinear, and relatively fast MIMO system. Furthermore, this opti-
mization method should be able to account for the major measurable disturbance of FT online
for precision enhancing.
MPC is widely recognized as a practical and well-performed control technology for pro-
cess control, especially for MIMO system. The measurable disturbance can also be taken into
account through the prediction model of MPC. Thus, MPC can be a good selection for this
system. As shown in Figure 11.2, the desired geometrically location-dependent temperatures
are selected at the locations l , l , … , l as the reference temperatures with the notation
1 2 N
[ ] T
r = r r ··· r N (11.5)
2
1
Here, l , l , … , l correspond to the locations of the exit of each header group and the loca-
1 2 N
tions of the pyrometers used to measure FT and CT. The optimization objective is to minimize
P M
∑ ∑
2
J = ‖y(k + t|k)− r(k + t)‖ + 2 (11.6)
Q ‖Δu(k + h − 1|k)‖ R
t=1 h=1
T
where y =[y ··· y ] , y (s = 1, … , N) is the average temperature of strip at position l , u,the
s
1
s
N
manipulated variable vector, refers to the future sequence of water flux, Δu is the increment of
manipulated variable vector u, P is the prediction horizon, and M is the control horizon. The
weighting matrices Q and R are positive definite and have block-diagonal forms.