Page 183 - Distributed model predictive control for plant-wide systems

Networked Distributed Predictive Control with Information Structure Constraints 157

Preheating Zone Heating Zone Soaking Zone
Thermometer
Burner
⊕ ⊕ ⊕
Billet

Charging Discharging

⊕ ⊕ ⊕

Figure 7.13 Structure of a walking beam reheating furnace

Thermal transmission is carried through only from the end to the head of the furnace, the
dynamic model of the reheating furnace is derived using material and energy balances [110].
The linear model of the reheating furnace for networked MPC design can be described as

⎧ 0.002757
y (s)=
1
⎪ 1 u (s)
s + 0.00572
⎪
⎪ 0.003983 −32.8s 0.001009 −52.5s
⎨ y (s)= e u (s)+ e y (s)
2
2
1
s + 0.001891 s + 0.001907
⎪
⎪ 0.001088 −33.2s 0.003224
⎪y (s)= e u (s)+ y (s)
2
3
3
⎩ s + 0.003857 s + 0.004634
where y , y and y are the furnace temperatures of the soaking, heating and preheating zones,
3
1
2
and u , u and u are fuel feed flows of the soaking, heating and preheating zones, respectively.
1
3
2
With the proposed networked MPC scheme, the reheating furnace process can be decom-
posed into three subsystems, they are subsystems of soaking zone (the first subsystem), heating
zone (the second subsystem) and preheating zone (the third subsystem), respectively, i.e.
⎧ 0.002757
y (s)=
⎪ 1 u (s)
1
s + 0.00572
⎪
⎪ 0.003983 −32.8s
⎨ y (s)= e u (s)
2
2
s + 0.001891
⎪
⎪ 0.001088 −33.2s
⎪y (s)= e u (s)
3
3
⎩ s + 0.003857
The local performance index for each subsystem employs the expression in (36), With
regards to neighborhood optimization, the new performance index for each subsystem is as
follows:
J (k)= J (k)+ J (k)+ J (k)
3
i
1
2
each subsystem are set with P = 30, M = 10, Q = 10, R = 2(i = 1, 2, 3), using sampling time
i
i
of 1 min. MATLAB-based simulation results (Figure 7.14) show the furnace temperatures and
the fuel feed flows of three zones running for 4 h. It can be seen that the furnace temperatures
of three zones in this distributed structure follow their set-points (shown as the dotted lines in
the figure) satisfactorily and that the interaction between the channels is effectively reduced.