Page 278 - Distributed model predictive control for plant-wide systems
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252                           Distributed Model Predictive Control for Plant-Wide Systems


                650
                                                                     Measurement of CT
                640                                                  Prediction of CT
              Temperature (°C)  620
                630

                610
                600
                590
                580
                   0      2      4      6      8      10     12      14     16     18
                                               Time (s)

                   Figure 11.5 Comparison between the predictive CT and the measurement of CT



                      1000
                     Temperature (°C)  800


                       600

                       400
                         6
                              4
                         Layer     2                                  25    30
                                                           15    20
                                                      10
                                        0  0    5
                                                            Position
                            Figure 11.6  Initial states of process model and observer


           11.4.2   Convergence of EKF
           The convergence of EKF is verified through a simulation here. The initial states (the temper-
           ature of each volume) of process model and observer are shown in Figure 11.6, where the
                                        ◦
           initial states of the observer are 30 C higher than those of the process model. The states of
           header groups are [1,1,1,1,1,1,0,0,0,1,1,1], where 1 stands for opening and 0 means closing.
           The coiling speed v equals to10.74 m s − 1 . The water fluxes in the main cooling section and the
                                                                            ◦
                                        2
                                                  3
                                   3
                                                       2
           fine cooling section are 200 m /(s m ) and 150 m /(s m ), respectively. FT is 870 C. For spa-
           tial reason, the temperatures of 2nd, 6th, 10th, and 14th subsystems at layers from top surface
           to central of strip are selected as examples to illustrate the convergence of EKF. Figure 11.7
           shows that the temperatures observed by EKF are convergent to temperatures estimated by the
           process model.
           11.4.3   Performance of DMPC Comparing with Centralized MPC
           Since the main disturbance comes from FT, FT step signal is sent into a closed-loop system
           to compare the performance of the DMPC framework proposed and that of centralized MPC.
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