For each of the sections, a linearized model for the furnace was derived near the midpoint of the respective section (e.g., for section4 the model was linearized near T2 = 910��Celsius).MLD hybrid model generated from the HYSDEL file for the multimodel linearized problem has 25 continuous states, 9 inputs (4 continuous, 5 binary), and 3 continuous outputs. The HYSDEL Temsirolimus model has 22 continuous auxiliary and 15 binary auxiliary variables. The optimization problem to be solved has 118 mixed-integer linear inequalities. The sampling time of the system is 0.5 minutes. If comparison to the hybrid model of the furnace linearized in one operating point whose HYSDEL representation has only 38 mixed-integer linear inequalities, it is obvious that the complexity of the optimization problem is significantly increased with the introduction of multimodel linearization.

This affects the computation time of the optimization algorithm and favors the one point linearization method for implementation if it has satisfactory behavior.3. Simulation ResultsIn order to compare the quality of the designed controllers, we have designed equivalent simulation conditions for the four algorithms. In this study, we will compare the linear MPC, multiple-model MPC, hybrid MPC, and hybrid multiple-model MPC.The disturbance signals from the front and the back hatches and the timing of the pipe entering in the first zone of the furnace are graphically represented on Figure 4. In Figure 4, the logic variable for pipes entering zone 1 is presented. The logic variables for zones 2 and 3 have deterministic dependence on this value with fixed delay.

In reality, this delay is represented through the line speed of the conveyor driving the pipes in the furnace, but this is to be done in near future. During this simulation, a fixed delay time of 10 minutes between zones is adopted. During the simulation, the continuous disturbance signal has value of 15��Celsius.Figure 4Disturbances during the experiment.The Anacetrapib main results are presented in Figures Figures5,5, ,6,6, and and77 where the temperatures in the respective zones of the furnace are presented long with the reference signal. The control signals applied to the three control valves, respectively, are presented in Figures Figures8,8, ,9,9, and and10.10. Figure 5Temperature in the first zone.Figure 6Temperature in the second zone.Figure 7Temperature in the third zone.Figure 8Control actions of the first valve.Figure 9Control actions of the second valve.Figure 10Control actions of the third valve.From the presented results, it is obvious that introducing the hybrid control approach for high consumption industrial furnace improves the quality of the control.