The hybrid MPC, one linearized model method, has also satisfactory results. HTS The multiple-model MPC also shows satisfactory results, but there is oscillatory behavior at the reference values. Since we have linearized models, the tracking of the referent trajectory is best when it is near the linearization point(s), and as the referent trajectory moves from this point we have bigger error in the control algorithm. This is more expressed in the hybrid controller with only one linearization point, which is linearized near 800�� degrees. In this case, it is obvious that output tracks the reference without any problem near this region, but if we have work plans that require a lot of temperature changes throughout the temperature domain of the furnace, the multimodel hybrid approach is to be considered.

The previous remark, regarding the performance of the controller near the linearization point, also stands for the multimodel hybrid approach. The difference here is that we have several models, and the difference between the set-point and the active model cannot be very big. Logically, if we introduce more models linearized in different operating points we will increase the performance of the controller, but also we will increase the complexity and the time necessary to perform the optimization. Regarding the control signals, on all three figures (Figures (Figures8,8, ,9,9, and and10)10) we can note that the hybrid controllers have fast reaction time to the disturbances. When there is new pipe entering in one of the zones of the furnace, the control signal in the respective zone acts towards stabilization of the temperature.

Also, we can note that when the furnace is operating near 800�� degrees, all three controllers generate the same control value, but if we move far from this central linearization point, the calculated values for the control action differ a lot.4. ConclusionIn order to obtain real measure of the controller’s quality, we must compare their performances. Therefore, we have designed a complete test scenario, which defines the conditions during the simulation. Of course we must keep in mind that the proposed algorithms are specific to the problem they address. Anyway, these differences will be explained in detail in this chapter. In Table 1, we present the abbreviations used to specify the algorithms along with the full names.

Table Dacomitinib 1Abbreviations and full meaning of the algorithm’s names.Discrete automaton for the furnaces states on the first zone.We have run several simulations for each of the controllers with the same simulation conditions. During these simulations, we have properly tuned up the controllers so we can compare their best performances. Also during the simulations, we have tested the robustness of the controllers by adding small disturbances (opening of the front and back hatches).