## 2 Identification of the Dynamic Behavior of the Steel Slab Reheating Furnace  
The steel slab reheating furnace under study belongs to the Aceros Arequipa Corporation, which is the most important steel bar producing company in the country. One of the fundamental stages of the corrugated bar production process is the slab reheating process, in which the slabs are heated in order to adopt ductility properties for the customer rolling process [27]. The stage of slab heating is one of the most important processes in the manufacture of corrugated iron. Therefore, the control of the heating zone temperature in the slab reheating furnaces is key. This is due to the fact that a high temperature can generate an excessive increase of the grains (crystallites) producing cracks in the slabs, and a low temperature can produce the decrease of the flexibility of the steel increasing the resistance to deformation and causing damage to the equipment during the rolling process [28; 29]. The slab reheating furnace under study is composed of an automation system for control of the heating zone temperature which consists of a feedback mechanism widely used in the industry. Since the slabs must reach a certain uniform temperature, if the necessary operational measures are not taken to control the temperature of the zones that make up the furnace, serious damage to the mechanics of the system can be generated [30]. The controllers used for the control of the heating temperature in this slab reheating furnaces are the well-known PI/PID controller, which does not ensure the effective control of industrial processes characterized by a difficult dynamic behavior [31; 32; 33]. For the design of effective industrial controllers, mathematical models that characterize the dynamic behavior of the processes under study are required, see, e.g., [34; 35]. However, in the case of slab reheating furnaces, it is very complicated to obtain this kind of model using mass and energy balance equations (first principles) [1]. Currently, system identification is a powerful tool for obtaining mathematical models of the complex dynamical processes using real-time data of their observed variables, such as input variables and output variables [36; 37]. The slab reheating furnace under study is provided with a heating zone temperature sensor, air flow, and fuel flow sensors, as well as two proportional valves for the control of the critical variables. Additionally, this furnace has a SCADA supervision system (WinCC) for monitoring the entire production process, which favors the work of collecting and storing input and output data [38; 39; 40; 41]. For the development of the systems identification experiments, the variation of the fuel flow \(\left(Q_{f}(t)\right)\) that feed the furnace burner were considered as input variable (manipulated) \(\left(\Delta u(t)\right)\), and as output variable the heating zone temperature variation inside the slab reheating furnace \(\left(\Delta y(t)\right)\). In addition, this process is influenced by different disturbances among which are the variation in the number of slabs that enter the reheating furnace, the calorific power of the fuel, the air temperature, etc. Figure 1 shows a diagram of the experimental arrangement for the collection of output/input data in operating conditions of the slab reheating furnace under study. For the development of this experiment the following instruments were used: An industrial PC, a programmable logic controller (PLC), and a temperature sensor. To obtain the mathematical model that describes the nominal dynamic behavior of the heating zone temperature, an experiment with a step signal was initially developed, with the purpose of calculating a first estimate of the order and parameters of the model of the said process. The fuel flow valve was excited in order to obtain a variation of the heating zone temperature in the slab reheating furnace.