## 1 Introduction
However, a deficient control leading to an excessive rise in temperature can cause high fuel consumption and generate high pollution by emitting toxic gases into the environment [28]. Consequently, effective temperature control in the precalciner is decisive to guarantee a high-quality clinker and efficient energy use [29]. Currently, the precalciner temperature control is mainly carried out using conventional PID controllers [24; 30; 31]. However, the dynamic performance of the precalciner is characterized by non-linear behaviour, time delays [32; 33], parameter uncertainties, as well as large disturbances [34; 35]. Thus, the precalciner is categorised as process with complex dynamic behaviour [36; 37]. It is well-known that when processes have complex behaviours, the PID must perform well, see, e.g., [38; 39; 40]. Moreover, processes with time delays are problematic to control by conventional controllers due to control system instability [41; 42; 43]. Accurate control of these processes is very important [44; 45; 46]. These arguments constitute a strong motive for the design of advanced controllers [47; 48] that will enable effective temperature control in the precalciner, as well as improve the clinker production process, reduce damage to mechanical equipment, increase the quality of the powdered cement and reduce energy-consumption and environmental pollution. The dead-time compensator robust Hoo state feedback control (DTC-H\(\infty\)-SFC) is a novel advanced control technique that could greatly contribute to the improvement of productive processes because it combines the advantages of the robust Hoo state feedback control with the advantages of the dead-time compensator (Smith predictor) [49; 50; 51]. A review of time delay control systems and of the Smith predictor control system can be found in [52; 53]. Robustness is of vital significance in controller design, since real industrial processes are susceptible to external disturbances, measurement noises, and unmodelled plant dynamics [54; 55; 56]. The objective of this work is to design a DTC-H\(\infty\)-SFC controller for the operative temperature control in a precalciner of a cement rotary kiln. The DTC-H\(\infty\)-SFC controller harnesses a mathematical model of the controlled process to compute control signals through the state feedback, which allows the controller to develop while taking into account only the free part of the process model without the time delay because the time delay is removed from the state feedback [57; 58]. Unlike the PID controllers, the DTC-Hoo-SFC controller shows a certain insensitivity to disturbances that take place in the productive processes allowing for a compensation of the time delay effect in the feedback. Among the characteristics of the DTC-Hoo-SFC controller is the need to have an accurate process model and continuous feedback on the state of the system to achieve closed-loop stability [59; 60]. A benefit of this controller is the option of having state feedback and output feedback [61]. A sequence of controller actions is estimated and these are computed considering the process dynamics. The first component of the sequence becomes a reference point of the actuator element. If the system receives new sensor measurements, the calculation is repeated, and a new sequence is estimated. The key results of this paper are the following: (1) A mathematical model that accurately described the temperature in a precalciner is obtained; (2) A DTC-Hoo-SFC controller for the operative temperature control in a precalciner is developed. This paper is planned as follows. In Section 2, a mathematical model of the process studied is obtained using systems identification techniques, and the design of the DTC-Hoo-SFC controller is developed. Section 3 shows the discussions of the attained results. Lastly, a few conclusions are given in Section 4.