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Top1. Introduction
Automatic control system is very important for realizing some automatic operations in practical industry and monitoring of complex industrial processes, such as paper, glass, automotive and aircraft etc (Daraz et al., 2022, 2021; Ibraheem et al., 2020a,b; Abdul-Adheem et al., 2020a,b; Soliman et al., 2020; Gorripotu et al, 2021, 2019; Meghni et al., 2017, 2018). Practical industrial processes require some critical process variables to be maintained around their given values, for example, temperature, flow level, pressure and press. The amplitude fluctuations of process variables need to be carefully chosen and continuously controlled to achieve the products, while keeping the desired quality with the minimum raw materials and energy. Then automatic control technology was developed with this mission, being used to ensure the smooth and safe operation for industrial process or maximum corporate benefit. Generally, at present, automatic control technology has been widely used in electric power, oil refining, paper making chemical industry, energy and other industrial production fields (Mahdi et al., 2022; Sain et al., 2022; Fekik et al., 2022a,b, 2021a,b,c,d, 2020a,b; Ali et al., 2022, 2021a,b; Acharyulu et al., 2021; Ajel et al., 2021). More specifically to obtain the qualified productions during the industrial production, some key process variables are usually required to meet certain performance index. Then this performance index will eventually be realized by deigning one suitable controller. Most of the current controller design methods are model-based, so the accuracy of the considered process used in the controller design will ultimately affect the performance of the control loop system (Toumi et al., 2022; Saidi et al., 2022; Serrano et al., 2022; Humaidi et al., 2022, 2020; Hamida et al., 2022; Ben Njima et al., 2021; Ghoudelbourk et al., 2021; Pilla et al., 2021a,b; Ajeil et al. 2020a,b; Azar and Serrano, 2015). Model mismatch will deteriorate the performance of the control loop, for example, having larger overshot, longer adjustment time, oscillation, etc. All above factors lead to substandard product quality, bring great harm to the enterprise. Even if the controller designed based on the current model or identified model can meet the performance index, an improved process model can better describe the dynamic changes of the process, then one controller with better performance can be yielded from this improved process model, so that the raw material and energy consumption are reduced. Actually, most industrial processes in practice present complex nonlinear or parameter varying characteristics. Typically, controllers are designed according to a single, locally linearized model at a certain operating point, in order to achieve the specified performance requirements (Mittal et al., 2021; Al-Qassar et al., 2021a,b; Ammar et al., 2020, 2019, 2018; Kazim et al., 2022, 2021a,b; Najm et al., 2021a,b, 2020; Vaidyanathan et al., 2019, 2018a,b, 2017a,b,c; Radwan et al., 2018; Abdelmalek et al., 2018; Ouannas et al., 2020, 2017a,b,c,d, 2016a,b; Azar et al., 2018a,b; Singh et al., 2021, 2017). However practical industrial process usually has a wide operating range, and process operating points are caused by production planning, such as product grade changes, economic optimization etc., or work environment changes. But a single locally linearized model cannot describe the global dynamic behavior of the considered process, which will greatly deteriorate the performance of controller, designed based on this locally linearized model. Even this approximated linear model leads to the instability of the closed loop system or process. It can be seen that good model used to describe the global dynamic behavior of the process, is a prerequisite for the latter control design or other interesting tasks.