The H_∞ Sliding Mode Control (H_∞ SMC) approach was introduced at the onset of this millennium as a proficient strategy integrating sliding mode and H_∞ control principles to leverage their robust attributes while avoiding inherent limitations, thereby facilitating the control of complex perturbed nonlinear systems. This review study explores noteworthy advances in the academic community of H_∞ SMC from January 2019 to September 2024, revealing notable progress with cutting-edge achievements in design methods and applications. First, the importance of H_∞ SMC is explained with its primary perspectives. The motivation and contribution of this paper are then discussed in light of the lack of review works on the topic of interest. After that, the problem systems controlled using H_∞ SMC and the challenges and perturbations included in each previous study are presented. In addition, the H_∞SMC design methods are qualitatively and quantitatively analyzed, with extensive critique reported for each reported method. Figures and tables are provided for overall review. Finally, remaining issues and new study directions are provided to help scholars improve and grow the research subject. The observations of this review show that more contributions are needed to compensate different applications using further novel design methods.

This paper delves into the intricate dynamics of industrial fluid catalytic cracking, a pivotal process in refining universal oil products (UOP). At the core of this investigation is the endeavor to derive a comprehensive mathematical model that captures the essence of mass and energy balances within a UOP fluid catalytic cracking unit. The study’s central objective is to explore and apply a ratio control algorithm in two distinct operational scenarios. In the first scenario, the ratio controller is strategically positioned after the control valve for the regenerator’s input air, while in the second, it precedes the control valve. The primary focus here is the meticulous control of outlet temperatures for both the riser and regenerator reactors. Leveraging the capabilities of MATLAB software, the research methodically simulates the fluid catalytic cracking process. It introduces variables such as the gas oil feed rate, along with the temperatures of the gas oil feed and air, to rigorously test the efficacy of the proposed ratio control algorithm. The results of this investigation reveal a notable superiority of the ratio control in case one over case two. In the riser and regenerator reactors, this advantage is demonstrated by improved stability and operational efficiency, as evidenced by lower integral absolute error (IAE) readings and a quicker approach to the intended setpoint temperatures.

Efficient flowrate control is paramount for the seamless operation and reliability of petroleum transportation systems, where precise control of fluid movement ensures not only operational efficiency but also safety and cost-effectiveness. The main aim of this paper is to develop a highly effective modified model reference PID controller, tailored to ensure optimal flowrate control of petroleum products throughout their transportation. Initially, the petrol transportation process is analyzed to establish a suitable mathematical model based on vital factors like pipeline diameter, length, and pump attributes. However, using a basic first-order time delay model for petrol transportation systems is limiting due to inaccuracies, variable delay issues, safety oversights, and real-time control complexities. To improve this, the delay portion is approximated as a third-order transfer function to better reflect complex physical conditions. Subsequently, the PID controller is synthesized by modifying its structure to address flowrate control issues. These modifications primarily focus on the controller’s derivative component, involving the addition of a first-order filter and alterations to its structure. To optimize the proposed controller, the genetic, black hole, and zebra optimization techniques are employed, aiming to minimize an integral time absolute error cost function and ensure that the outlet flow of the controlled system closely follows the response of an appropriate reference model. They are chosen for their proficiency in complex optimization to enhance the controller's effectiveness by optimizing parameters within constraints, adapting to system dynamics, and ensuring optimal conditions. Through simulations, it is demonstrated that the proposed controller significantly enhances the stability and efficiency of the control system, while maintaining practical control signals. Moreover, the proposed modifications and intelligent tuning of the PID controller yield remarkable improvements compared to previous related work, resulting in a 36% reduction in rise time, a 63% reduction in settling time, an 80% reduction in overshoot, and a 98% reduction in cost value.