# Optimal Design of I-PD and PI-D Industrial Controllers Based on Artificial Intelligence Algorithm
## 2 Literature Review  
Among the promising frontiers for artificial intelligence in the oil and gas sector, modeling and optimizing various processes hold significant potential [8]. This involves employing artificial intelligence to control technological processes, including the pursuit of optimal solutions. Achieving these objectives involves harnessing artificial intelligence optimization algorithms, which are extensively documented in contemporary literature [9]. Intelligent algorithms such as the Dragonfly Algorithm (DA) [10], Genetic Algorithm (GA), Ant Colony Optimization (ACO) [11], Particle Swarm Algorithm (PSA) [12], and Cuckoo Search (CS) [13] have been successfully applied to synthesizing optimal controllers for automatic control systems. These intelligent algorithms encompass a wide spectrum of capabilities, each with its own advantages and limitations. Their selection should be contextually driven by factors like the specific oil and gas industry process, desired system dynamics and quality, and the optimization problem at hand. For instance, these algorithms are adept at parametrically tuning standard PID controllers to synthesize optimal controls aimed at minimizing selected performance criteria. Although AI algorithms have been widely used to tune PID controllers in single-input, single-output (SISO) systems, there is particular interest in using AI techniques to fine-tune variable-structure controllers, including I-PD, PD-PI, and PI-D. Methods for synthesizing I-PD and PD-PI controllers have emerged using intelligent techniques such as Particle Swarm Optimization (PSO) [14], Cuckoo Search (CS) [15], and Swarm Intelligence [16]. Among the array of algorithms, the artificial immune system (AIS) algorithms have demonstrated notable efficacy in intelligent PID-controller adjustment [17; 18]. These al gorithms, which are based on the clonal selection principle, exhibit several distinctive characteristics, including accuracy calculations, convergence rate, and robustness in situations where information about the plant under control is incomplete [19; 20]. Notably, the AES algorithm excels in discovering global optimal solutions, outperforming conventional tuning methods in metrics like rise time, control time, steady-state tracking error, and overshoot [21]. This effectiveness has been demonstrated for SISO systems and is even more important for MIMO systems [22]. Currently, various variants of PID controllers have been developed that significantly extend the capabilities of classical control systems. One such variant is the fractional integral PID controller (FOPID), which uses fractional orders of integration and differentiation [23]. This allows for more flexible system tuning and improved dynamic performance [24]. The sigmoid PID is another variation that is characterized by the use of a sigmoid function to control the output signal [25]. This smooths out abrupt changes and makes the control system more robust to overload and noise. Neuroendocrine-PID controller is an integration of the principles of neural networks and the endocrine system [26]. This controller uses artificial neural networks to adapt parameters in real-time, allowing the system to respond more effectively to changing conditions. BELBIC PID controller (Brain Emotional Learning Based Intelligent Controller) is based on the emotional learning model of the brain [27]. It uses algorithms that mimic emotional learning, allowing the system to adapt effectively to external changes and uncertainties. BELBIC PID controllers find applications in robotics, aviation, and other areas where high reliability and fast adaptability are required [28]. The PIDA controller is an extension of the classical PID controller by adding an integral component [29]. This improves control in the presence of integral errors and makes the system more robust to long-term perturbations [30]. Thus, the variety of PID controller variants makes it possible to improve the performance of controlled systems.