# Optimal Design of I-PD and PI-D Industrial Controllers Based on Artificial Intelligence Algorithm
## 1 Introduction  
The optimal synthesis of I-PD (Integral-Proportional Derivative) and PI-D (Proportional-Integral Derivative) industrial controllers is connected with the development of effective process control systems [1]. At present, the synthesis of only PID controllers is well developed. The process of developing and implementing optimal I-PD and PI-D controllers can lead to improvements in the accuracy and performance of control systems, which is important for various industrial and technical applications. The development of efficient optimization algorithms used in optimal I-PD and PI-D controllers is important to research. Efficiency and practical realization in real industrial control systems are the reasons for using I-PD and PI-D controllers for the MIMO system in this research. I-PD and PI-D controllers provide improved control by separately affecting proportional, integral, and differential components, allowing for finer tuning of the system to achieve an optimal balance between responsiveness and stability. These controllers are also easier to tune and apply compared to more complex methods, making them preferred for many industrial and engineering applications where reliability and technical feasibility are important [2]. Technological processes are characterized by multivariable complexity, large amounts of data, and the use of microprocessor technologies [3]. Using the latest advances in AI can significantly improve optimal control algorithms for MIMO control systems. These algorithms can be used to tune the parameters of I-PD and PI-D controllers to achieve optimal results according to specific performance criteria or given requirements. Artificial intelligence algorithms such as artificial immune systems (AIS), genetic algorithms (GA), particle swarm (PSO), or optimization algorithms using artificial neural networks can work with a variety of criteria, which allows you to adjust the controls taking into account several aspects of performance [4; 5]. In particular, artificial immune systems (AIS) are based on a natural immune system with the ability to learn and adapt to changing conditions. This property gives an advantage to AIS algorithms over other AI algorithms. The primary objective of this research is to develop more efficient methods for tuning I-PD and PI-D controllers of multivariable industrial systems through the use of AI algorithms such as the AIS algorithm. In this article, the following research questions are considered. Development of an optimal controller using AIS technology. Transformation of the performance criterion for the successful configuration of I-PD and P-ID controllers using intelligent algorithms. Design AIS algorithm to tune the parameters of I-PD and P-ID optimal controllers. Application of this algorithm to industrial processes in oil and gas MIMO systems. Obtaining results from the comparison analysis of different controllers. Evaluating the effectiveness of AIS algorithms for distillation column control systems in the oil and gas industry. The successful integration of industrial artificial intelligence has become an important factor, especially within multivariable sectors like the oil and gas industry [6; 7]. The proposed approach involves the development of more efficient intelligent algorithms based on artificial immune systems for the optimal control of multivariable industrial processes in the oil and gas industry. Research on applying AIS for tuning controllers of multivariable systems has the potential to bring significant benefits to both the industry and the academic community, contributing to increased efficiency and automation of control processes. The structure of the paper is organized as follows. Section 1 provides an overview of the research questions and objectives of the present study. Section 2 examines previous studies on AI technology and PID controllers. Section 3 describes the AIS algorithm for industrial controllers.