This paper proposes a novel hybrid arithmetic–trigonometric optimization algorithm (ATOA) using different trigonometric functions for complex and continuously evolving real-time problems. The proposed algorithm adopts different trigonometric functions, namely sin, cos, and tan, with the conventional sine cosine algorithm (SCA) and arithmetic optimization algorithm (AOA) to improve the convergence rate and optimal search area in the exploration and exploitation phases. The proposed algorithm is simulated with 33 distinct optimization test problems consisting of multiple dimensions to showcase the effectiveness of ATOA. Furthermore, the different variants of the ATOA optimization technique are used to obtain the controller parameters for the real-time pressure process plant to investigate its performance. The obtained results have shown a remarkable performance improvement compared with the existing algorithms.

The multivariable process plays a significant role in industrial applications, and designing a controller for the Multi-Input Multi-Output process is challenging due to dynamic process changes and interactions between system variables. Traditionally, the PI family of controllers has been used for its simple design, easy tuning, and quick deployment. However, these processes require complex control actions due to multiple loops in process plants. Thus, this paper proposes an Iterative Learning Controller Dead-time compensating PI, which utilizes the newly developed hybrid Simulated Annealing-Ant Lion Optimization algorithm for Single-Input Single-Output process simulation and real-time experimentation on the Quadruple Tank System. To validate the effectiveness of the developed controller, Machine Learning techniques such as regression and ensemble trees are used to accurately predict the actual system response using error values from respective processes. The simulation and experimental results demonstrate that the proposed controller achieved better performance. The regression and ensemble tree algorithm models effectively predicted the actual response. The obtained data shows that the proposed controller improved system stability and robustness by minimizing nearly half of the overshoot and improving settling time, with an average of 29.9596% faster than the other controller in the SISO process and 14.6116% in the MIMO process.