PID control of MIMO systems represented by the MIMO ARX Meixner-like model: Application to a neonatal incubator and a 2-DOF helicopter systems

This paper addresses the challenges of modeling and controlling Multiple Input Multiple Output (MIMO) systems characterized by complex and often nonlinear interactions between inputs and outputs. We propose a novel control approach based on the MIMO ARX (auto-regressive model with external input) Meixner-like model, which reduces complexity while accurately capturing system dynamics. PID (proportional–integral–derivative) controllers are widely used in industry due to their simplicity, robustness, and cost-effectiveness. However, traditional PID tuning methods, such as Ziegler-Nichols and Cohen-Coon, are limited in handling complex MIMO systems with nonlinearities and external disturbances. To overcome these limitations, we propose optimizing PID gains using advanced optimization algorithms, namely particle swarm optimization and gray wolf optimization. These methods enable dynamic and efficient tuning of PID parameters, ensuring optimal performance even in the presence of nonlinear dynamics and disturbances. The proposed approach is validated through simulations on a neonatal incubator system and a two Degrees Of Freedom helicopter process, demonstrating its effectiveness in achieving robust and adaptive control. This study highlights the potential of combining traditional PID control with modern optimization techniques to address the challenges of complex MIMO systems.