Data-driven variable tracking differentiation sigmoid proportional-integral-derivative controller for nonlinear multiple input multiple output system with white noise

Modern industrial systems often operate under complex nonlinear dynamics with multi-input-multi-output (MIMO) configurations, where conventional PID controllers struggle due to high sensitivity to noise and inadequate adaptability. To overcome these limitations, this study introduces a novel data-driven Variable Tracking Differentiation Sigmoid PID (VTD-SPID) controller for nonlinear MIMO systems affected by white noise disturbances. The research contribution is the integration of a Variable Tracking Differentiator (VTD) into a sigmoid-base PID structure, optimized using the Safe Experimentation Dynamics Algorithm (SEDA), enabling enhanced noise filtration and improved control accuracy. The proposed VTD-SPID adapts controller inputs based on error and error rate feedback, with SEDA employed to optimize control parameters without requiring a mathematical model of the plant. Simulation was conducted on a Twin Rotor MIMO System (TRMS), known for its significant coupling and nonlinearity. The VTD-SPID controller outperformed conventional PID, SPID, and traditional TD-SPID controllers in all evaluated metrics. Results show a 14.58% improvement in tracking accuracy over TD-SPID, along a 14.93% reduction in the total error norm and a 4.37% reduction in control input energy. These improvements lead to smoother response trajectories, quicker settling times, and improved stability. Convergence analysis validated the effectiveness of SEDA in tuning high-dimensional control parameters efficiently. The study concludes that the VTD-SPID controller offers a superior, noise-resilient, and model-free control solution for nonlinear MIMO systems, with strong potential for broader application in real-world noisy environments.