Comparative Evaluation of Recent Metaheuristic Optimizers for LQR Weight Selection in Coupled Twin Rotor MIMO Systems

Abstract

Choosing the right weighting matrices for a Linear Quadratic Regulator (LQR) is one of those problems that looks simple on paper but quickly becomes a challenge in practice, especially when the system being controlled is as complex as the Twin Rotor MIMO System (TRMS). The TRMS is a laboratory benchmark that behaves much like a helicopter: two rotors, strong aerodynamic coupling between pitch and yaw, and nonlinear dynamics that make any classical tuning method fall short. In this work, we take a close, fair, and reproducible look at six nature-inspired optimization algorithms published between 2021 and 2024 RIME, the Dung Beetle Optimizer (DBO), Parrot Optimizer (PO), Artificial Rabbits Optimization (ARO), the Weighted Mean of Vectors algorithm (INFO), and the Gorilla Troops Optimizer (GTO) and compare them against the Dragonfly Algorithm (DA) as a well-established baseline. All seven algorithms are used to automatically search for the best Q and R matrices that minimize a composite performance index combining ITAE and ISE criteria over closed-loop simulations. We evaluate each optimized controller on six practical metrics: rise time and settling time for both the pitch and yaw channels, percentage overshoot on each axis, and computation time. Our results show that the newer algorithms especially RIME, DBO, and PO consistently produce better controllers than DA, with RIME offering the best overall trade-off between solution quality and computational efficiency. Step-response curves, convergence plots, bar charts, and a radar chart are all provided to make the comparison as transparent as possible. This study gives engineers and researchers a practical, grounded guide for picking the right optimization tool when designing LQR controllers for coupled aeromechanical MIMO systems.