Hybrid LQR-SMC/STSMC with BB-BC Optimization for Enhanced Transient Performance and Chattering Suppression in a 3-DOF Hover System

Abstract

This study presents a novel hierarchical hybrid control architecture for the attitude stabilization of a 3-Degree-of-Freedom (3-DOF) hover system. Operating on a linearized state-space model, a Linear Quadratic Regulator (LQR) is deployed as the optimal inner-loop core to guarantee baseline multi-variable stability. To dramatically improve transient performance and suppress high-frequency oscillations, Sliding Mode Control (SMC) and Super-Twisting Sliding Mode Control (STSMC) are incorporated not as conventional additive inputs, but as dynamic reference-reshaping supervisory mechanisms in the outer loop. This structural decoupling preserves the optimal characteristics of the LQR while effectively attenuating chattering, thereby preventing physical actuator fatigue. Furthermore, the Big Bang-Big Crunch (BB-BC) metaheuristic algorithm is employed to systematically optimize the design parameters of the supervisory layers, enabling effective steady-state error reduction with a remarkably low computational cost. Comparative evaluations demonstrate that the proposed LQR-STSMC framework significantly accelerates system responsiveness, reducing rise times by approximately 80% to 90% and consistently lowering settling times across all operational axes while achieving a reduction of up to two orders of magnitude in overall tracking errors (ITAE) relative to the baseline LQR. Although evaluations involving Model Predictive Control (MPC) demonstrate improvements in transient response and a reduction in total error compared to the standard LQR, the proposed LQR-STSMC architecture exhibits significantly better overall performance and superior disturbance rejection capabilities. Simulation results under continuous aerodynamic perturbations (wind disturbances) confirm that the proposed hierarchical methodology effectively eliminates steady-state offsets, fundamentally outperforming both classical LQR and MPC in terms of robustness, precision, and ultra-fast transient performance.