High-Gain Observer-Based Backstepping Control for Real-Time Trajectory Tracking of a Twin Rotor MIMO System: Adaptive Tuning Functions Versus Metaheuristic Gain Optimization

This paper addresses the real-time trajectory tracking problem for the Twin Rotor MIMO System (TRMS), a nonlinear, strongly coupled, open-loop unstable aerodynamic laboratory benchmark whose six-dimensional state space is only partially observable through pitch and yaw angle encoders. A High-Gain Observer (HGO) is designed to reconstruct the four unmeasured states, comprising angular velocities and rotor torques, from encoder measurements alone. Three observer-based backstepping control architectures are proposed and experimentally validated on the physical TRMS platform at a 1 kHz embedded sampling rate: (i) adaptive backstepping with tuning functions, which eliminates the over-parametrization inherent in conventional adaptive formulations through a single unified parameter update law; (ii) backstepping with online Brain Storm Optimization (BSO) of the design gains; and (iii) backstepping with online Artificial Bee Colony (ABC) gain optimization. All three architectures achieve stable 100 s trajectory tracking, whereas the conventional non-adaptive backstepping baseline diverges after 42 s due to progressive yaw-channel instability exceeding 4 rad. The BSO- and ABC-optimized controllers achieve the highest pitch-axis tracking precision (reducing pitch root-mean-square errors by 68% relative to the baseline), while the adaptive tuning functions architecture yields the best yaw-axis stability (0.2244 rad RMSE, a 91% reduction). The tuning functions architecture primarily resolves the yaw-channel instability caused by parametric over-parametrization, while the metaheuristic optimizers primarily improve pitch tracking precision through online gain refinement. Closed-loop stability is rigorously established via Lyapunov analysis and the nonlinear separation principle. The High-Gain Observer is directly validated on the two measured states through comparison of its pitch and yaw angle estimates against the incremental encoder signals over the full 100 s trial; the angular velocity and rotor torque estimates are only indirectly supported by the sustained stability of the closed loop, since no velocity or torque sensor is available on the rig. Comprehensive simulation and real-time experimental comparisons quantify the performance, robustness, and computational feasibility of each architecture under identical operating conditions.