Observer-Based Hybrid Backstepping–Super-Twisting Control of a Twin Rotor MIMO System with Windowed Metaheuristic Gain Scheduling: Real-Time Tracking Experiments and Numerical Disturbance Analysis

Twin Rotor Multi-Input Multi-Output (TRMS) platforms combine strong aerodynamic cross-coupling, gravitational loading on the vertical axis, friction-dominated horizontal dynamics, and systematic mismatch between idealised models and laboratory hardware. The platform provides only two optical encoders, so the angular rates and the rotor states are unavailable for feedback. This paper presents an observer-based output-feedback architecture that addresses both difficulties. A high-gain observer built on the fully coupled six-state model, including the gyroscopic terms that the control design cannot retain, reconstructs the four unmeasured states from the two encoder angles. The reconstructed states drive a Hybrid Backstepping–Super-Twisting (B-STA) controller in which a second-order continuous sliding mode is embedded at the final recursive step through a composite surface. Because backstepping requires strict-feedback structure, which the centralised coupled model does not possess, the controller is synthesised on a decentralised design model and the residual coupling is rejected as a matched perturbation of the sliding variable. Closed-loop behaviour is analysed as a three-stage cascade covering observer error, sliding variable, and tracking error, yielding practical stability under bounded residuals with an explicit input-to-state gain. The residual bounds are evaluated numerically from the actuator saturation limit and the identified coefficients rather than assumed, and the resulting figures are shown to predict the marked difference in sliding-variable behaviour observed between the two axes. A second architecture applies a windowed Grey Wolf Optimiser (B-GWO) to the backstepping gains, in which each candidate is applied to the plant for a fixed test window, scored on its own accumulated integral of time-weighted absolute error, and followed by a settle window at the incumbent best. We prove that this windowing is a requirement rather than a convenience: a fitness evaluated at a single sample is common to all candidates, cancels from the population ranking, and reduces the search to the minimiser of its own regularisation term. Both schemes are implemented on a physical TRMS through a Simulink Desktop Real-Time interface at a control period of 10ms. On a 100s experimental run, B-STA attains a pitch tracking error of 0.0318rad RMS, 7.94% of the reference amplitude, and the lowest control energy on both axes among the strategies compared, reducing pitch control energy by 72.9% relative to a first-order Backstepping–Sliding Mode baseline recorded on the same interface. Numerical disturbance rejection tests on the fully coupled model confirm the mechanism: under a matched actuator step the super-twisting integrator state migrates to a new steady level that cancels the disturbance, driving the residual pitch error to 2×10−4rad, whereas the same recursive law without the second-order injection retains a permanent offset of 0.28rad.