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This article presents an optimal tracking controller retrofitted with a nonlinear adaptive integral compensator, specifically designed to ensure robust and accurate positioning of Vertical Take-Off and Landing (VTOL) Unmanned Aerial Vehicles (UAVs) that utilize contra-rotating motorized propellers for differential thrust generation. The baseline position controller is synthesized by employing a fixed-gain Linear Quadratic Integral (LQI) tracking controller that stabilizes position by tracking both state variations and pitch-axis tracking error integral, which adjusts the voltage to control each coaxial propeller’s speed accurately. Additionally, the baseline tracking control law is supplemented with a rate-varying integral compensator. It operates as a nonlinear scaling function of the tracking-error velocity and the braking acceleration to enhance the accuracy of reference tracking without sacrificing its robustness against exogenous disruptions. The controller’s performance is analyzed by performing experiments on a tailored hardware-in-the-loop aero-pendulum testbed, which is representative of VTOL UAV dynamics. Experimental results demonstrate significant improvements over the nominal LQI tracking controller, achieving 17.9%, 61.6%, 83.4%, 43.7%, 35.8%, and 6.8% enhancement in root mean squared error, settling time, overshoot during start-up, overshoot under impulsive disturbance, disturbance recovery time, and control energy expenditure, respectively, underscoring the controller’s effectiveness for potential UAV and drone applications under exogenous disturbances.
Saleem et al. (Sun,) studied this question.