Fuzzy Self-Tuning of Strictly Negative-Imaginary Controllers for Trajectory Tracking of a Quadcopter Unmanned Aerial Vehicle

Abstract

Robustness in the face of uncertainties is an integral part of designing a real-time control system. Based on negative imaginary (NI) systems theory, we design robust and adaptive control systems for accurate trajectory tracking of a quadcopter aerial vehicle. Considering the challenging dynamics of unmanned aerial vehicles, we employ knowledge-based fuzzy inference systems (FIS) to facilitate automatic tuning in our SNI controllers, leading to the development of adaptive SNI control systems. Unlike fixed-gain controllers that have no ability to adapt to the variations in environmental conditions or changes in the dynamics of the plant, our adaptive SNI controllers are able to perform self-tuning to constantly update their parameters. The concept of adaptive autopilots will enhance the ability of the closed-loop control systems to accommodate large uncertainties. To demonstrate their efficacy, we design and implement our adaptive SNI controllers in the three-position control loops of the AR.Drone quadcopter after conducting extensive computer simulations. We also perform a rigorous comparative study with respect to the performance of fixed-gain SNI controllers, fixed-gain NI systems, in addition to model-predictive-control systems, and proportional integral derivative (PID) control systems as our benchmarks. To complete the study, we conduct a stability analysis based on Kharitonov's Theorem.