Modeling, Analysis, Control and Design of Highly Maneuverable Quadcopters

With the revolution of low-cost microelectronics, rotary-wing vehicles have grown increasingly popular and important in the past two decades. With increased interest in quadcopters comes the need to for a systematic and rigorous framework to model, analyze, control, and design them. This thesis presents the beginning of such a framework.

The work presents the nonlinear equations of motion of a quadcopter. This includes the translational and rotational equations of motion, as well as an analysis of the nonlinear actuator dynamics. The work then analyzes the static properties of a quadcopter in forward flight equilibrium and shows how static properties change as physical properties of the vehicle are varied. Next, the dynamics of forward flight are linearized, and a dynamic analysis is provided.

After dynamic analysis, the work shows detailed hierarchical control system design trade studies, which includes attitude and translational inner-outer loop control. Among other designs, the following are presented: PD control, proportional control, pole-placement control. Each of these control architectures are employed for the inner loops and outer loops. The work also analyzes linear versus nonlinear simulation performance of a quadcopter, specifically for a step x-axis reference command. It is found that the nonlinear dynamics of the actuator cause significant discrepancy between linear and nonlinear simulation.

Finally, this thesis establishes directions for future graduate research. This includes hardware design, as well as moving toward design of a highly-maneuverable thrust-vectoring quadrotor which will be the focus of the proposed graduate PhD research. In summary, this thesis provides the beginning of a cohesive framework to model, analyze, control, and design quadcopters. It also lays the groundwork for graduate research and beyond.