Digital passive attitude and altitude control schemes for quadrotor aircraft

This paper presents a formal method to design a digital inertial control system for quad-rotor aircraft. In particular, it formalizes how to use approximate passive models in order to justify the initial design of passive controllers. Fundamental limits are discussed with this approach - in particular, how it relates to the control of systems consisting of cascades of three or more integrators in which input actuator saturation is present. Ultimately, two linear proportional derivative (PD) passive controllers are proposed to be combined with a nonlinear saturation element. It is also shown that yaw control can be performed independently of the inertial controller, providing a great deal of maneuverability for quad-rotor aircraft. A corollary, based on the sector stability theorem provided by Zames and later generalized for the multiple-input-output case by Willems, provides the allowable range of k for the linear negative feedback controller KI in which the dynamic system H₁ : x₁ ¿ y₁ is inside the sector [a₁, b₁], in which -¿ < a₁, 0 < b₁ ¿ ¿, and b₁ > a₁. This corollary provides a formal method to verify stability, both in simulation and in operation for a given family of inertial set-points given to the quad-rotor inertial controller. The controller is shown to perform exceptionally well when simulated with a detailed model of the STARMAC, which includes blade flapping dynamics.