PDE Boundary Control for Flexible Articulated Wings on a Robotic Aircraft

This paper presents a boundary control formulation for distributed parameter systems described by partial differential equations (PDEs) and whose output is given by a spatial integral of weighted functions of the state. This formulation is directly applicable to the control of small robotic aircraft with articulated flexible wings, where the output of interest is the net aerodynamic force or moment. The deformation of flexible wings can be controlled by actuators that are located at the root or the tip of the wing. The problem of designing a tracking controller for wing twist is addressed using a combination of PDE backstepping for feedback stabilization and feed-forward trajectory planning. We also design an adaptive tracking controller for wing tip actuators. For wing bending, we present a novel control scheme that is based on a two-stage perturbation observer. A trajectory planning-based feed-forward tracker is designed using only one component of the observer whose dynamics are homogeneous and amenable to trajectory planning. The two components, put together, estimate the external forces and unmodeled system dynamics. The effectiveness of the proposed controllers for twist and bending is demonstrated by simulations. This paper also reports experimental validation of the perturbation-observer-based controller for beam bending.