chapter  2
84 Pages

Modeling

A natural approach for reducing the complexity of large scale systems places a hierarchical structure on the system architecture. For example, in the common two-layer planning and control hierarchies, the planning level has a coarser system model than the lower control level. Furthermore, in general, an aircraft has two separate classes of control systems: the inner loop and the outer loop. One of the main challenges is the extraction of a hierarchy of models at various levels of abstraction while preserving properties of interest. The notion of abstraction refers to grouping the system states into equivalence classes. A hierarchy can be thought of as a finite sequence of abstractions. Consistent abstractions are property preserving abstractions, which can be discrete or continuous [66]. A fixed-wing aircraft has four actuators: forward thrust, ailerons, elevator and rudder. The aircraft’s thrust provides acceleration in the forward direction and the control surfaces exert various moments on the aircraft: rudder for yaw torque, ailerons for roll torque and elevator for pitch torque. The general aircraft’s configuration has six dimensions: three for the position and three for the orientation. With six degrees of freedom and four control inputs, the aircraft is an under-actuated system. Traditionally, aircraft dynamic models have been analytically determined from principles

of dynamic systems are usually determined through costly and time-consuming wind tunnel testing. These methods, while useful, have limitations when applied to small autonomous aircraft due to several differences which include [62, 69]:

1. Low Reynolds number and airspeed, 2. Increased dynamic rates due to decreased mass and moments of in-

ertia, 3. Dominance of propulsion dynamic forces and moments versus aero-

dynamic body forces and moments, 4. Asymmetric or atypical designs, 5. Aerobatic maneuvers not possible by manned aircraft.