Safe Set Maneuverability of Impaired Aircraft

The flight envelope can be viewed as a set within the state space of an aircraft. For various safety considerations an aircraft is required to remain within its prescribed flight envelope. The safe set is the largest controlled invariant set within the flight envelope. Thus, if an aircraft is to remain within its envelope it must stay within the safe set. When an aircraft is impaired, e.g., a jammed elevator or an engine loss, the safe set shrinks as would be expected. In this paper we consider the ability of an aircraft to maneuver within the safe set. Maneuverability performance is usually assessed by evaluating an aircraft’s capacity to regulate around and smoothly transition to desired steady motions, or trim points. In this paper we study the structure of trim points within the safe set and the ability to regulate around them. A trim point is a pair of constant state and control values that produces a steady motion with a fixed set of specified flight path parameters, such as airspeed and flight path angle, called the trim condition. It is shown that there may be zero, one, or more trim points corresponding to a given trim condition. Each of these trim points lies on a different branch of the aircraft equilibrium surface. The safe set trim point structure is organized by static bifurcation sets even though the bifurcation points are typically outside of the safe set. When impairment occurs, some trim points vanish so that flight at a desired trim condition may require switching to a different branch. In general, the aircraft zero dynamics differ from one branch to another so that switching from one trim point to another corresponding to the same trim condition requires a change in regulation strategy. These results are developed and explained in this paper. Examples are given.