Flight Control Law Clearance Using Optimal Control Theory

Abstract

This study explores the effectiveness of applying optimal control techniques to the flight control law clearance problem, which is the challenge of ensuring the safety of an aircraft’s flight control system for all allowable inputs. The specific criterion chosen was the angle-of-attack limit exceeding criterion, and two different cost functions were constructed that accurately describe it. Using Aero-Data Model in a Research Environment to obtain realistic aerodynamic coefficients, a longitudinal short-period model was developed. It was proven that the general system has a bang-bang worst-case input when the states are unbounded, and a possible bang-singular-bang worst-case input when one or more states are bounded. These results were validated with simulations using General Pseudospectral Optimal Control Software. In the physical domain these results translate into actuator rate limiting issues; thus, limited elevator deflection and rate of elevator deflection can lead to even more extreme worst-case performance. Experimenting with approximations of these input signals in the full model demonstrated that they achieve high maximum angle-of-attack outputs even in a complex system. Furthermore, it was confirmed that bang-singular-bang inputs in a realistic system, on average, attain a higher maximum angle of attack than bang-bang inputs.