Loss of control prediction system for the longitudinal and lateral dynamics of an aircraft using Laplace methods

Abstract

Loss-of-control events have contributed to many accidents worldwide to this date. A signi cant amount of research has been done to provide safer ight conditions and thus prevent such events from occurring. One such area of research is the use of predictive systems to warn pilots of impending entry into a Loss-of-control situation. This thesis explores the use of Laplace-based methods as an analytic approach to predicting LOC events by calculating the critical inputs needed for the pilot to reach prede ned limits. To illustrate the proposed concept, a Mass Spring Damper system was used. The position and velocity of the mass with respect to time were simulated using a state space model. An LOC position limit was de ned and the Laplace equations were used to calculate the force required to reach this limit within a speci ed time window. This process was repeated for a step, ramp, parabolic and sinusoidal inputs. MATLAB/Simulink R was used as the main platform to run the simulations. This basic framework was applied to the longitudinal and lateral dynamics of an aircraft. For the longitudinal dynamics, the Short Period mode of the NASA Generic Transport Model was used where the angle of attack was the limit while the critical elevator de ection was calculated. As for the lateral dynamics, the Roll mode and Dutch roll mode on a business jet was used. The limits assigned for both modes were the bank angle and sideslip angle while the critical inputs were the aileron de ection and rudder de ection respectively. Through this method, the remaining amount of control authority available to the pilot is found and the pilot can use this information to avert an LOC situation. A Fast Fourier Transform was also utilized to simulate Pilot Induced Oscillations for the Short Period and Dutch Roll mode. A 3-dimensional display was also developed for both these modes to show the pilots current position in relation to the critical control de ection, de ection rate and frequency boundary.