Study And Application Of Trajectory Optimization For Helicopter Flight Afterone Engine Failure

Engine failure is one of the most important reasons for helicopter flight accidents. According to statistics provided by foreign authorities, there is one engine failure in every 10,000 h of operation. Therefore, how to operate helicopter flight safely after engine failure has been a key to doing helicopter flight safety research. In order to ensure flight safety of aircrafts, the world’s countries have developed civil aviation airworthiness regulations. To provide a theoretical benchmark for helicopter safe flight after one engine failure, this thesis studies optimal helicopter flight trajectories and operations based on optimal control theory, and develops analytical methods of trajectory optimization for determining takeoff decision point and low speed height-velocity diagram, as well as exploring helicopter safe takeoff and landing operations in urban wind environment.Currently, two dimensional point mass models and longitudinal rigid body models with three degrees of freedom are widely used in the research on trajectory optimization for helicopter flight after engine failure. Three dimensional rigid body flight dynamics models of a helicopter after one engine failure with six degrees of freedom are first developed in the thesis to improve the prediction accuracy of helicopter flight trajectories and operations, including two different levels of complexity of main rotor aerodynamics models. The two main rotor models are identified, one of which uses quasi-steady uniform inflow model and quasi-steady, unsteady tip path plane flapping dynamics models, as well as the other model that uses dynamic inflow model and individual blade flapping dynamics model. Besides, ground effect and vortex ring state boundary are taken into account in each model. Also, first order response dynamics of the contingency power available are adopted for turbo shaft engines. Explicit differential equations of helicopter flight dynamics are subsequently established, therefore building the foundation for predicting helicopter flight trajectories and operations accurately.Different numerical optimization methods of trajectory optimization are then investigated to cater for the two different models, including the direct transcription, the direct multiple shooting, and the direct hybrid shooting approaches. By properly selecting cost functions, path constraints, boundary conditions, and considering the effects of pilot reaction time delay, helicopter flight procedures after one engine failure are formulated as nonlinear optimal control problems. The state and control variables of the optimal control problems are well normalized and scaled to benefit numerical optimization methods. The optimal flight trajectories and operations can be obtained by solving the optimal control problems using nonlinear programming methods.The autorotation landing procedure is then formulated as a nonlinear optimal control problem. For a UH-60 A helicopter, the optimal landing trajectories and operations are computed, and the present method is validated for autorotation landings from hover and forward flight initial conditions by the comparison with the existing flight test data. The optimal solutions with the three dimensional rigid body models are further compared with those obtained using a two dimensional point mass model and a longitudinal rigid body model with three degrees of freedom. It is found that the three dimensional rigid body models produce more realistic landing trajectories and operations.The low speed height-velocity diagrams are then analytically predicted at different gross weights based on the idea of minimizing the unsafe region of autorotation landing. Besides, the resulting optimal landing procedures from the high hover point, knee point and low hover point are presented, including the time histories of spatial positions and attitudes, three dimensional velocities and angular rates, main rotor rotational speed, as well as control inputs, thus providing an analysis tool for helicopter safe landing after one engine failure occurring in low-speed and low-altitude flight.The rejected takeoff and continued takeoff procedures are then formulated as nonlinear optimal control problems for both short takeoff and vertical takeoff operations. Takeoff decision points are determined respectively, for short takeoff with the concepts of balanced filed length and minimum energy, for vertical takeoff with the concepts of balanced weight and minimum energy. Extensive trajectory optimization tests are conducted to investigate the effects of the initial conditions and helicopter parameters on the optimal flight trajectories and operations, thus providing a reference of optimal operations for helicopter safe flight after one engine failure occurring in different takeoff procedures.A flight dynamics model of a helicopter in urban wind environment is developed finally, integrated with the urban airwake model and Dryden atmospheric turbulence model. The approach and landing procedure to urban heliport with all engine operating is then formulated as a nonlinear optimal control problem, and the direct hybrid shooting approach is implemented to compute optimal flight trajectories and operations. For a Z-9A helicopter, many trajectory optimization runs are made to investigate the effects of the wind conditions and heliport sites on the optimal landing trajectories and operations, hence paving the road to the research on the safety of helicopter takeoff and landing operations from/to urban heliport in the event of one engine failure.