Linear optimal regulator theory is applied to a nonlinear simulation of a transport aircraft performing a helical landing approach. A closed-form expression for the quasi-steady nominal flight path is presented along with the method for determining the corresponding constant nominal control inputs. The Jacobian matrices and the weighting matrices in the cost functional are time varying. A method of solving for the optimal feedback gains is reviewed. The control system is tested on several alternative landing approaches using both 3° and 6° flight path angles.On each landing approach, the aircraft was subjected to large random initial-state errors and to randomly directed crosswinds. The system was also tested for sensitivity to changes in the parameters of the aircraft and of the atmosphere. Performance of the optimal controller on all the 3° approaches was very good. Mean errors in the lateral, vertical, and longitudinal directions for the principal flight path (270° turn) were 0.8 m, -0.1 m, and -9.4 m. The magnitude of the respective ranges of these errors were 1.0 m, 1.9 m, and 26.7 m. The control system proved to be reasonably insensitive to parametric uncertainties. Performance was not as good on the 6° approaches. On the principal flight path, mean errors for the lateral, vertical, and the longitudinal directions were 9.4 m, -0.4 m, and -2.9 m and the magnitude of the respective ranges for these errors were 8.7 m, 3.2 m, and 45.2 m. A modification to the 6° flight path is proposed for the purpose of improving performance.
展开▼
