Multi-disciplinary optimization of a helicopter rotor and flight control system

Results are presented concerning the integrated optimization of a helicopter rotor and flight control system subject to simultaneous aeroelastic and handling qualities constraints. A representative subset of the ADS-33C handling qualities specifications are reformulated into inequality constraints. A simplified design model is used, consisting of three rotor design variables and of five control system design variables for each flight condition. The design space defined by the combined aeroelastic and handling qualities constraints is not convex. It is not possible to satisfy the entire set of aeroelastic and handling qualities constraints using just the three rotor design parameters. If the design is optimized for just one flight condition. optimizing simultaneously the rotor and the flight control system leads to substantially better designs than by sequentially optimizing the rotor first and the flight control system next. Two problems observed while carrying out a simultaneous rotor-flight control system optimization are the high computational expense and the non-robustness of the optimal designs. A new technique for the efficient calculation of gradients of constraints associated with the moderate amplitude attitude change specification of the ADS-33 handling qualities specifications is developed. Low order linear models, obtained by fitting their frequency response to that of the full order model, provide good approximate gradients of the moderate amplitude constraint. These low order models however are not appropriate for calculating the value of the constraint itself. This method of calculating gradients is between one and two orders of magnitude faster than the usual finite difference method and requires no modifications to existing flight dynamics simulation codes. The approximate gradients when used in a integrated rotor control optimization cause it to converge to designs close to those obtained using the full non-linear model. A linear Taylor series expansion of the constraint in terms of the design variables matches the full non-linear constraint value for small perturbation sizes, but correlates poorly for larger perturbations. Expansion in terms of typical intermediate variables as used in structural design problems, does not improve the correlation. A Taylor series expansion in terms of system level intermediate variables, like the bandwidth and the theoretical amplitude of the single axis linear system step response, are more successful. In order to improve the robustness of the optimal designs a robust performance constraint is formulated for the non-linear rotor-flight control system optimization problem. This constraint, however, is always violated at the hover flight condition and no reduction can be obtained even when this constraint is made the objective function. A robust stability constraint, however, shows modest reductions as a result of rotor control optimization. An off-design study of the final design of the robust rotor-control optimization shows improvement of the off-design performance as compared to the non-robust design. However several constraints are still violated under off-design conditions.