Efficient Treatment of Moderate Amplitude Constraints for Helicopter Handling Qualities Design Optimization

Abstract

This paper describes a new technique for the calculation of gradients of constraints associated with the moderate amplitude criteria of the ADS-33 helicopter handling qualities specifications. The gradients are calculated using low-order linear approximations to the full nonlinear model of the helicopter. The low-order models approximate the gradients well and reduce the additional cost of calculating the gradient by a factor of about 50. Most of the reduction in the objective function obtainable using the exact gradients are retained, with no additional infeasible intermediate designs. The accuracy of linear Taylor-series expansions of the constraint in terms of the design variables is found to depend on the size of the changes of each design variable. The accuracy is not improved by using intermediate design variables, such as reciprocals and cubes of the design variables, but it improves if the bandwidth or derivative ratios such as L θ1c /L p used as intermediate variables in the expansions.