Flight Control Law Testing Using Optimal Control and Postoptimal Sensitivity Analysis

Abstract

The present study enhances state of the art methods for optimization based clearance of flight control laws by the use of Optimal Control Theory and Postoptimal Sensitivity Analysis. Within this scope we present a methodology to refine results obtained from global optimization by a direct optimal control approach. The first step of the workflow is Latin Hypercube Sampling in order to obtain good starting points for the global optimization. In a second step, we use Differential Evolution to obtain worst case results with respect to parametric uncertainties, e.g. mass or moment of inertia and additionally continuous inputs like wind disturbances. The results from global optimization are then used as initial guess for solving an optimal control problem by means of direct methods in order to refine the solution. The last step consists of Postoptimal Sensitivity Analysis. This analysis is based on the Fiacco sensitivity equation applied to the solution of the optimal control problem. In contrast to standard sensitivity analysis, Postoptimal Sensitivity Analysis reveals how the solution of the optimization problem (worst case) changes when we perturb the parameters under consideration. The method is illustrated by testing a vertical take-off and landing vehicle with an Incremental Nonlinear Dynamic Inversion controller for height loss during the transition phase.