Numerical Time-Scale Separation for Rotorcraft Nonlinear Optimal Control Analyses

Abstract

This paper proposes a numerical technique for an efficient nonlinear optimal control analysis in which the system dynamics presents multiplicity in its time scale corresponding to a high-fidelity rotorcraft model. For this purpose, the integration of the fast dynamics is carried out separately from the integration of the slow dynamics using a pseudospectral method. The resultant nonlinear programming problem can be efficiently solved with a small number of computational nodes for the slow dynamics without degrading the fidelity of the original model. The integration process of each dynamics uses different nodes and shares the information for the states and controls by means of local Lagrange interpolation. In the algorithm implementation, the moving horizon approach and residualization method are investigated to guarantee solution convergence and to preserve the sensitivity of the cost and constraint functions to the slow states, respectively. To verify the proposed approach, two simulation studies are presented. First, the dynamic responses of the Bo-105 helicopter due to longitudinal doublet inputs are analyzed, which successfully provide the same level of integration accuracy as the Runge–Kutta method. Second, an optimal autorotational landing problem is considered as an example to prove the effectiveness of the proposed time-scale separation technique.