Nonlinear Optimal Control Analysis of Helicopter Maneuver Problems Using the Indirect Method

Abstract

This paper deals with a nonlinear optimal control approach to helicopter inverse simulation. The reference trajectory is prescribed in prior, and the integral deviation from this trajectory is treated as an additional penalty cost to convert the system optimality to an unconstrained optimal control problem. The resultant two-point boundary value problem has been solved by a multiple-shooting algorithm. The nonlinear helicopter model in this study includes main rotor flap dynamics and a dynamic inflow model. The applications cover the inverse simulation for bob up, turn, and slalom maneuvers. This paper focuses on resolving the convergence issue using the indirect method, the main root causes of which are related to the inherent system instability of the helicopter and with poor initial guesses on state and costate variables. For this reason we will investigate the effect of the shooting node number on convergence and use a hybrid-model approach, where the optimal state and costate variables, calculated using the linear model, are used as initial guesses for those using the nonlinear model. The analyses show good convergence history and capability of tracking the prescribed trajectory. So the results in this paper can provide a valuable motivation for applying indirect methods to nonlinear helicopter flight mechanic analysis.

Rotorcraft Trajectory Tracking Using the State-Dependent Riccati Equation Controller

“…[14][15][16] A trajectory can be expressed as the sum of the states at a maneuver entry and its variation during the maneuver. 17) The detailed procedures are well documented in Ref. 17).…”

A Comparative Study of Transcription Techniques for Nonlinear Optimal Control Problems Using a Pseudo-Spectral Method

“…The pseudospectral (PS) method is a direct collocation method, which generally outperforms indirect methods, owing to their large radii of convergence, and solves nonlinear optimal control problems (NOCPs) with any type of constraint [1][2][3][4]. In a PS method, the collocation points are specially designed to utilize the highly accurate quadrature formulas and the corresponding analysis converges at an exponential rate for problems with a smooth and well-behaved solution [5][6][7].…”