Real-time Capable Nonlinear Model Predictive Controller Design for The Upper Stage of a Launch Vehicle

Abstract

In this paper, a real-time capable Nonlinear Model Predictive Controller (NMPC) is implemented for the attitude control of an upper stage launch vehicle with liquid propellant. A mass spring model is used as an analogy to simulate the disturbance generated by the sloshing propellant. For the implementation of the NMPC, an optimal control problem (OCP) is defined with finite time horizon. The objective function is minimized while satisfying constraints on the control inputs. The resulting OCP is transcribed using single shooting method to parametrize the control inputs using uniform discretization points. The continuous control inputs are obtained by linear interpolation. A dedicated discretization algorithm in FORTRAN is coupled with a solver which used quasi-Newton algorithm to generate solutions fast. Approximation of the Hessian matrix is used to reduce computational requirements. Furthermore, the algorithm can perform parallel computation of the derivatives of the objective function with respect to optimization variables. This results in a real-time capability of generating solutions in the order of milliseconds for each iteration. The algorithm is applied for attitude maneuver and disturbance rejection for the upper stage of a launch vehicle.