Guidance of low-thrust spacecraft

Rosemary Chia-Hua Huang, Purdue University

Abstract

Low-thrust engines are appealing for use on both earth-based satellites and interplanetary spacecraft. The advantage to using low-thrust engines as the primary means of propulsion is in their high specific impulse, which means that a spacecraft can operate longer and/or carry less fuel. These engines are only capable of very low-thrust, which means they have to operate continuously. A challenge in using such engines is in the trajectory design where traditional methods used for high-thrust engines do not apply. This dissertation presents several techniques, both open-loop and closed-loop, for the guidance of low thrust spacecraft. First, computationally simple strategies are proposed for both the open-loop trajectory design and the closed-loop control of both two-dimensional and three-dimensional low-thrust transfers. The open-loop design approach is based on constructing the acceleration vector so that certain characteristics of the trajectory follow desired profiles. These profiles are designed to guide a low-thrust spacecraft from an initial circular orbit to a different circular orbit. In the two-dimensional case, the orbits will be coplanar. For the three-dimensional case, there will be an inclination change. In addition, the way in which the acceleration vector is constructed allows for its maximum magnitude to be adjusted to be arbitrarily small by making the total transfer time arbitrarily large. The closed-loop guidance strategy is to formulate the acceleration so that orbital characteristics will follow the profiles constructed through the open-loop design process even with disturbances acting on the spacecraft. Both the open-loop and closed-loop strategies will be applicable to both interplanetary and planet-centered transfers. In addition, the control laws are designed so that the acceleration components have analytical form. Next, novel numerical methods for solving nonlinear optimal control problems based on differential transformation (DT) are proposed for the first time to solve low-thrust interplanetary trajectory problems. The differential transformation algorithm is being used for solving the two-point boundary value problems (TPBVP) that result from the indirect optimization approach. This algorithm converts the system of differential equations and its boundary conditions to a set of nonlinear algebraic equations, where solutions can be obtained more quickly. Moreover, the algorithm finds solutions in an analytical form. In this dissertation, the DT is shown to be faster than the multiple shooting method for solving TPBVP's. It is then applied to find several optimal interplanetary trajectories using as initial guesses the trajectories from the open-loop computationally simple controllers. Further, one of the computationally simple controllers is used to prove that there is no solution to the optimal control problem where the final time is free. This fact is also demonstrated by trying to solve a TPBVP where both the final state and final time are free, as the DT algorithm does not converge to a solution. However, the DT algorithm does converge to a solution for the TPBVP when the final time is free but the final state is fixed. This contradiction is due to the fact that the TPBVP is derived from necessary but not sufficient conditions. Finally, a nonlinear model predictive control algorithm (NMPC) is proposed that incorporates a differential transformation based algorithm for the repeated solution of the open-loop optimal control problem every time there is a new state measurement. Then this new NMPC algorithm is applied to several interplanetary low-thrust trajectory tracking problems. It is shown to be more robust with respect to measurment delays than the linear quadratic regulator. The NMPC algorithm is also adapted to quickly find a new optimal trajectory after a severe disruption such as from engine failures.

Degree

Ph.D.

Advisors

Corless, Purdue University.

Subject Area

Aerospace engineering

COinS