Partially independent control scheme for spacecraft rendezvous in near-circular orbits

Abstract

Due to the complexity and inconstancy of the space environment, accurate mathematical models for spacecraft rendezvous are difficult to obtain, which consequently complicates the control tasks. In this paper, a linearized timevariant plant model with external perturbations is adopted to approximate the real circumstance. To realize the robust stability with optimal performance cost, a partially independent control scheme is proposed, which consists of a robust anti-windup controller for the in-plane motion and a H ∞ controller for the out-of-plane motion. Finally, a rendezvous simulation is given to corroborate the practicality and advantages of the partially independent control scheme over a coupled control scheme.Widely applied to crew exchange, large-scale assembly, spacecraft maintenance, docking, interception, formation flying and other astronautic missions involving more than one spacecraft, autonomous spacecraft rendezvous has been regarded as a crucial operational technology in aerospace engineering. As the autonomous control scheme is a cardinal and decisive issue that determines the success of the rendezvous, it has been and continues to be an engaging area of study.Most of the mathematical models employed in investigating spacecraft rendezvous are derived from the two-body problem. Because of their concise and linearized form, Clohessy-Wiltshire equations (Clohessy and Wiltshire, 1960) were favored by many researchers, though this model was initially developed to describe the rendezvous in circular orbits. The models put forward by De Vries (1963) and Tschauner (1967) extended our knowledge to the rendezvous in elliptical orbits; however, nonlinear terms were involved, which circumscribed their broader implementations in control engineering.Considering the fact that most of the rendezvous missions were conducted in near-circular orbits with small eccentricities, researchers began to search for some eclectic models that are linearized and sufficiently precise. A comprehensive survey on these efforts was given by Carter (1998); nevertheless, all the linearization results introduced in this literature are in terms of either the true or eccentric anomaly of one spacecraft and require the solution of the Kepler problem, which is time and computational consuming. A time-explicit dynamical model overcoming this defect was first introduced by Anthony and Sasaki (1965), and a more recent development on time-explicit models was contributed by Melton (2000). Robust guaranteed cost control was first raised by Chang and Peng (1972) to optimize preassigned cost function, and many of the following literatures were carried out based on their works. Petersen and McFarlane (1994) synthesized a state feedback guaranteed cost controller via a Riccati equation approach. Yu and Chu (1999) designed a guaranteed cost controller for linear uncertain time-delay systems via a linear matrix inequality (LMI) method. Esfahani and Petersen (2000) solved the guaranteed cost output feedback control problem in a matrix substitution ma...

Sliding-mode control for a rolling-missile with input constraints

“…Liu et al [19] proposed a novel AWC based on robust tracking control, and simulation study was carried out to illustrate its anti-saturation ability and great tracking performance. In [20], a robust anti-windup controller was adopted for an in-plane motion, which showed some advantages. In [21], input saturation was solved by designing an AWC, and simulation results demonstrated its effectiveness.…”