Linear control of underactuated spacecraft with two reaction wheels made feasible by solar radiation pressure

This paper describes a method of recovering linear controllability of an underactuated spacecraft by accounting for the effects of solar radiation pressure (SRP) in the spacecraft attitude dynamics model. The developments are based on a spacecraft model with a four wheel reaction wheel array of which two wheels have failed and two wheels are functioning. The model for SRP torque as a function of spacecraft attitude is incorporated into the state-space description of the system. Under suitable assumptions, the linearization of the underacted spacecraft model (with SRP effects included) is shown to be linearly controllable. This conclusion is exploited to define a novel approach for handling reaction wheel failures based on conventional Linear Quadratic (LQ) controllers. The results of the linear and non-linear simulations illustrate the ability to recover pointing by controlling two functioning reaction wheels while two other wheels undergo subsequent failures.