A nonlinear control algorithm for fuel optimal attitude control using reaction jets

Abstract

We present the analysis and design of a weighted nonlinear time-fuel optimal control algorithm for spacecraft attitude dynamics using on-off gas jets. In the development of a controller, we explore four control algorithms within a single-step control framework where the step is the fundamental update time of the digital controller. The benchmark controller is a basic pulse-width modulator (PWM) with a proportional derivative controller driving the feedback loop. The second is a standard rate-ledge controller (RLC) with full-on or full-off pulse commands, while the third varies the duration of the RLC pulse commands based on the location of the states in the phase plane. The RLC algorithm is shown to well-approximate a continuous-time weighted time-fuel optimal controller. The fourth control algorithm consists of a combination of the variable-pulse RLC algorithm and a tracking-fuel optimal controller that reduces the residual error relative to the latter algorithm. Experimental data from a dynamic air-bearing testbed at Lawrence Livermore National Laboratory are used to compare the four control algorithms. The PWM scheme proves to be robust to disturbances and unmodeled dynamics and quite fast, but yields excessive fuel consumption from frequent switching. The standard RLC algorithm gives poor closed-loop performance in the presence of unmodeled dynamics and ends up being equally as fuel costly as the PWM scheme. The third algorithm, the RLC with variable pulses, significantly improves the transient and steady-state responses of the first two controllers. Via parameter tuning, we observe that this modified RLC gives excellent steady-state fuel consumption as well as reasonably fast settling times. The fourth algorithm, although more fuel efficient than the PWM and standard RLC controllers, is less efficient than the variable RLC algorithm. Matlab simulations of the four control algorithms studied are corroborated by these test results.