Suboptimal Predictive Control for Satellite Detumbling

Abstract

Rate damping in the initial acquisition phase of a magnetically controlled small satellite is a big challenge for the control system. In this phase, the main difficulties are dynamic nonlinearities due to high body rates, time-varying control due to the change in Earth’s magnetic field, inherent underactuation, and constraints on available power. The control system is required to minimize the detumbling time with minimal use of onboard resources. In comparison to the existing control techniques used in the initial acquisition phase, predictive control can be considered a suitable choice for handling such conflicting objectives in the presence of constraints. In this work, performance of two existing nonlinear model predictive control schemes that guarantee closed-loop stability are analyzed. Nonlinear model predictive control gives improved performance by reducing the detumbling time compared to classical control techniques based on the rate of change of Earth’s magnetic field; however, the computational requirements are high. Furthermore, it is demonstrated that, when the body rates increase, the computational burden of nonlinear model predictive control to reach an optimal point becomes prohibitively large. For these situations, an algorithm is presented that allows early termination of the optimizer by imposing an additional constraint on the cost reduction. The early termination criteria of the optimizer can be chosen based on the available computational resources. The imposed cost reduction constraint also helps in further reducing the detumbling time. Extensive numerical simulations show that the presented algorithm works well in practice for a good range of initial body rates.