A Controller Design Method for Drag-Free Spacecraft Multiple Loops With Frequency Domain Constraints

Abstract

Space-based gravitational wave detection requires a strict level of residual acceleration ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\sim$</tex-math></inline-formula> <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$10^{-15} \mathrm{~m/s}^{2} / \sqrt{\text{Hz}}$</tex-math></inline-formula> in the frequency band of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$0.1\text{mHz}\sim 1\text{Hz}$</tex-math></inline-formula> ) on the test masses along the sensitive axes. Because of the configuration of the detection spacecraft with two test masses, there are complex couplings between the spacecraft attitude, drag-free and suspension control loops in the drag-free and attitude control system. Moreover, the space environment disturbances and the limited noise levels of the actuators and sensors make it difficult for multiple control degrees of freedom to meet the index requirements at the same time. Currently, PID and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_\infty$</tex-math></inline-formula> methods are mainly used for its controller design, where the system is decoupled and divided into relatively independent control loops, and the controllers are designed to meet the requirements separately. However, parameter tuning usually requires empirical trial and error, leading to the low design efficiency. And the coupling relationships between loops cannot be well described and treated mathematically. Therefore, a controller design method for drag-free spacecraft multi loops is proposed in this paper, where the index requirements are transformed into frequency domain constraints and the optimization objectives are designed for better performances according to the control characteristics of different loops. Then the controllers are tuned by multi-population genetic algorithm improving the design efficiency. As mentioned, under the premise that the index requirements are all met, the couplings between loops are considered and some of the performances of the system can be optimized, such as the residual acceleration acting on the test masses. Numerical simulation and comparison verify the effectiveness of this method.