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

Space-based gravitational wave detection requires a strict level of residual acceleration ($\sim$$10^{-15}\;\mathrm{m/s}^{2} / \sqrt{\text{Hz}}$ in $\text{0.1}\;\text{mHz}\text{--} {1}\;\text{Hz}$) 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 different 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 to meet all the index requirements. Currently, proportional-integral-derivative (PID) and $H_\infty$ methods are mainly used for its controller design, where the system is decoupled into relatively independent loops, and the controllers are designed 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 multiple loops is proposed in this article, 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 multipopulation 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.