Computationally-efficient modeling and optimization of strain-actuated solar arrays with tailored viscoelastic damping for spacecraft attitude control

Abstract

The recently-introduced strain-actuated solar array (SASA) spacecraft attitude control system (ACS) is expected to enable new levels of pointing precision for next-generation space observatories. Previous work has shown that tailored passive viscoelastic damping can help mitigate control system complexity by using passive damping to manage high-frequency vibration modes, while the active control system focuses on lower-frequency dynamics. Viscoelastic materials (VEMs) exhibit hysteretic behavior, requiring the use of computationally-expensive models based on integro-differential equations. A class of approximations is presented here where convolution integrals are replaced with linear time-invariant state-space equations with auxiliary states to reduce computational expense significantly, supporting the application of control co-design optimization, while maintaining requisite accuracy. This approach eliminates time history integration needed for derivative function calculation, which opens up the possibility of using general optimal control toolkits as well as advanced computationally-efficient methods for approximating system dynamics derivative functions.