Input Load Estimation for Bistable Spacecraft Booms using Data-Driven Rational Approximation

Bistable tape spring booms enable compact, self-deploying space structures, but the uncontrolled deployment can generate mechanical loads that risk damaging sensitive components. Direct measurement of these deployment-induced forces is often infeasible due to the difficulty of integrating a force transducer at the exact point of application, as well as data transmission limitations for small satellites. A critical challenge is that the tape spring’s dynamic response is highly nonlinear and sensitive to operational conditions such as varying input force and temperature. Here, we present a first step towards an experimental framework for estimating deployment-induced loads on tape spring booms by solving the inverse problem of calculating input loads from measured tip velocities. To capture the effect of varying load intensities, data-driven state-space models are developed using Vector Fitting (VF) at 15 distinct load levels by exciting a parabolic cross-section composite tape spring at its base using a single-axis reference input signal. The input forces are captured via a load cell attached to an electrodynamic shaker, and out-of-plane velocity responses are measured using a Scanning Laser Doppler Vibrometer (SLDV). For validation of the method, various input signals such as sinusoidal, square, triangle, and burst random are used to excite the boom, and the input loads are calculated inversely from the previously developed transfer function model using inversion in the frequency domain. This work establishes that accurate model performance depends on case-specific tuning, proving the need for adaptive frameworks in the future.