Predicting the Optical Performance of the Space Interferometry Mission Using a Modeling, Testing, and Validation Methodology

Abstract

This paper presents the modeling, testing, and validation methodologies developed to predict the optical performance of the Space Interferometry Mission (SIM) at the Jet Propulsion Laboratory (JPL). The modeling methodology combines structural, optical, and control system design within a common state space framework and incorporates reaction wheel assembly (RWA) disturbances to evaluate the end-to-end performance of the system requirements. The validation methodology uses the Micro-Precision Interferometer (MPI) testbed, which is a ground-based, representative hardware model of SIM. In this study, the integrated model of the MPI testbed was used to calculate the transfer functions from RWA input to optical performance output. The model-predicted transfer functions were compared with the MPI testbed measurements, and the accuracy of the integrated model was quantified using a metric that was based on output power of the transfer functions. The RWA disturbances were then propagated through the modeled and measured transfer functions to predict the optical performance of the MPI testbed. This method is called the “decoupled disturbance analysis” and relies on the “blocked” RWA disturbances, measured with the RWA hardmounted to a rigid surface. These predictions were compared with the actual (measured) optical performance of MPI, measured with the RWA mounted to MPI, to evaluate the accuracy of the decoupled disturbance analysis method. The results show that this method is not an accurate representation of the coupled boundary conditions that occurs when the RWA is mounted to the flexible MPI structure. In order to correct for the blocked RWA disturbance boundary conditions, the “coupled disturbance analysis” method was developed. This method uses “force filters” that depend on estimates of the interface accelerances of the RWA and the MPI structure to effectively transform the blocked RWA disturbance measurements into their corresponding “coupled” disturbances (the disturbances that would occur at the coupled RWA-MPI interface). Compared to the decoupled method, the coupled method more accurately predicts the system’s performance. Additionally, the RWA cross-spectral density terms were found to be influential in matching the performance predictions to the measured optical performance of MPI.

Dynamic Mass of a Reaction Wheel Including Gyroscopic Effects: An Experimental Approach

“…Earlier works on RWAs have shown that the diagonal coecients (D wii with i = 1, 2, 3, 4, 5, 6) are generally the most important ones [29,32]. Moreover, the four cross-DoF terms D w15 , D w24 , D w42 , and D w51 have also to be considered, in particular for non-symmetric congurations (i.e.…”

“…Its parameters will, in fact, not only change as a function of the frequency but also of the speed of the rotary ywheel. In [29,32], analytical expressions of RWA dynamic mass including the gyroscopic eect based on a RWA hard-mounted microvibration model were derived and used for coupled microvibration analysis. Although the results were improved, the modes of vibration of the RWA were not included hence limiting the quality of predictions.…”

Microvibrations Induced by a Cantilevered Wheel Assembly with a Soft-Suspension System

“…(22), and expressing explicitly the moment produced by the rotation of the point mass m e (see Fig. 6), the following alternative form of the equations is obtained: (25) where r is the radius of the flywheel. Equation (25) is then used to calculate numerically !…”

“…However, in [23] the development of the mathematical model of the RWA (cantilevered flywheel with rigid bearing in this case) is not included, and input disturbance data are empirical (from RWA vibration tests). This method was then applied to assess the optical performance of the Space Interferometry Mission in [24,25].…”

Coupled disturbance analysis of a pulse tube cryocooler

“…However, this method is not an accurate representation of the coupled boundary conditions that occur when the PTC is mounted to a structure. With the aim to analytically reproduce the coupled dynamics, a dynamic mass method was developed to evaluate the coupled performance [11][12][13]. Although the results are accurate, this method is significantly challenging in terms of test configuration and computational effort.…”