Lawrence W. Taylor

Timoshenko Beam Modeling for Parameter Estimation of NASA Mini-Mast Truss

In this paper a distributed parameter model for the estimation of modal characteristics of NASA Mini-Mast truss is proposed. A closed-form solution of the Timoshenko beam equation, for a uniform cantilevered beam with two concentrated masses, is derived so that the procedure and the computational effort for the estimation of modal characteristics are improved. A maximum likelihood estimator for the Timoshenko beam model is also developed. The resulting estimates from test data by using Timoshenko beam model are found to be comparable to those derived from other approaches.

SIZE AND SHAPE FROM STELLAR OCCULTATION OBSERVATIONS OF THE DOUBLE JUPITER TROJAN PATROCLUS AND MENOETIUS

We present results of a stellar occultation by the Jupiter Trojan asteroid Patroclus and its nearly equal size moon, Menoetius. The geocentric mid-time of the event was 2013 October 21 06:43:02 UT. Eleven sites out of 36 successfully recorded an occultation. Seven chords across Patroclus yielded an elliptical limb fit of 124.6 by 98.2 km. There were six chords across Menoetius that yielded an elliptical limb fit of 117.2 by 93.0 km. There were three sites that got chords on both objects. At the time of the occultation we measured a separation of 664.6 km (0.247 arcsec) and a position angle for Menoetius of 2657 measured eastward from J2000 north. Combining this occultation data with previous light curve data, the axial ratios of both objects are 1.3 : 1.21 : 1, indicative of a mostly oblate ellipsoid with a slight asymmetry in its equatorial projection. The oblate shape is not an equilibrium shape for the current rotation period, but would be if it were rotating with an ~8 h period. This faster period is consistent with a pre-evolved state of the system with an orbital separation that is 50% smaller. Our best estimate of the system density is 0.88 g cm−3.

Likelihood estimation for distributed parameter models of large beam-like structures

Abstract In this paper, a maximum likelihood estimation for distributed parameter models of large flexible structures has been formulated. Distributed parameter models involve far fewer unknown parameters than independent modal characteristics or finite element models. The closed form solutions for the partial differential equations with corresponding boundary conditions have been derived. The closed form expressions of the sensitivity functions lead to highly efficient algorithms for analyzing ground or on-orbit test results. For illustration of this approach, experimental data of the NASA Mini-Mast truss have been used. The estimations of modal properties involve its lateral bending modes and torsional modes. The results show that distributed parameter models are promising in the parameter estimation of large flexible structures.

Maximum likelihood estimation for distributed parameter models of flexible spacecraft

Abstract Because of the large size and flexibility of certain spacecraft, it is not possible to determine with suitable accuracy their structural dynamic characteristics from ground tests. It is necessary, therefore, to analyze orbital response data to refine the a priori parameters of models of the structural dynamics. Because of the high order and complexity of the relationships, the number of unknown model parameters can become unmanageable if each is assumed to be independent of each other. For many spacecraft it is possible to use distributed parameter models, thereby reducing the number unknown parameters. An important side benefit is that the model accuracy is increased. Experimental data from the NASA Solar Array Flight Experiment (SAFE) is analyzed by applying a maximum likelihood estimation algorithm to the task of estimating the unknown parameters of a distributed parameter model of the SAFE configuration. Both the out-of-plane bending and torsion of the solar array are modeled using partial differential equations. A truncated form of the model is used in the estimation algorithm and the higher modes are deduced from the distributed parameter model. The use of maximum likelihood estimation and distributed parameter models results in the most accurate model possible. The Solar Array Flight Experiment offers a unigue opportunity to demonstrate the procedures for modelling complex, flexible spacecraft in the preparation for more complex configurations such as the NASA Manned Space Station.

On-orbit systems identification of flexible spacecraft

Abstract The process of on-orbit systems identification of flexible spacecraft is examined in terms of the difficulties that are expected because of the potentially unmanageable number of unknown model parameters due to the very high order system models Involved. A Jordon block canonical form and global model parameters are used to reduce the number of unknown parameters to manageable numbers. A Bayesian approach is discussed which enables the merging of theoretical models with ground or on-orb1t test results by using Unconditional Maximum Likelihood Parameter Estimation. A Modified Newton-Raphson technique is proposed for determining the model parameter estimates and an expected fit error criterion is recommended for the determination of the model structure and order reduction.

A new criterion for modeling systems

The criterion that is proposed is an expected value of the mean square response error as an alternative to testing a model against new data. Modeling with respect to this new criterion does not change the estimate for a given model format from a maximum likelihood estimate or mean square response error estimate. The new criterion does, however, provide a means of comparing models with different formats and varying complexity. A numerical example is used to illustrate the application of the proposed criteria and the problem of searching for the best model. For all but the most trivial system identification problems, it is shown that a prohibitive number of combinations of terms of the model must be investigated to ensure the final model is best.

Continuum modeling of the Space Shuttle Remote Manipulator System

The formulation of structural dynamics models for the Space Shuttle Remote Manipulator System (RMS) is discussed. Continuum models are used instead of finite element models because of the improved accuracy, the reduced number of model parameters, the avoidance of model order reduction, and the ability to represent the structural dynamics and control system dynamics in the same system of equations. Dynamics analysis of both linear and nonlinear versions of the model is performed and compared with finite element model results. A distributed parameter model of the Space Shuttle-RMS payload was generated using the transfer matrix method and the software PDEMOD. The model included an active control system which generated damping at the RMS joints. A stability and control analysis was then performed to detemine the reduction in settling time for RMS operations.<<ETX>>

On the use of maximum likelihood estimation for the assembly of Space Station Freedom

Distributed parameter models of the Solar Array Flight Experiment, the Mini-MAST truss, and Space Station Freedom assembly are discussed. The distributed parameter approach takes advantage of (1) the relatively small number of model parameters associated with partial differential equation models of structural dynamics, (2) maximum-likelihood estimation using both prelaunch and on-orbit test data, (3) the inclusion of control system dynamics in the same equations, and (4) the incremental growth of the structural configurations. Maximum-likelihood parameter estimates for distributed parameter models were based on static compliance test results and frequency response measurements. Because the Space Station Freedom does not yet exist, the NASA Mini-MAST truss was used to test the procedure of modeling and parameter estimation. The resulting distributed parameter model of the Mini-MAST truss successfully demonstrated the approach taken. The computer program PDEMOD enables any configuration that can be represented by a network of flexible beam elements and rigid bodies to be remodeled.<<ETX>>

Parameter Estimation for Distributed Parameter Models of Complex, Flexible Structures

Abstract Distributed parameter modeling of structural dynamics has been limited to simple spacecraft configurations because of the difficulty of handling several distributed parameter systems linked at their boundaries. Because of this limitation the computer software PDEMOD is being developed for the purposes of modeling, control system analysis, parameter estimation and control/structure optimization. PDEMOD is capable of modeling complex, flexible spacecraft which consist of a 3-dimensional network of flexible beams and rigid bodies. Each beam element has bending in two planes, torsion and axial deformation. PDEMOD was used for parameter estimation for the Mini-MAST truss based on matching experimental modal frequencies and static deflection test data, thereby reducing significantly the instrumentation requirements for on-orbit tests.

An optimal modal-space controller for structural damping enhancements

A stochastic optimum-based compensator is developed to enhance structural damping with collocated rate sensors/actuators. This controller is based on explicit solutions for the Riccati equations from a modal-space model. The performance of each controlled mode can be easily adjusted by the corresponding design parameters in the controller. NASAs Spacecraft Control Laboratory Experiment (SCOLE) facility is used to demonstrate the effectiveness of this control design. A distributed parameter model is first obtained by using the Holzers transfer matrix method and the corresponding modal parameters are identified. Then the distributed parameter model is reduced to a finite-dimensional modal-space model for the controller design. Three torque actuators and three collocated rate sensors are used to suppress the vibration of the first five modes. Analytical and experimental results show that the proposed controller is effective in damping enhancements for large flexible structures.