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NASA NTRS1986

Active Control Evaluation for Spacecraft (ACES)

The Air Force goal is to develop vibration control techniques for large flexible spacecraft by addressing sensor, actuator, and control hardware and dynamic testing. The Active Control Evaluation for Spacecraft (ACES) program will address the Air Force goal by looking at two leading control techniques and implementing them on a structural model of a flexible spacecraft under laboratory testing. The first phase in the ACES program is to review and to assess the High Authority Control/Low Authority Control (HAC/LAC) and Filter accomodated Model Error Sensitivity Suppression (FAMESS) control techniques for testing on the modified VCOSS structure. Appropriate sensors and actuators will be available for use with both techniques; locations will be the same for both techniques. The control actuators will be positioned at the midpoint and free end of the structure. The laser source for the optical sensor is mounted on the feed mast. The beam will be reflected from a mirror on the offset antenna onto the detectors mounted above the shaker table bay. The next phase is to develop an analysis simulation with the control algorithms implemented for dynamics verification. The third phase is to convert the control laws into high level computer language and test them in the NASA-MSFC facility. The final phase is to compile all analytical and test results for performance comparisons.

Pearson, J.↗

NASA NTRS1986

Robust multivariable controller design for flexible spacecraft

Large, flexible spacecraft are typically characterized by a large number of significant elastic modes with very small inherent damping, low, closely spaced natural frequencies, and the lack of accurate knowledge of the structural parameters. Summarized here is some recent research on the design of robust controllers for such spacecraft, which will maintain stability, and possible performance, despite these problems. Two types of controllers are considered, the first being the linear-quadratic-Gaussian-(LQG)-type. The second type utilizes output feedback using collocated sensors and actuators. The problem of designing robust LQG-type controllers using the frequency domain loop transfer recovery (LTR) method is considered, and the method is applied to a large antenna model. Analytical results regarding the regions of stability for LQG-type controllers in the presence of actuator nonlinearities are also presented. The results obtained for the large antenna indicate that the LQG/LTR method is a promising approach for control system design for flexible spacecraft. For the second type of controllers (collocated controllers), it is proved that the stability is maintained in the presence of certain commonly encountered nonlinearities and first-order actuator dynamics. These results indicate that collocated controllers are good candidates for robust control in situations where model errors are large.

Joshi, Suresh M.↗

NASA NTRS1987

Vibration isolation for line of sight performance improvement

Diagrams of the Reaction Wheel Assembly (RWA) are presented along with charts and graphs illustrating jitter error model, induced vibration tests, radial displacement transfer function, and axial displacement power spectra density. The RWA isolator specification requirements are listed.

Rodden, J. J.↗

NASA NTRS1987

Robust time and frequency domain estimation methods in adaptive control

A robust identification method was developed for use in an adaptive control system. The type of estimator is called the robust estimator, since it is robust to the effects of both unmodeled dynamics and an unmeasurable disturbance. The development of the robust estimator was motivated by a need to provide guarantees in the identification part of an adaptive controller. To enable the design of a robust control system, a nominal model as well as a frequency-domain bounding function on the modeling uncertainty associated with this nominal model must be provided. Two estimation methods are presented for finding parameter estimates, and, hence, a nominal model. One of these methods is based on the well developed field of time-domain parameter estimation. In a second method of finding parameter estimates, a type of weighted least-squares fitting to a frequency-domain estimated model is used. The frequency-domain estimator is shown to perform better, in general, than the time-domain parameter estimator. In addition, a methodology for finding a frequency-domain bounding function on the disturbance is used to compute a frequency-domain bounding function on the additive modeling error due to the effects of the disturbance and the use of finite-length data. The performance of the robust estimator in both open-loop and closed-loop situations is examined through the use of simulations.

Lamaire, Richard Orville↗

NASA NTRS1986

A theoretical analysis of the round-off propagation in different Kalman filter implementations

A theoretical analysis is made of the error propagation due to numerical round-off for four different Kalman filter implementations: the conventional Kalman filter, the square root covariance filter, the square root information filter and the Chandrasekhar square root filter. From these error models, new insights about the applicability of the different filters and their sensitivity to round-off, is obtained. It is shown that the CKF may become completely unreliable when the original plant is unstable, and that this is easily circumvented by a number of techniques. The square root filters, often quoted to possess a conditioning or sensitivity that is the square root of that of the CKF, are shown to possess this property only for the computation of the covariance of the filtered signal and not for the computation of the Kalman gain or the filtered estimate. Finally, the Chandrasekhar filter is shown to be numerically unstable.

Verhaegen, M.↗

NASA NTRS1987

Simplified solution for a class of fading memory filters

A fading memory filter is a least squares estimator (LSE) that applies an exponentially decaying weight to past measurements. When compared with a standard Kalman filter, its key advantages are asymptotic stability and reduced sensitivity to modeling errors. This paper derives a simple solution for a class of fading memory filters, resulting in a reduction in computational complexity. Steady state filter solutions are obtained for second- and third-order filters used in a global positioning system (GPS) receiver for high dynamic vehicles.

Statman, Joseph I.↗

NASA NTRS1987

Studies of multi-baseline spaceborne interferometric synthetic aperture radars

A set of Seasat SAR data that were obtained in nearly repeat ground track orbits is utilized to simulate the performance of spaceborne interferometric synthetic aperture radar (ISAR) systems. A qualitative assessment of the topography measurement capability is presented. A phase measurement error model is described and compared with the data obtained at various baseline separations and signal-to-noise ratios. Finally, the implications of these results on the future spaceborne ISAR design are discussed.

Li, F.↗

NASA NTRS1988

Using ridge regression in systematic pointing error corrections

A pointing error model is used in the antenna calibration process. Data from spacecraft or radio star observations are used to determine the parameters in the model. However, the regression variables are not truly independent, displaying a condition known as multicollinearity. Ridge regression, a biased estimation technique, is used to combat the multicollinearity problem. Two data sets pertaining to Voyager 1 spacecraft tracking (days 105 and 106 of 1987) were analyzed using both linear least squares and ridge regression methods. The advantages and limitations of employing the technique are presented. The problem is not yet fully resolved.

Guiar, C. N.↗

NASA NTRS1988

Precise interferometric tracking of spacecraft at low sun-earth-probe angles

When a spacecraft is at low sun-earth-probe (SEP) angle, phase perturbations induced in the spacecraft's signal by the solar plasma can impede the acquisition of meaningful spacecraft Very Long Baseline Interferometry (VLBI) measurements. This phenomenon imposes limitations on our ability to successfully acquire the spacecraft signal, and also introduces unmodeled errors into data that are successfully acquired. In this paper, an analysis of the solar plasma induced error on interferometric delay rate as a function of SEP angle is performed. In addition, the probability of correct signal phase connection as a function of SEP angle and plasma variability is calculated for 2.3 GHz and 8.4 GHz signals. In December 1986, an experiment was conducted to demonstrate VLBI navigation at low SEP angles, using the Voyager 2 spacecraft. The results of this experiment are consistent with the conclusions reached in the low SEP analysis and are also consistent with a theoretical error model for water vapor fluctuations in the earth's troposphere.

Kahn, Robert D.↗

NASA NTRS1988

Interfacial tension and vapor-liquid equilibria in the critical region of mixtures

In the critical region, the concept of two-scale-factor universality can be used to accurately predict the surface tension between near-critical vapor and liquid phases from the singularity in the thermodynamic properties of the bulk fluid. In the present work, this idea is generalized to binary mixtures and is illustrated using the data of Hsu et al. (1985) for CO2 + n-butane. The pressure-temperature-composition-density data for coexisting, near-critical phases of the mixtures are fitted with a thermodynamic potential comprised of a sum of a singular term and nonsingular terms. The nonuniversal amplitudes characterizing the singular term for the mixtures are obtained from the amplitudes for the pure components by interpolation in a space of thermodynamic 'field' variables. The interfacial tensions predicted for the mixtures from the singular term are within 10 percent of the data on three isotherms in the pressure range (Pc - P)/Pc of less than 0.5. This difference is comparable to the combined experimental and model errors.

Moldover, Michael R.↗

NASA NTRS1988

Observability analysis of inertial navigation systems during in-flight alignment

In this work the observability of an Inertial Navigation System (INS) during In-Flight Alignment (IFA) is investigated. A systematic approach to the observability analysis of a piece-wise constant system is presented and its use is justified mathematically. As a tool for the investigation a Stepped Observability Matrix (SOM) is constructed and a corresponding Stepped Space is defined. The INS error model is transformed into the Stepped Space during a specially chosen IFA trajectory and a full observability is carried out. The results of the mathematical analysis are checked against the results of covariance simulation and a full agreement is found between the two. Finally, the practical implications of this analysis are outlined.

Bar-Itzhack, I. Y.↗

NASA NTRS1988

ACES program - Lessons learned

The ACES Program involved the experimental evaluation of three LSS (large space structures) control design techniques at the LSS GTF (ground test facility) at NASA/MSFC. The three techniques were developed under the ACOSS (active control of space structures) Program specifically for application to LSS. The techniques included FAMESS (filter accommodated model error sensitivity suppression), HAC/LAC (high authority control/low authority control), and positivity. Some of the lessons that have been learned during the course of the ACES program are examined.

Jones, Victoria L.↗

NASA NTRS1988

Precise orbit determination for NASA's earth observing system using GPS (Global Positioning System)

An application of a precision orbit determination technique for NASA's Earth Observing System (EOS) using the Global Positioning System (GPS) is described. This technique allows the geometric information from measurements of GPS carrier phase and P-code pseudo-range to be exploited while minimizing requirements for precision dynamical modeling. The method combines geometric and dynamic information to determine the spacecraft trajectory; the weight on the dynamic information is controlled by adjusting fictitious spacecraft accelerations in three dimensions which are treated as first order exponentially time correlated stochastic processes. By varying the time correlation and uncertainty of the stochastic accelerations, the technique can range from purely geometric to purely dynamic. Performance estimates for this technique as applied to the orbit geometry planned for the EOS platforms indicate that decimeter accuracies for EOS orbit position may be obtainable. The sensitivity of the predicted orbit uncertainties to model errors for station locations, nongravitational platform accelerations, and Earth gravity is also presented.

Williams, B. G.↗

NASA NTRS1987

Simple robust control laws for robot manipulators. Part 1: Non-adaptive case

A new class of exponentially stabilizing control laws for joint level control of robot arms is introduced. It has been recently recognized that the nonlinear dynamics associated with robotic manipulators have certain inherent passivity properties. More specifically, the derivation of the robotic dynamic equations from the Hamilton's principle gives rise to natural Lyapunov functions for control design based on total energy considerations. Through a slight modification of the energy Lyapunov function and the use of a convenient lemma to handle third order terms in the Lyapunov function derivatives, closed loop exponential stability for both the set point and tracking control problem is demonstrated. The exponential convergence property also leads to robustness with respect to frictions, bounded modeling errors and instrument noise. In one new design, the nonlinear terms are decoupled from real-time measurements which completely removes the requirement for on-line computation of nonlinear terms in the controller implementation. In general, the new class of control laws offers alternatives to the more conventional computed torque method, providing tradeoffs between robustness, computation and convergence properties. Furthermore, these control laws have the unique feature that they can be adapted in a very simple fashion to achieve asymptotically stable adaptive control.

Wen, J. T.↗

NASA NTRS1989

A new state reconstructor for digital controls systems using weighted-average measurements

A state reconstructor is presented for a linear continuous-time plant driven by a zero-order-hold. It takes a continuous-time output vector from the plant and convolutes it with a weighting-function matrix whose elements are time dependent. This result is integrated over T second intervals to generate weighted-averaged measurements, every T seconds, that are used in the state reconstruction process. If the plant is noise-free and can be modeled precisely, the output of this state reconstructor exactly equals the true state of the plant and accomplishes this without knowledge of the plant's initial state. If noise or modeling errors are a problem, it can be catenated with a state observer or a Kalman filter for a synergistic effect.

Polites, Michael E.↗

NASA NTRS1988

Precise orbit determination for NASA's Earth Observing System using GPS

A precision orbit determination technique for NASA's Earth Observing System (EOS) is discussed. The technique exploits the redundant geometric information from GPS carrier phase and P-code pseudorange measurements and minimizes the requirements for precision dynamical modeling. Performance estimates for the application of the technique to the orbit geometry planned for the EOS platforms show that decimeter accuracies of orbit position may be obtained. The sensitivity of the predicted orbit uncertainties to model errors for station locations, nongravitational platform accelerations, and earth gravity are presented.

Williams, Bobby G.↗

NASA NTRS1989

Sensor failure detection using generalized parity relations for flexible structures

Analytical redundancy may be preferable to hardware redundancy in failure detection/isolation tasks for such large-scale systems as space structures. Generalized single-sensor parity relations are presently applied to this problem; they are noted to yield a very simple isolation logic, and their generation is found to be extremely rapid, even in the case of extremely complex systems, provided only that the eigenstructure of the system be known. Their implementation is, however, extremely sensitive to modeling errors and noise.

Mercadal, Mathieu↗

NASA NTRS1988

On the design of the dissipative LQG-type controllers

The design of dissipative linear-quadratic-Gaussian-type compensators for positive real plants is considered. It is shown that if the noise covariance matrices (used as weighting matrices) satisfy certain conditions, the compensator has a strictly positive real transfer function matrix. The stability of the resulting closed-loop system is guaranteed regardless of modeling errors as long as the plant remains positive real. In view of this property, the controller is expected to be useful for vibration suppression in large, flexible space structures.

Lozano-Leal, R.↗