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At least 1,279 records · Page 71

Design of a LQR Controller of Reduced Inputs for Multiple Spacecraft Formation Flying

Regarding multiple spacecraft formation flying, the observation is made that control thrust need only be applied coplanar to the local horizon to achieve complete controllability of a two-satellite formation. Without the need for zenith-nadir (radial) thrust, simplifications and reduction of the weight of the propulsion system may be accomplished. This work focuses on the validation of this radial-excluding control system on its own merits, and in comparison to a related system which does provide thrust parallel to the orbital radius. Simulations are performed using commercial ODE solvers to propagate the Keplerian dynamics of a controlled satellite relative to an uncontrolled, leader satellite. The conclusion is drawn that, despite the exclusion of the radial thrust axis, the remaining control thrust available still provides enough control to design a gain matrix of adequate performance using linear-quadratic regulator (LQR) techniques.

Starin, Scott R.↗

Linear-Quadratic-Gaussian Regulator Developed for a Magnetic Bearing

Linear-Quadratic-Gaussian (LQG) control is a modern state-space technique for designing optimal dynamic regulators. It enables us to trade off regulation performance and control effort, and to take into account process and measurement noise. The Structural Mechanics and Dynamics Branch at the NASA Glenn Research Center has developed an LQG control for a fault-tolerant magnetic bearing suspension rig to optimize system performance and to reduce the sensor and processing noise. The LQG regulator consists of an optimal state-feedback gain and a Kalman state estimator. The first design step is to seek a state-feedback law that minimizes the cost function of regulation performance, which is measured by a quadratic performance criterion with user-specified weighting matrices, and to define the tradeoff between regulation performance and control effort. The next design step is to derive a state estimator using a Kalman filter because the optimal state feedback cannot be implemented without full state measurement. Since the Kalman filter is an optimal estimator when dealing with Gaussian white noise, it minimizes the asymptotic covariance of the estimation error.

Choi, Benjamin B.↗

The Many Worlds of Transition Research.

The transition from laminar to turbulent flow in a boundary layer is a complex phenomenon that may take different routes, each involving distinct stages governed by different, often not-yet unraveled dynamical principles. There are, surprisingly, questions concerning virtually every stage in the process, beginning with receptivity to external disturbances, the linear stability of spatially developing flows, different possible nonlinear end games, the formation and propagation of turbulent spots and the emergence of fully developed turbulent flow. There seems no doubt that the flow has to be seen as a forced, nonlinear spatio-temporal system, but the system is so complex that to extract simple insights is still very difficult.

Narasimha, R.↗

A Fiber-Optic Aircraft Lightning Current Measurement Sensor

A fiber-optic current sensor based on the Faraday Effect is developed for aircraft installations. It can measure total lightning current amplitudes and waveforms, including continuing current. Additional benefits include being small, lightweight, non-conducting, safe from electromagnetic interference, and free of hysteresis and saturation. The Faraday Effect causes light polarization to rotate in presence of magnetic field in the direction of light propagation. Measuring the total induced light polarization change yields the total current enclosed. The system operates at 1310nm laser wavelength and can measure approximately 300 A - 300 kA, a 60 dB range. A reflective polarimetric scheme is used, where the light polarization change is measured after a round-trip propagation through the fiber. A two-detector setup measures the two orthogonal polarizations for noise subtraction and improved dynamic range. The current response curve is non-linear and requires a simple spline-fit correction. Effects of high current were achieved in laboratory using combinations of multiple fiber and wire loops. Good result comparisons against reference sensors were achieved up to 300 kA. Accurate measurements on a simulated aircraft fuselage and an internal structure illustrate capabilities that maybe difficult with traditional sensors. Also tested at a commercial lightning test facility from 20 kA to 200 kA, accuracy within 3-10% was achieved even with non-optimum setups.

Nguyen, Truong X.↗

Fuzzy Model-based Pitch Stabilization and Wing Vibration Suppression of Flexible Wing Aircraft.

This paper presents a fuzzy nonlinear controller to regulate the longitudinal dynamics of an aircraft and suppress the bending and torsional vibrations of its flexible wings. The fuzzy controller utilizes full-state feedback with input constraint. First, the Takagi-Sugeno fuzzy linear model is developed which approximates the coupled aeroelastic aircraft model. Then, based on the fuzzy linear model, a fuzzy controller is developed to utilize a full-state feedback and stabilize the system while it satisfies the control input constraint. Linear matrix inequality (LMI) techniques are employed to solve the fuzzy control problem. Finally, the performance of the proposed controller is demonstrated on the NASA Generic Transport Model (GTM).

Stability and Control↗

Flap-lag dynamics of hingeless helicopter blades at moderate and high advance ratios

Equations for large amplitude coupled flaplag motion of a hingeless elastic helicopter blade in forward flight are derived. Only a torsionally rigid blade exicted by quasi-steady aerodynamic loads is considered. The effects of reversed flow together with some new terms due to forward flight are included. Using Galerkin's method the spatial dependence is eliminated and the equations are linearized about a suitable equilibrium position. The resulting system of equations is solved using multivariable Floquet-Liapunov theory, and the transition matrix at the end of the period is evaluated by two separate methods. Results illustrating the effects of forward flight and various important blade parameters on the stability boundaries are presented.

Friedman, P.↗

Assessment and Verification of SLS Block 1-B Exploration Upper Stage State and Stage Disposal Performance

One of the SLS Navigation System's key performance requirements is a constraint on the payload system's delta-v allocation to correct for insertion errors due to vehicle state uncertainty at payload separation. The SLS navigation team has developed a Delta-Delta-V analysis approach to assess the effect on trajectory correction maneuver (TCM) design needed to correct for navigation errors. This approach differs from traditional covariance analysis based methods and makes no assumptions with regard to the propagation of the state dynamics. This allows for consideration of non-linearity in the propagation of state uncertainties. The Delta-Delta-V analysis approach re-optimizes perturbed SLS mission trajectories by varying key mission states in accordance with an assumed state error. The state error is developed from detailed vehicle 6-DOF Monte Carlo analysis or generated using covariance analysis. These perturbed trajectories are compared to a nominal trajectory to determine necessary TCM design. To implement this analysis approach, a tool set was developed which combines the functionality of a 3-DOF trajectory optimization tool, Copernicus, and a detailed 6-DOF vehicle simulation tool, Marshall Aerospace Vehicle Representation in C (MAVERIC). In addition to delta-v allocation constraints on SLS navigation performance, SLS mission requirement dictate successful upper stage disposal. Due to engine and propellant constraints, the SLS Exploration Upper Stage (EUS) must dispose into heliocentric space by means of a lunar fly-by maneuver. As with payload delta-v allocation, upper stage disposal maneuvers must place the EUS on a trajectory that maximizes the probability of achieving a heliocentric orbit post Lunar fly-by considering all sources of vehicle state uncertainty prior to the maneuver. To ensure disposal, the SLS navigation team has developed an analysis approach to derive optimal disposal guidance targets. This approach maximizes the state error covariance prior to the maneuver to develop and re-optimize a nominal disposal maneuver (DM) target that, if achieved, would maximize the potential for successful upper stage disposal. For EUS disposal analysis, a set of two tools was developed. The first considers only the nominal pre-disposal maneuver state, vehicle constraints, and an a priori estimate of the state error covariance. In the analysis, the optimal nominal disposal target is determined. This is performed by re-formulating the trajectory optimization to consider constraints on the eigenvectors of the error ellipse applied to the nominal trajectory. A bisection search methodology is implemented in the tool to refine these dispersions resulting in the maximum dispersion feasible for successful disposal via lunar fly-by. Success is defined based on the probability that the vehicle will not impact the lunar surface and will achieve a characteristic energy (C3) relative to the Earth such that it is no longer in the Earth-Moon system. The second tool propagates post-disposal maneuver states to determine the success of disposal for provided trajectory achieved states. This is performed using the optimized nominal target within the 6-DOF vehicle simulation. This paper will discuss the application of the Delta-Delta-V analysis approach for performance evaluation as well as trajectory re-optimization so as to demonstrate the system's capability in meeting performance constraints. Additionally, further discussion of the implementation of assessing disposal analysis will be provided.

Patrick, Sean↗

Improved Understanding of the Modeled QBO Using MLS Observations and MERRA Reanalysis

The Quasi-Biennial Oscillation (QBO) dominates the variability of the tropical stratosphere on interannual time scales. The QBO has been shown to extend its influence into the chemical composition of this region through dynamical mechanisms. We have started our analysis using the realistic QBO internally generated by the Goddard Earth Observing System Version 5 (GEOS-5) general circulation model coupled to a comprehensive stratospheric and tropospheric chemical mechanism forced with observed sea surface temperatures over the past 33 years. We will show targeted comparisons with observations from NASAs Aura satellite Microwave Limb Sounder (MLS) and the Modern Era Retrospective-Analysis for Research and Applications (MERRA) reanalysis to provide insight into the simulation of the primary and secondary circulations associated with the QBO. Using frequency spectrum analysis and multiple linear regression we can illuminate the resulting circulations and deduce the strengths and weaknesses in their modeled representation. Inclusion of the QBO in our simulation improves the representation of the subtropical barriers and overall tropical variability. The QBO impact on tropical upwelling is important to quantify when calculating trends in sub-decadal scale datasets.

MERRA↗

Dynamic model verification of large structural systems

The objective of the present methodology is two-fold: (1) to process test data obtained from either modal survey tests, or slow sine-sweep tests, to extract a set of orthogonal modes best matching the test data while being commensurate with the dynamic model, and (2) to modify submatrices of the dynamic model mass and stiffness matrices to adjust the model to best fit the test data. The method has been implemented using a linear statistical sequential estimator for computation on a CDC computer. Demonstration problems involving Space Shuttle quarter-scale vibration test data and dynamic models have been run. This paper will discuss the general methodology and experience to date.

Lee, L. T.↗

Singular perturbation equations for flexible satellites

The dynamic model of a flexible satellite with n generalized structural position coordinates requires the solution of a set of N coupled nonlinear ordinary or partial differential equations. For single composite body satellites, N is equal to (n + 3). For dual-spin systems, N is equal to (n + 9). These equations usually involve time derivatives up to the second order. For large values of n, linearization of the system has so far been the only practicable way of solution. The present study shows a method of avoiding this linearization by reducing the N equations to three or nine nonlinear, coupled, first-order ordinary differential equations involving only the angular velocities of the composite bodies. The solutions for these angular velocities lead to linear equations in the n generalized structural position coordinates, which can then be solved by known methods.

Huang, T. C.↗

On the use of first order rotor dynamics in multiblade coordinates

This paper is directed to the question of how to represent most efficiently rotor/body coupling in a linear flight dynamics analysis. Rigid body pitch, roll and vertical motions are considered for the rotor/body coupling studies. Flapping stability limits, eigenvalues, transient responses to control step inputs, to step gusts and to random gusts are determined for a hypothetical hingeless compound helicopter operating up to .8 advance ratio. Data are obtained for the basic helicopter and for the craft with two simple control feedback systems. While complete periodic system modeling is necessary for determining flapping stability limits and vibrations, constant system modeling using first order dynamics in each of the multiblade rotor coordinates was found to be adequate for rotor-craft stability and response computations.

Hohenemser, K. H.↗

Compensator improvement for multivariable control systems

A theory and the associated numerical technique are developed for an iterative design improvement of the compensation for linear, time-invariant control systems with multiple inputs and multiple outputs. A strict constraint algorithm is used in obtaining a solution of the specified constraints of the control design. The result of the research effort is the multiple input, multiple output Compensator Improvement Program (CIP). The objective of the Compensator Improvement Program is to modify in an iterative manner the free parameters of the dynamic compensation matrix so that the system satisfies frequency domain specifications. In this exposition, the underlying principles of the multivariable CIP algorithm are presented and the practical utility of the program is illustrated with space vehicle related examples.

Mitchell, J. R.↗

Design of feedforward-cascade controllers for multivariable systems

The problems of disturbance decoupling and command matching in linear multivariable systems by means of feedforward and cascade controllers are formulated and solved in a transfer-function setting. It is shown that a necessary and sufficient condition for existence of the required controllers is that the plant zero polynomial is not identically zero and is stable. The required controllers are realized by parallel combination of a proportional-multiple-derivative term and a dynamic term, where the order of the dynamic term does not exceed the number of plant transmission zeros. The control scheme proposed in the paper is composed of a stabilizing feedback controller to enhance system stability, a feedforward controller to achieve disturbance decoupling and a cascade controller to ensure command matching. The three controllers have no effect on each other and can therefore be designed independently. A numerical example is given for illustration.

Seraji, H.↗

Optimal pre-scheduling of problem remappings

A large class of scientific computational problems can be characterized as a sequence of steps where a significant amount of computation occurs each step, but the work performed at each step is not necessarily identical. Two good examples of this type of computation are: (1) regridding methods which change the problem discretization during the course of the computation, and (2) methods for solving sparse triangular systems of linear equations. Recent work has investigated a means of mapping such computations onto parallel processors; the method defines a family of static mappings with differing degrees of importance placed on the conflicting goals of good load balance and low communication/synchronization overhead. The performance tradeoffs are controllable by adjusting the parameters of the mapping method. To achieve good performance it may be necessary to dynamically change these parameters at run-time, but such changes can impose additional costs. If the computation's behavior can be determined prior to its execution, it can be possible to construct an optimal parameter schedule using a low-order-polynomial-time dynamic programming algorithm. Since the latter can be expensive, the performance is studied of the effect of a linear-time scheduling heuristic on one of the model problems, and it is shown to be effective and nearly optimal.

Nicol, David M.↗

Second-order discrete Kalman filtering equations for control-structure interaction simulations

A general form for the first-order representation of the continuous, second-order linear structural dynamics equations is introduced in order to derive a corresponding form of first-order Kalman filtering equations (KFE). Time integration of the resulting first-order KFE is carried out via a set of linear multistep integration formulas. It is shown that a judicious combined selection of computational paths and the undetermined matrices introduced in the general form of the first-order linear structural systems leads to a class of second-order discrete KFE involving only symmetric, N x N solution matrix.

Park, K. C.↗

Role of shock dynamics in transonic flutter

A computational study of the influence of shock motion on flutter and divergence in transonic flow is presented. The numerical scheme models the entire fluid-structure system as a single continuum dynamics problem, by using a mixed Eulerian-Lagrangian formulation. No assumptions of small displacements are made, but the effect of viscosity is neglected. The results from this study indicate that the shock dynamics gives rise to limit cycles and highly nonlinear aeroelastic phenomena, such as weak divergence and flutter-divergence interactions. Although the shocks typically are destabilizing at the linear flutter boundary, they often have a strongly stabilizing effect for moderate-amplitude motions. The shocks are thus capable of quenching an emerging bending-torsion flutter motion and turning it into limit cycle flutter. The usefulness of classical flutter and divergence boundary diagrams is severely limited in transonic flow, because much of the global dynamic stability information is lost in such a presentation.

Bendiksen, Oddvar O.↗

Nonlinear system guidance in the presence of transmission zero dynamics

An iterative procedure is proposed for computing the commanded state trajectories and controls that guide a possibly multiaxis, time-varying, nonlinear system with transmission zero dynamics through a given arbitrary sequence of control points. The procedure is initialized by the system inverse with the transmission zero effects nulled out. Then the 'steady state' solution of the perturbation model with the transmission zero dynamics intact is computed and used to correct the initial zero-free solution. Both time domain and frequency domain methods are presented for computing the steady state solutions of the possibly nonminimum phase transmission zero dynamics. The procedure is illustrated by means of linear and nonlinear examples.

Meyer, G.↗

Disuse bone loss in hindquarter suspended rats: partial weightbearing, exercise and ibandronate treatment as countermeasures

The purpose of this study was to evaluate potential countermeasures for bone loss during long-term space missions in the hindquarter suspended rat, including partial weight bearing (surrogate for artificial gravity) episodic full weight bearing (2 hour/day full weight bearing) and treatment with the third generation bisphosphonate ibandronate (Roche). Graded mechanical loading was studied by housing the animals on a novel servo controlled force plate system which permitted the titration of mechanical force at varying frequency and amplitude and different levels of weight bearing. The force plate, which forms the cage floor, is a glass platform supported by an 18" diameter speaker cone filled with expanding polyurethane foam. An infrared optical sensor attached to the speaker cone yields a voltage linearly related to vertical displacement of the glass platform. The dynamic force on the paw was computed as a product of the apparent mass of the animal on the platform at rest and the acceleration of the platform determined from the second derivative of the optical sensor output. The mass of the animal on the platform was varied by adjusting tension on the tether suspending the animal. Mechanical impact loading was titrated with the force plate resonating at different frequencies, including 3 Hz and 16 Hz.

Non-NASA Center↗