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NASA NTRS1991

Linear stability of free planetary waves in the presence of radiative-photochemical feedbacks

The diabatic effects of Newtonian cooling and ozone-dynamics interaction on the linear stability of free planetary waves in the atmosphere have been studied using a simple beta-plane model. The model couples radiative transfer, ozone advection, and ozone photochemistry with the quasi-geostrophic dynamical circulation. An analytical expression is derived which demonstrates the following: (1) the influence of meridional ozone advection on wave growth or decay depends on the wave and basic state vertical structures; and (2) photochemically accelerated cooling, which predominates in the upper stratosphere, augments the Newtonian cooling rate and is stabilizing. Attention is also given to the 1D linear stability problem which is numerically solved for a Charney basic state and for zonal mean basic states. It is shown that ozone heating generated by ozone-dynamics interaction in the stratosphere can reduce (enhance) the damping rates due to Newtonian cooling by as much as 50 percent for planetary waves of large vertical scale and maximum amplitude in the stratosphere.

Nathan, Terrence R.↗

NASA NTRS2025

Mission-Maps For Outbound Cislunar Transfer Trajectories

This study quantifies the robustness and sensitivity of an outbound cislunar trajectory for a lunar lander in the form of mission-maps, or topological maps that allows either a computer program or mission designer to intuitively optimize the placement of critical outbound correction burns from the derived sensitivity data. The non-linear multi-body dynamics are applied to generate an outbound cislunar reference profile used by a linear covariance analysis (LinCov) tool to compute the expected Δv and trajectory dispersions due to the initial state uncertainty, sensor errors, maneuver execution errors, and disturbance accelerations along the outbound cislunar profile. The rapid performance analysis capabilities of LinCov are complimented with parallel processing techniques to evaluate hundreds and thousands of different translational burn locations, placements, and targeting constraints to identify the combination that minimizes the total Δv usage (nominal plus 3σ Δv) and trajectory dispersions at lunar orbit insertion. This study utilizes a generalized reference targeting algorithm to quickly assess the integrated closed-loop GN&C system performance due to different targeting configurations and constraints. The resulting mission maps provide an intuitive insight to ascertain each trajectory correction maneuver’s (TCM) sensitivity to different burn times along an outbound cislunar trajectory and quickly identify desirable engineering tradeoffs when performing analysis on the number and placement of these burns that nominally zero. Multiple mission maps are generated for a variety of different performance parameters that allow engineers to visually identify optimal solutions for trajectory correction maneuver placements, the number of correction burns, and the targeting constraints for each burn.

GN&C↗

NASA NTRS2007

Development of a Linear Stirling System Model with Varying Heat Inputs

The linear model of the Stirling system developed by NASA Glenn Research Center (GRC) has been extended to include a user-specified heat input. Previously developed linear models were limited to the Stirling convertor and electrical load. They represented the thermodynamic cycle with pressure factors that remained constant. The numerical values of the pressure factors were generated by linearizing GRC's nonlinear System Dynamic Model (SDM) of the convertor at a chosen operating point. The pressure factors were fixed for that operating point, thus, the model lost accuracy if a transition to a different operating point were simulated. Although the previous linear model was used in developing controllers that manipulated current, voltage, and piston position, it could not be used in the development of control algorithms that regulated hot-end temperature. This basic model was extended to include the thermal dynamics associated with a hot-end temperature that varies over time in response to external changes as well as to changes in the Stirling cycle. The linear model described herein includes not only dynamics of the piston, displacer, gas, and electrical circuit, but also the transient effects of the heater head thermal inertia. The linear version algebraically couples two separate linear dynamic models, one model of the Stirling convertor and one model of the thermal system, through the pressure factors. The thermal system model includes heat flow of heat transfer fluid, insulation loss, and temperature drops from the heat source to the Stirling convertor expansion space. The linear model was compared to a nonlinear model, and performance was very similar. The resulting linear model can be implemented in a variety of computing environments, and is suitable for analysis with classical and state space controls analysis techniques.

Regan, Timothy F.↗

NASA NTRS1989

A nearly-linear computational-cost scheme for the forward dynamics of an N-body pendulum

The dynamic equations of motion of an n-body pendulum with spherical joints are derived to be a mixed system of differential and algebraic equations (DAE's). The DAE's are kept in implicit form to save arithmetic and preserve the sparsity of the system and are solved by the robust implicit integration method. At each solution point, the predicted solution is corrected to its exact solution within given tolerance using Newton's iterative method. For each iteration, a linear system of the form J delta X = E has to be solved. The computational cost for solving this linear system directly by LU factorization is O(n exp 3), and it can be reduced significantly by exploring the structure of J. It is shown that by recognizing the recursive patterns and exploiting the sparsity of the system the multiplicative and additive computational costs for solving J delta X = E are O(n) and O(n exp 2), respectively. The formulation and solution method for an n-body pendulum is presented. The computational cost is shown to be nearly linearly proportional to the number of bodies.

Chou, Jack C. K.↗

NASA NTRS1986

Numerical approximation for the infinite-dimensional discrete-time optimal linear-quadratic regulator problem

An abstract approximation framework is developed for the finite and infinite time horizon discrete-time linear-quadratic regulator problem for systems whose state dynamics are described by a linear semigroup of operators on an infinite dimensional Hilbert space. The schemes included the framework yield finite dimensional approximations to the linear state feedback gains which determine the optimal control law. Convergence arguments are given. Examples involving hereditary and parabolic systems and the vibration of a flexible beam are considered. Spline-based finite element schemes for these classes of problems, together with numerical results, are presented and discussed.

Gibson, J. S.↗

NASA NTRS1988

Numerical approximation for the infinite-dimensional discrete-time optimal linear-quadratic regulator problem

Gibson, J. S.↗

NASA NTRS2016

Dynamic Range Enhancement of High-Speed Electrical Signal Data via Non-Linear Compression

Systems and methods for high-speed compression of dynamic electrical signal waveforms to extend the measuring capabilities of conventional measuring devices such as oscilloscopes and high-speed data acquisition systems are discussed. Transfer function components and algorithmic transfer functions can be used to accurately measure signals that are within the frequency bandwidth but beyond the voltage range and voltage resolution capabilities of the measuring device.

Laun, Matthew C.↗

NASA NTRS1985

Dynamic Identification for Control of Large Space Structures

This is a compilation of reports by the one author on one subject. It consists of the following five journal articles: (1) A Parametric Study of the Ibrahim Time Domain Modal Identification Algorithm; (2) Large Modal Survey Testing Using the Ibrahim Time Domain Identification Technique; (3) Computation of Normal Modes from Identified Complex Modes; (4) Dynamic Modeling of Structural from Measured Complex Modes; and (5) Time Domain Quasi-Linear Identification of Nonlinear Dynamic Systems.

Ibrahim, S. R.↗

NASA NTRS2002

Experimental Feedback Control of Flow Induced Cavity Tones

An experimental study of the application of discrete-time, linear quadratic control design methods to the cavity tone problem is described. State space models of the dynamics from a synthetic jet actuator at the leading edge of the cavity to two pressure sensors in the cavity were computed from experimental data. Variations in model order, control order, control bandwidth, and properties of a Kalman state estimator were studied. Feedback control reduced the levels of multiple cavity tones at Mach 0.275, 0.35, and 0.45. Closed loop performance was often limited by excitation of sidebands of cavity tones, and creation of new tones in the spectrum. State space models were useful for explaining some of these limitations, but were not able to account for non-linear dynamics, such as interactions between tones at different frequencies.

Cabell, Randolph H.↗

NASA NTRS1975

Testing the linearity of response of gated photomultipliers in wide dynamic range laser radar systems

Laser radar data acquisition systems have been utilized in conjunction with a light emitting diode to evaluate photomultipliers for laser radar use. Light pulses with an exponential decay rate of approximately one decade per sixty microseconds, as well as other pulse shapes, were used to drive the tubes. Properties studied in the analog mode include nonlinearity at high output currents, transient behavior upon gating, gate holdoff, dynamic range limitations because of light-induced noise, and the effect of dynode gating on tubes without a focus grid. Some of these properties were also studied in the photon counting mode, along with single photoelectron pulse shape and afterpulsing. A brief description of the laser radar technique of atmospheric measurements is included.

Hunt, W. H.↗

NASA NTRS1976

Linear and nonlinear analysis of orbital telescope/space shuttle dynamics and control

Work completed on the design and study of an annular suspension and pointing (ASP) system for the space shuttle was presented. This system makes use of a magnetically suspended vernier pointing assembly. The following objectives were pursued in this study: (1) development of a detailed mathematical model of the Space Shuttle/ASP system, (2) design of control laws in order to obtain the desired pointing performance, and (3) prediction of the statistical pointing accuracies in the presence of stochastic disturbances such as crew-motion, and sensor and actuator noise. The first two of these objectives are documented in this report.

Roberts, A. S., Jr.↗

NASA NTRS1988

Dynamical criterion for a marginally unstable, quasi-linear behavior in a two-layer model

A two-layer quasi-geostrophic flow forced by meridional variations in heating can be in regimes ranging from radiative equilibrium to forced geostrophic turbulence. Between these extremes is a regime where the time-mean (zonal) flow is marginally unstable. Using scaling arguments, it is concluded that such a marginally unstable state should occur when a certain parameter, measuring the strength of wave-wave interactions relative to the beta effect and advection by the thermal wind, is small. Numerical simulations support this proposal. A transition from the marginally unstable regime to a more nonlinear regime is then examined through numerical simulations with different radiative forcings. It is found that transition is not caused by secondary instability of waves in the marginally unstable regime. Instead, the time-mean flow can support a number of marginally unstable normal modes. These normal modes interact with each other, and if they are of sufficient amplitude, the flow enters a more nonlinear regime.

Ebisuzaki, W.↗

NASA NTRS1990

Influence of linear profile modification and loading conditions on the dynamic tooth load and stress of high contact ratio gears

A computer simulation for the dynamic response of high-contact-ratio spur gear transmissions is presented. High contact ratio gears have the potential to produce lower dynamic tooth loads and minimum root stress but they can be sensitive to tooth profile errors. The analysis presented examines various profile modifications under realistic loading conditions. The effect of these modifications on the dynamic load (force) between mating gear teeth and the dynamic root stress is presented. Since the contact stress is dependent on the dynamic load, minimizing dynamic loads will also minimize contact stresses. It is shown that the combination of profile modification and the applied load (torque) carried by a gear system has a significant influence on gear dynamics. The ideal modification at one value of applied load will not be the best solution for a different load. High-contact-ratio gears were found to require less modification than standard low-contact-ratio gears. High-contact-ratio gears are more adversely affected by excess modification than by under modification. In addition, the optimal profile modification required to minimize the dynamic load (hence the contact stress) on a gear tooth differs from the optimal modification required to minimize the dynamic root (bending) stress. Computer simulation can help find the design tradeoffs to determine the best profile modification to satisfy the conflicting constraints of minimizing both the load and root stress in gears which must operate over a range of applied loads.

Lee, Chinwai↗

NASA NTRSDate not supplied

Electromagnetic Modeling of Wind tunnel Magnetic Suspension and Balance Systems

An analytical framework for the open-loop behavior of a permanent magnet element levitated within an applied magnetic field are shown, in the context of application to wind tunnel Magnetic Suspension and Balance Systems (MSBS). Various modes of motion are identified, which correlate with observed behavior of the NASA/ODU 6-inch MSBS. This system is being developed as a technology demonstrator for dynamic stability testing of atmospheric entry capsules, with possible application to a supersonic wind tunnel. The analytic equations are populated with field information from experimental measurements and a finite element model. Finally, a system simulation can provide alternative estimates of system dynamic behavior via model linearization, with preliminary comparisons presented. Taken together, the analytical framework, experimental measurement, finite element analysis, and dynamic simulation provide a complete understanding of the characteristics and behavior of the MSBS.

magnetic suspension↗

NASA NTRS1966

Research in and application of modern automatic control theory to nuclear rocket dynamics and control, volume I Semiannual status report

Linear optimal feedback control theory for nuclear rocket dynamics and control problems

LIAPUNOV FUNCTION↗

NASA NTRS1991

A modal aeroelastic analysis scheme for turbomachinery blading

An aeroelastic analysis is developed which has general application to all types of axial-flow turbomachinery blades. The approach is based on linear modal analysis, where the blade's dynamic response is represented as a linear combination of contributions from each of its in-vacuum free vibrational modes. A compressible linearized unsteady potential theory is used to model the flow over the oscillating blades. The two-dimensional unsteady flow is evaluated along several stacked axisymmetric strips along the span of the airfoil. The unsteady pressures at the blade surface are integrated to result in the generalized force acting on the blade due to simple harmonic motions. The unsteady aerodynamic forces are coupled to the blade normal modes in the frequency domain using modal analysis. An iterative eigenvalue problem is solved to determine the stability of the blade when the unsteady aerodynamic forces are included in the analysis. The approach is demonstrated by applying it to a high-energy subsonic turbine blade from a rocket engine turbopump power turbine. The results indicate that this turbine could undergo flutter in an edgewise mode of vibration.

Smith, Todd E.↗

NASA NTRS2005

Experimental Feedback Control of Flow Induced Cavity Tones

Discrete-time, linear quadratic methods were used to design feedback controllers for reducing tones generated by flow over a cavity. The dynamics of a synthetic jet actuator mounted at the leading edge of the cavity as observed by two microphones in the cavity were modeled over a broad frequency range using state space models computed from experimental data. Variations in closed loop performance as a function of model order, control order, control bandwidth, and state estimator design were studied using a cavity in the Probe Calibration Tunnel at NASA Langley. The controller successfully reduced the levels of multiple cavity tones at the tested flow speeds of Mach 0.275, 0.35, and 0.45. In some cases, the closed loop results were limited by excitation of sidebands of the cavity tones, or the creation of new tones at frequencies away from the cavity tones. Nonetheless, the results validate the combination of optimal control and experimentally-generated state space models, and suggest this approach may be useful for other flow control problems. The models were not able to account for non-linear dynamics, such as interactions between tones at different frequencies.

Cabell, Randolph H.↗

NASA NTRS1991

A game theoretic approach to a finite-time disturbance attenuation problem

A disturbance attenuation problem over a finite-time interval is considered by a game theoretic approach where the control, restricted to a function of the measurement history, plays against adversaries composed of the process and measurement disturbances, and the initial state. A zero-sum game, formulated as a quadratic cost criterion subject to linear time-varying dynamics and measurements, is solved by a calculus of variation technique. By first maximizing the quadratic cost criterion with respect to the process disturbance and initial state, a full information game between the control and the measurement residual subject to the estimator dynamics results. The resulting solution produces an n-dimensional compensator which expresses the controller as a linear combination of the measurement history. A disturbance attenuation problem is solved based on the results of the game problem. For time-invariant systems it is shown that under certain conditions the time-varying controller becomes time-invariant on the infinite-time interval. The resulting controller satisfies an H(infinity) norm bound.

Rhee, Ihnseok↗