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NASA NTRS1993

Hybrid state-space self-tuning control of uncertain linear systems

The paper presents a hybrid state-space self-tuner using a new dual-rate sampling scheme for digital adaptive control of continuous-time uncertain linear systems. A state-space-based recursive least-squares algorithm, together with a variable forgetting factor, is used for direct estimations of both the equivalent discrete-time uncertain linear system parameters and the associated discrete-time state of a continuous-time uncertain linear system from the sampled input and output data. An analogue optimal regional pole-placement design method is used for designing an optimal observer-based analogue controller. A suboptimal observer-based digital controller is then designed from the designed analogue controller using digital redesign technique. To enhance the robustness of parameter identification and state estimation algorithms, a dynamic bound for a class of uncertain bilinear parameters and a fast-rate digital controller are developed at each fast-sampling period. Also, to accommodate computation loads and computation delay for developing the advanced hybrid self-tuner, the designed analogue controller and observer gains are both updated at each slow-sampling period. This control technique has been successfully applied to benchmark control problems.

Shieh, L. S.↗

NASA NTRS1992

Linear dynamic analysis of the Space Station Freedom thermal/environmental control system

A methodology for dynamic analysis of the Space Station Freedom thermal/environmental control system is described which uses linear system analysis techniques to determine the ability of the system to accommodate thermal load transients. A nonlinear integrated model of the system as it exists at Stage 6, Man Tended Capability (MTC), is described which encompasses the cabin air cooling system, avionics air cooling system, internal and external thermal control systems. The nonlinear model is linearized at an assumed design operating point, and the linear model is evaluated by comparison with the nonlinear model. Transfer functions are derived to determine the response of the heat rejection system to time-varying thermal loads applied at various points in the heat acquisition system. The frequency response calculated from the transfer functions is used to determine allowable operating envelopes of thermal load magnitude and frequency for each point of application of thermal load. The dynamic operating envelopes provide a quantitative indication of the degree and duration of peak loads which the thermal/environmental system is able to transport and reject.

Tandler, John↗

NASA NTRS1993

Linear, multivariable robust control with a mu perspective

The structured singular value is a linear algebra tool developed to study a particular class of matrix perturbation problems arising in robust feedback control of multivariable systems. These perturbations are called linear fractional, and are a natural way to model many types of uncertainty in linear systems, including state-space parameter uncertainty, multiplicative and additive unmodeled dynamics uncertainty, and coprime factor and gap metric uncertainty. The structured singular value theory provides a natural extension of classical SISO robustness measures and concepts to MIMO systems. The structured singular value analysis, coupled with approximate synthesis methods, make it possible to study the tradeoff between performance and uncertainty that occurs in all feedback systems. In MIMO systems, the complexity of the spatial interactions in the loop gains make it difficult to heuristically quantify the tradeoffs that must occur. This paper examines the role played by the structured singular value (and its computable bounds) in answering these questions, as well as its role in the general robust, multivariable control analysis and design problem.

Packard, Andy↗

NASA NTRS1989

Linear quadratic tracking problems in Hilbert space - Application to optimal active noise suppression

A unified treatment of the linear quadratic tracking (LQT) problem, in which a control system's dynamics are modeled by a linear evolution equation with a nonhomogeneous component that is linearly dependent on the control function u, is presented; the treatment proceeds from the theoretical formulation to a numerical approximation framework. Attention is given to two categories of LQT problems in an infinite time interval: the finite energy and the finite average energy. The behavior of the optimal solution for finite time-interval problems as the length of the interval tends to infinity is discussed. Also presented are the formulations and properties of LQT problems in a finite time interval.

Banks, H. T.↗

NASA NTRS1955

From linear mechanics to nonlinear mechanics

Consideration is given to the techniques used in telecommunication where a nonlinear system (the modulator) results in a linear transposition of a signal. It is then shown that a similar method permits linearization of electromechanical devices or nonlinear mechanical devices. A sweep function plays the same role as the carrier wave in radio-electricity. The linearizations of certain nonlinear functionals are presented.

RESEARCH TECHNIQUE, MATHEMATICS↗

NASA NTRS1993

Three-stage linear, split-Stirling cryocooler for 1 to 2K magnetic cold stage

A long-life, linear, high efficiency 8K split Stirling cycle cryocooler was designed, built, and tested. The refrigerator is designed for cooling a 50 mW, 1.5K magnetic cold stage. Dual opposed piston compressors are driven by moving-coil linear motors. The three stage expander, although not completed, is also driven by a linear motor and is designed to produce 1 SW at 60K, 4W at 16K, and 1.2W at 8K. The cold regenerator employs a parallel gap construction for high efficiency. The key technology areas addressed include warm and cold flexible suspension bearings and a new cold regenerator geometry for high efficiency at 8K.

Longsworth, R. C.↗

NASA NTRS1993

Linear encoding device

A Linear Motion Encoding device for measuring the linear motion of a moving object is disclosed in which a light source is mounted on the moving object and a position sensitive detector such as an array photodetector is mounted on a nearby stationary object. The light source emits a light beam directed towards the array photodetector such that a light spot is created on the array. An analog-to-digital converter, connected to the array photodetector is used for reading the position of the spot on the array photodetector. A microprocessor and memory is connected to the analog-to-digital converter to hold and manipulate data provided by the analog-to-digital converter on the position of the spot and to compute the linear displacement of the moving object based upon the data from the analog-to-digital converter.

Leviton, Douglas B.↗

NASA NTRS1992

Ejecta patterns of Meteor Crater, Arizona derived from the linear un-mixing of TIMS data and laboratory thermal emission spectra

Accurate interpretation of thermal infrared data depends upon the understanding and removal of complicating effects. These effects may include physical mixing of various mineralogies and particle sizes, atmospheric absorption and emission, surficial coatings, geometry effects, and differential surface temperatures. The focus is the examination of the linear spectral mixing of individual mineral or endmember spectra. Linear addition of spectra, for particles larger than the wavelength, allows for a straight-forward method of deconvolving the observed spectra, predicting a volume percent of each endmember. The 'forward analysis' of linear mixing (comparing the spectra of physical mixtures to numerical mixtures) has received much attention. The reverse approach of un-mixing thermal emission spectra was examined with remotely sensed data, but no laboratory verification exists. Understanding of the effects of spectral mixing on high resolution laboratory spectra allows for the extrapolation to lower resolution, and often more complicated, remotely gathered data. Thermal Infrared Multispectral Scanner (TIMS) data for Meteor Crater, Arizona were acquired in Sep. 1987. The spectral un-mixing of these data gives a unique test of the laboratory results. Meteor Crater (1.2 km in diameter and 180 m deep) is located in north-central Arizona, west of Canyon Diablo. The arid environment, paucity of vegetation, and low relief make the region ideal for remote data acquisition. Within the horizontal sedimentary sequence that forms the upper Colorado Plateau, the oldest unit sampled by the impact crater was the Permian Coconino Sandstone. A thin bed of the Toroweap Formation, also of Permian age, conformably overlays the Coconino. Above the Toroweap lies the Permian Kiabab Limestone which, in turn, is covered by a thin veneer of the Moenkopi Formation. The Moenkopi is Triassic in age and has two distinct sub-units in the vicinity of the crater. The lower Wupatki member is a fine-grained sandstone, while the upper Moqui member is a fissile siltstone. Ejecta from these units are preserved as inverted stratigraphy up to 2 crater radii from the rim. The mineralogical contrast between the units, relative lack of post-emplacement erosion and ejecta mixing provide a unique site to apply the un-mixing model. Selection of the aforementioned units as endmembers reveals distinct patterns in the ejecta of the crater.

Ramsey, Michael S.↗

NASA NTRS1994

Development of long-life, low-noise linear bearings for atmospheric interferometry

This paper describes the development of dry-lubricated linear bearings for use on the Michelson interferometer for passive atmospheric sounding (MIPAS). Two candidate bearing systems were developed and tested. In the first, use was made of linear roller (needle) bearings equipped with a pulley-and-cable arrangement to prevent cage drift and to minimize roller slip. The second design was of a roller-guided bearing system in which guidance was provided by all bearings rolling along guide rods. The paper focuses on the development of these linear bearings systems and describes the approach taken in terms of bearing design, lubrication methods, screening programs, and thermal-vacuum testing. Development difficulties are highlighted and the solutions ultimately adopted are described.

Roberts, E. W.↗

NASA NTRS1992

Linear stability theory and three-dimensional boundary layer transition

The viewgraphs and discussion of linear stability theory and three dimensional boundary layer transition are provided. The ability to predict, using analytical tools, the location of boundary layer transition over aircraft-type configurations is of great importance to designers interested in laminar flow control (LFC). The e(sup N) method has proven to be fairly effective in predicting, in a consistent manner, the location of the onset of transition for simple geometries in low disturbance environments. This method provides a correlation between the most amplified single normal mode and the experimental location of the onset of transition. Studies indicate that values of N between 8 and 10 correlate well with the onset of transition. For most previous calculations, the mean flows were restricted to two-dimensional or axisymmetric cases, or have employed simple three-dimensional mean flows (e.g., rotating disk, infinite swept wing, or tapered swept wing with straight isobars). Unfortunately, for flows over general wing configurations, and for nearly all flows over fuselage-type bodies at incidence, the analysis of fully three-dimensional flow fields is required. Results obtained for the linear stability of fully three-dimensional boundary layers formed over both wing and fuselage-type geometries, and for both high and low speed flows are discussed. When possible, transition estimates form the e(sup N) method are compared to experimentally determined locations. The stability calculations are made using a modified version of the linear stability code COSAL. Mean flows were computed using both Navier Stokes and boundary-layer codes.

Spall, Robert E.↗

NASA NTRS1994

Random vibration of nonlinear beams by the new stochastic linearization technique

In this paper, the beam under general time dependent stationary random excitation is investigated, when exact solution is unavailable. Numerical simulations are carried out to compare its results with those yielded by the conventional linearization techniques. It is found that the modified version of the stochastic linearization technique yields considerably more accurate results for the mean square displacement of the beam than the conventional equivalent linearization technique, especially in the case of large nonlinearity.

Fang, J.↗

NASA NTRS1994

On the removal of boundary errors caused by Runge-Kutta integration of non-linear partial differential equations

It has been previously shown that the temporal integration of hyperbolic partial differential equations (PDE's) may, because of boundary conditions, lead to deterioration of accuracy of the solution. A procedure for removal of this error in the linear case has been established previously. In the present paper we consider hyperbolic (PDE's) (linear and non-linear) whose boundary treatment is done via the SAT-procedure. A methodology is present for recovery of the full order of accuracy, and has been applied to the case of a 4th order explicit finite difference scheme.

Abarbanel, Saul↗

NASA NTRS1992

Quasi-linear regime of gravitational instability as a clue to understanding the large-scale structure in the Universe

In the late seventies, an image of the large-scale structure in the Universe began to emerge as a result of the accumulation of the galaxy redshifts. Most of the galaxies are found to concentrate in large filaments and perhaps sheets leaving most of the volume empty. Similar structures were predicted theoretically in the frame of the adiabatic theory of galaxy formation (Zeldovich) and later in the hot dark matter cosmology. However, both scenarios have been ruled out by the observations. With these scenarios the dynamical part of the scenario was also erroneously rejected by many as well. In this talk, I derive the Zeldovich approximation from the exact dynamic equations and show that it is always better than the standard linear approximation. The advantage of the Zeldovich approximation is the greatest in the quasi-linear regime when delta(sub rms) is less than 1 (delta identical to delta(rho)/rho), but the displacement of the matter is essential. The range of scales in the quasi-linear regime depends upon the slope of the initial spectrum and increases with decreasing n, where n is the exponent, if the initial spectrum is approximated by a simple power law P(k) varies as k(exp n).

Shandarin, Sergei F.↗

NASA NTRS1995

Allan deviation computations of a linear frequency synthesizer system using frequency domain techniques

Allan Deviation computations of linear frequency synthesizer systems have been reported previously using real-time simulations. Even though it takes less time compared with the actual measurement, it is still very time consuming to compute the Allan Deviation for long sample times with the desired confidence level. Also noises, such as flicker phase noise and flicker frequency noise, can not be simulated precisely. The use of frequency domain techniques can overcome these drawbacks. In this paper the system error model of a fictitious linear frequency synthesizer is developed and its performance using a Cesium (Cs) atomic frequency standard (AFS) as a reference is evaluated using frequency domain techniques. For a linear timing system, the power spectral density at the system output can be computed with known system transfer functions and known power spectral densities from the input noise sources. The resulting power spectral density can then be used to compute the Allan Variance at the system output. Sensitivities of the Allan Variance at the system output to each of its independent input noises are obtained, and they are valuable for design trade-off and trouble-shooting.

Wu, Andy↗

NASA NTRS1995

Linear and nonlinear properties of the ULF waves driven by ring-beam distribution functions

The problem of the exitation of obliquely propagating magnetosonic waves which can steepen up (also known as shocklets) is considered. Shocklets have been observed upstream of the Earth's bow shock and at comets Giacobini-Zinner and Grigg-Skjellerup. Linear theory as well as two-dimensional (2-D) hybrid (fluid electrons, particle ions) simulations are used to determine the properties of waves generated by ring-beam velocity distributions in great detail. The effects of both proton and oxygen ring-beams are considered. The study of instabilities excited by a proton ring-beam is relevant to the region upstream of the Earth's bow shock, whereas the oxygen ring-beam corresponds to cometary ions picked up by the solar wind. Linear theory has shown that for a ring-beam, four instabilities are found, one on the nonresonant mode, one on the Alfven mode, and two along the magnetosonic/whistler branch. The relative growth rate of these instabilities is a sensitive function of parameters. Although one of the magnetosonic instabilities has maximum growth along the magnetic field, the other has maximum growth in oblique directions. We have studied the competition of these instabilities in the nonlinear regime using 2-D simulations. As in the linear limit, the nonlinear results are a function of beam density and distribution function. By performing the simulations as both initial value and driven systems, we have found that the outcome of the simulations can vary, suggesting that the latter type simulations is needed to address the observations. A general conclusion of the simulation results is that field-aligned beams do not result in the formation of shocklets, whereas ring-beam distributions can.

Killen, K.↗

NASA NTRS1995

Linear Proof-Mass Actuator

Linear proof-mass actuator (LPMA) is friction-driven linear mass actuator capable of applying controlled force to structure in outer space to damp out oscillations. Capable of high accelerations and provides smooth, bidirectional travel of mass. Design eliminates gears and belts. LPMA strong enough to be used terrestrially where linear actuators needed to excite or damp out oscillations. High flexibility designed into LPMA by varying size of motors, mass, and length of stroke, and by modifying control software.

Holloway, Sidney E., III↗

NASA NTRS1995

Development work for a superconducting linear collider

For future linear e(+)e(-) colliders in the TeV range several alternatives are under discussion. The TESLA approach is based on the advantages of superconductivity. High Q values of the accelerator structures give high efficiency for converting RF power into beam power. A low resonance frequency for the RF structures can be chosen to obtain a large number of electrons (positrons) per bunch. For a given luminosity the beam dimensions can be chosen conservatively which leads to relaxed beam emittance and tolerances at the final focus. Each individual superconducting accelerator component (resonator cavity) of this linear collider has to deliver an energy gain of 25 MeV/m to the beam. Today s.c. resonators are in use at CEBAF/USA, at DESY/Germany, Darmstadt/Germany KEK/Japan and CERN/Geneva. They show acceleration gradients between 5 MV/m and 10 MV/m. Encouraging experiments at CEA Saclay and Cornell University showed acceleration gradients of 20 MV/m and 25 MV/m in single and multicell structures. In an activity centered at DESY in Hamburg/Germany the TESLA collaboration is constructing a 500 MeV superconducting accelerator test facility (TTF) to demonstrate that a linear collider based on this technique can be built in a cost effective manner and that the necessary acceleration gradients of more than 15 MeV/m can be reached reproducibly. The test facility built at DESY covers an area of 3.000 m2 and is divided into 3 major activity areas: (1) The testlinac, where the performance ofthe modular components with an electron beam passing the 40 m long acceleration section can be demonstrated. (2) The test area, where all individual resonators are tested before installation into a module. (3) The preparation and assembly area, where assembly of cavities and modules take place. We report here on the design work to reach a reduction of costs compared to actual existing superconducting accelerator structures and on the facility set up to reach high acceleration gradients in a reproducible way.

Matheisen, Axel↗

NASA NTRS1995

On absorbing boundary conditions for linearized Euler equations by a perfectly matched layer

Recently, Berenger introduced a Perfectly Matched Layer (PML) technique for absorbing electromagnetic waves. In the present paper, a perfectly matched layer is proposed for absorbing out-going two-dimensional waves in a uniform mean flow, generated by linearized Euler equations. It is well known that the linearized Euler equations support acoustic waves, which travel with the speed of sound relative to the mean flow, and vorticity and entropy waves, which travel with the mean flow. The PML equations to be used at a region adjacent to the artificial boundary for absorbing these linear waves are defined. Plane waves solutions to the PML equations are developed and wave propagation and absorption properties are given. It is shown that the theoretical reflection coefficients at an interface between the Euler and PML domains are zero, independent of the angle of incidence and frequency of the waves. As such, the present study points out a possible alternative approach for absorbing out-going waves of the Euler equations with little or no reflection in computation. Numerical examples that demonstrate the validity of the proposed PML equations are also presented.

Hu, Fang Q.↗