Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “linear dynamical systems”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 883 records · Page 49

Nonlinear and distributed parameter models of the mini-mast truss

Large spacecraft such as Space Station Freedom employ large trusses in their construction. The structural dynamics of such trusses often exhibit nonlinear behavior and little damping which can impact significantly the performance of control systems. The Mini-MAST truss was constructed to research such structural dynamics and control systems. The Mini-MAST truss is an object of study for the guest investigator program as part of NASA's controls-structures interaction program. The Mini-MAST truss is deployable and about 65 ft long. Although the bending characteristics of the Mini-MAST truss are essentially linear, the angular deflection under torsional loading has exhibited significant hysteresis and nonlinear stiffness. It is the purpose to develop nonlinear and distributed parameter models of the truss and to compare the model dynamics with actual measurements. Distributed parameter models have the advantage of requiring fewer model parameters. A tangent function is used to describe the nonlinear stiffness in torsion, partly because of the convenience of its easily expressed inverse. Hysteretic slip elements are introduced and extended to a continuum to account for the observed hysteresis in torsion. The contribution of slipping to the structural damping is analyzed and found to be strongly dependent on the applied loads. Because of the many factors which affect the damping and stiffness in a truss, it is risky to assume linearity.

Taylor, Lawrence W., Jr.↗

Megawatt Class Nuclear Space Power Systems (MCNSPS) conceptual design and evaluation report. Volume 1: Objectives, summary results and introduction

The objective was to determine which reactor, conversion, and radiator technologies would best fulfill future Megawatt Class Nuclear Space Power System Requirements. Specifically, the requirement was 10 megawatts for 5 years of full power operation and 10 years systems life on orbit. A variety of liquid metal and gas cooled reactors, static and dynamic conversion systems, and passive and dynamic radiators were considered. Four concepts were selected for more detailed study. The concepts are: a gas cooled reactor with closed cycle Brayton turbine-alternator conversion with heat pipe and pumped tube-fin heat rejection; a lithium cooled reactor with a free piston Stirling engine-linear alternator and a pumped tube-fin radiator; a lithium cooled reactor with potassium Rankine turbine-alternator and heat pipe radiator; and a lithium cooled incore thermionic static conversion reactor with a heat pipe radiator. The systems recommended for further development to meet a 10 megawatt long life requirement are the lithium cooled reactor with the K-Rankine conversion and heat pipe radiator, and the lithium cooled incore thermionic reactor with heat pipe radiator.

Wetch, J. R.↗

Error estimates for approximate dynamic systems

Two approaches are investigated for obtaining estimates on the error between approximate and exact solutions of dynamic systems. The first method is primarily useful if the system is nonlinear and of low dimension. The second requires construction of a system of v-functions but is useful for higher dimensional systems, either linear or nonlinear.

Gunderson, R. W.↗

The dynamics of spin stabilized spacecraft with movable appendages, part 2

The dynamics and stability of a spin stabilized spacecraft with a hinged appendage system are treated analytically and numerically. The hinged system consists of a central hub with masses attached to (assumed) massless booms of fixed length whose orientation relative to the main part can change. The general three dimensional deployment dynamics of such a hinged system is considered without any restriction on the location of the hinge points. The equations of motion for the hinged system, with viscous damping at both hinge points, are linearized about the nominal equilibrium position where the booms are orthogonal to the nominal spin axis for the case of two dimensional and three dimensional motion. Analytic stability criteria are obtained from the necessary condition on the sign of all the coefficients in the system characteristic equation.

Bainum, P. M.↗

Simplified simulation models for control studies of turbojet engines

The essential dynamical characteristics of a simple single spool turbojet engine were determined through simulation of low order system models on an analog computer. An accurate model was studied and system complexity was reduced through various linearizations and approximations. A derivation of a seventh order simplified simulation model is presented with a derivation of an even simpler third order model, and simulation results from each. The control problem studied is one of getting from zero fuel flow equilibrium to a high thrust equilibrium while taking into account surge margin and turbine inlet temperature constraints.

Brennan, T. C.↗

Multivariable control of VTOL aircraft for shipboard landing

The problem of the automatic landing of VTOL aircraft on small ships is considered. Linear quadratic optimal control theory is used to design a VTOL ship motion tracking controller. Optimal root-loci and step responses are obtained to study the dynamics of the closed-loop system. Standard deviations of the ship motion tracking errors, and of the VTOL control amplitudes are computed, illustrating the tradeoff between accurate tracking, and limited control authority. Multivariable robustness margins are also obtained. The tracking of the vertical motion presents the difficulty of requiring large variations of the VTOL total thrust, a control which is limited both in amplitude and in bandwidth. Lateral controls are less restricted, but the motions are strongly coupled, with some adverse couplings in the ship motions, and in the aircraft dynamics. The advantage of the LQ control theory is demonstrated however, by its ability to account for these couplings in a robust manner, and, when possible, to use them to limit the control amplitudes.

Bodson, M.↗

Issues in modeling and controlling the SCOLE configuration

The parametric study of the in-plane Spacecraft Control Laboratory Experiment (SCOLE) system, the Floquet Stability Analysis, and three dimensional formulations of the SCOLE system dynamics are examined. Control issues are discussed, such as: control of large structures with delayed input in continuous time; control with delayed input in discrete time; control law design for SCOLE using Linear Quadratic Gaussian (LQC)/TRR technique; and optimal torque control for SCOLE slewing maneuvers.

Bainum, Peter M.↗

Guidance and Control strategies for aerospace vehicles

A neighboring optimal guidance scheme was devised for a nonlinear dynamic system with stochastic inputs and perfect measurements as applicable to fuel optimal control of an aeroassisted orbital transfer vehicle. For the deterministic nonlinear dynamic system describing the atmospheric maneuver, a nominal trajectory was determined. Then, a neighboring, optimal guidance scheme was obtained for open loop and closed loop control configurations. Taking modelling uncertainties into account, a linear, stochastic, neighboring optimal guidance scheme was devised. Finally, the optimal trajectory was approximated as the sum of the deterministic nominal trajectory and the stochastic neighboring optimal solution. Numerical results are presented for a typical vehicle. A fuel-optimal control problem in aeroassisted noncoplanar orbital transfer is also addressed. The equations of motion for the atmospheric maneuver are nonlinear and the optimal (nominal) trajectory and control are obtained. In order to follow the nominal trajectory under actual conditions, a neighboring optimum guidance scheme is designed using linear quadratic regulator theory for onboard real-time implementation. One of the state variables is used as the independent variable in reference to the time. The weighting matrices in the performance index are chosen by a combination of a heuristic method and an optimal modal approach. The necessary feedback control law is obtained in order to minimize the deviations from the nominal conditions.

Hibey, J. L.↗

A preliminary look at techniques used to obtain airdata from flight at high angles of attack

Flight research at high angles of attack has posed new problems for airdata measurements. New sensors and techniques for measuring the standard airdata quantities of static pressure, dynamic pressure, angle of attack, and angle of sideslip were subsequently developed. The ongoing airdata research supporting NASA's F-18 high alpha research program is updated. Included are the techniques used and the preliminary results. The F-18 aircraft was flown with three research airdata systems: a standard airdata probe on the right wingtip, a self-aligning airdata probe on the left wingtip, and a flush airdata system on the nose cone. The primary research goal was to obtain steady-state calibrations for each airdata system up to an angle of attack of 50 deg. This goal was accomplished and preliminary accuracies of the three airdata systems were assessed and are presented. An effort to improve the fidelity of the airdata measurements during dynamic maneuvering is also discussed. This involved enhancement of the aerodynamic data with data obtained from linear accelerometers, rate gyros, and attitude gyros. Preliminary results of this technique are presented.

Moes, Timothy R.↗

Hypersonic vehicle control law development using H infinity and mu-synthesis

Applicability and effectiveness of robust control techniques to a single-stage-to-orbit (SSTO) airbreathing hypersonic vehicle on an ascent accelerating path and their effectiveness are explored in this paper. An SSTO control system design problem, requiring high accuracy tracking of velocity and altitude commands while limiting angle of attack oscillations, minimizing control power usage and stabilizing the vehicle all in the presence of atmospheric turbulence and uncertainty in the system, was formulated to compare results of the control designs using H infinity and mu-synthesis procedures. The math model, an integrated flight/propulsion dynamic model of a conical accelerator class vehicle, was linearized as the vehicle accelerated through Mach 8. Controller analysis was conducted using the singular value technique and the mu-analysis approach. Analysis results were obtained in both the frequency and the time domains. The results clearly demonstrate the inherent advantages of the structured singular value framework for this class of problems. Since payload performance margins are so critical for the SSTO mission, it is crucial that adequate stability margins be provided without sacrificing any payload mass.

Gregory, Irene M.↗

Hypersonic vehicle control law development using H infinity and mu-synthesis

Applicability and effectivness of robust control techniques to a single-stage-to-orbit (SSTO) airbreathing hypersonic vehicle on an ascent accelerating path and their effectivness are explored in this paper. An SSTO control system design problem, requiring high accuracy tracking of velocity and altitude commands while limiting an angle of attack oscillations, minimizing control power usage and stabilizing the vehicle all in the presence of atmospheric turbulence and uncertainty in the system, was formulated to compare results of the control designs using H infinity and mu-synthesis procedures. The math model, an integrated flight/propulsion dynamic model of a conical accelerator class vehicle, was linearized as the vehicle accelerated through Mach 8. Controller analysis was conducted using the singular value technique and the mu-analysis approach. Analysis results were obtained in both the frequency and the time domains. The results clearly demonstrate the inherent advantages of the structured singular value framework for this class of problems. Since payload performance margins are so critical for the SSTO mission, it is crucial that adequate stability margins be provided without sacrificing any payload mass.

Gregory, Irene M.↗

An MSK Radar Waveform

The minimum-shift-keying (MSK) radar waveform is formed by periodically extending a waveform that separately modulates the in-phase and quadrature- phase components of the carrier with offset pulse-shaped pseudo noise (PN) sequences. To generate this waveform, a pair of periodic PN sequences is each passed through a pulse-shaping filter with a half sinusoid impulse response. These shaped PN waveforms are then offset by half a chip time and are separately modulated on the in-phase and quadrature phase components of an RF carrier. This new radar waveform allows an increase in radar resolution without the need for additional spectrum. In addition, it provides self-interference suppression and configurable peak sidelobes. Compared strictly on the basis of the expressions for delay resolution, main-lobe bandwidth, effective Doppler bandwidth, and peak ambiguity sidelobe, it appears that bi-phase coded (BPC) outperforms the new MSK waveform. However, a radar waveform must meet certain constraints imposed by the transmission and reception of the modulation, as well as criteria dictated by the observation. In particular, the phase discontinuity of the BPC waveform presents a significant impediment to the achievement of finer resolutions in radar measurements a limitation that is overcome by using the continuous phase MSK waveform. The phase continuity, and the lower fractional out-of-band power of MSK, increases the allowable bandwidth compared with BPC, resulting in a factor of two increase in the range resolution of the radar. The MSK waveform also has been demonstrated to have an ambiguity sidelobe structure very similar to BPC, where the sidelobe levels can be decreased by increasing the length of the m-sequence used in its generation. This ability to set the peak sidelobe level is advantageous as it allows the system to be configured to a variety of targets, including those with a larger dynamic range. Other conventionally used waveforms that possess an even greater spectral efficiency than the MSK waveform, such as linear frequency modulation (LFM) and Costas frequency hopping, have a fixed peak sidelobe level that is therefore not configurable, and can be exceeded by high contrast targets. Furthermore, in the case of a multistatic experiment observing a target in motion, self-interference from the transmitter to the receiver is mitigated by the MSK waveform. Waveforms that have delay Doppler coupling, such as LFM, provide no such protection.

Quirk, Kevin J.↗

High Fidelity Adaptively Refined CFD and Reduced Order Models of a High Aspect Ratio Aeroelastic Wing Wind-Tunnel Model

The NASA Advanced Air Transport Technology (AATT) goal of reduced fuel burn for transport aircraft has led to the NASA N+3 High Aspect Ratio Wing (HARW) subproject. This project requires identifying, developing, and demonstrating key technologies and integrated multidisciplinary solutions to enable a safe, high performance, aeroelastic wing. Since this aircraft will have a high aspect ratio wing, aeroelasticity is expected to be a major issue in the design. In this paper high fidelity computational fluid dynamics (CFD) is performed with flow adapted meshes. A system identification of the aerodynamics is developed using both a multi-modal multi-sine time-marching and a multi-mode linear frequency domain method. GLA, MLA and flutter suppression simulations will be performed.

Robert Bartels↗

Effect of chordwise forces and deformations and deformations due to steady lift on wing flutter

This investigation explores the effects of chordwise forces and deformations and steady-state deformation due to lift on the static and dynamic aeroelastic stability of a uniform cantilever wing. Results of this analysis are believed to have practical applications for high-performance sailplanes and certain RPV's. The airfoil cross section is assumed to be symmetric and camber bending is neglected. Motions in vertical bending, fore-and-aft bending, and torsion are considered. A differential equation model is developed, which included the nonlinear elastic bending-torsion coupling that accompanies even moderate deflections. A linearized expansion in small time-dependent deflections is made about a steady flight condition. The stability determinant of the linearized system then contains coefficients that depend on steady displacements. Loads derived from two-dimensional incompressible aerodynamic theory are used to obtain the majority of the results, but cases using three-dimensional subsonic compressible theory are also studied. The stability analysis is carried out in terms of the dynamically uncoupled natural modes of vibration of the uniform cantilever.

Boyd, W. N.↗

A robust momentum management and attitude control system for the space station

A game theoretic controller is synthesized for momentum management and attitude control of the Space Station in the presence of uncertainties in the moments of inertia. Full state information is assumed since attitude rates are assumed to be very assurately measured. By an input-output decomposition of the uncertainty in the system matrices, the parameter uncertainties in the dynamic system are represented as an unknown gain associated with an internal feedback loop (IFL). The input and output matrices associated with the IFL form directions through which the uncertain parameters affect system response. If the quadratic form of the IFL output augments the cost criterion, then enhanced parameter robustness is anticipated. By considering the input and the input disturbance from the IFL as two noncooperative players, a linear-quadratic differential game is constructed. The solution in the form of a linear controller is used for synthesis. Inclusion of the external disturbance torques results in a dynamic feedback controller which consists of conventional PID (proportional integral derivative) control and cyclic disturbance rejection filters. It is shown that the game theoretic design allows large variations in the inertias in directions of importance.

Speyer, J. L.↗

Robust momentum management and attitude control system for the Space Station

A game theoretic controller is synthesized for momentum management and attitude control of the Space Station in the presence of uncertainties in the moments of inertia. Full state information is assumed since attitude rates are assumed to be very accurately measured. By an input-output decomposition of the uncertainty in the system matrices, the parameter uncertainties in the dynamic system are represented as an unknown gain associated with an internal feedback loop (IFL). The input and output matrices associated with the IFL form directions through which the uncertain parameters affect system response. If the quadratic form of the IFL output augments the cost criterion, then enhanced parameter robustness is anticipated. By considering the input and the input disturbance from the IFL as two noncooperative players, a linear-quadratic differential game is constructed. The solution in the form of a linear controller is used for synthesis. Inclusion of the external disturbance torques results in a dynamic feedback controller which consists of conventional PID (proportional integral derivative) control and cyclic disturbance rejection filters. It is shown that the game theoretic design allows large variations in the inertias in directions of importance.

Rhee, Ihnseok↗

Practical Methodology for the Inclusion of Nonlinear Slosh Damping in the Stability Analysis of Liquid-Propelled Space Vehicles

One of the challenges of developing flight control systems for liquid-propelled space vehicles is ensuring stability and performance in the presence of parasitic minimally damped slosh dynamics in the liquid propellants. This can be especially difficult when the fundamental frequencies of the slosh motions are in proximity to the frequency used for vehicle control. The challenge is partially alleviated since the energy dissipation and effective damping in the slosh modes increases with amplitude. However, traditional launch vehicle control design methodology is performed with linearized systems using a fixed slosh damping corresponding to a slosh motion amplitude based on heritage values. This papers presents a method for performing the control design and analysis using damping at slosh amplitudes chosen based on the resulting limit cycle amplitude of the vehicle thrust vector system due to a control-slosh interaction under degraded phase and gain margin conditions.

Ottander, John A.↗

Practical Methodology for the Inclusion of Nonlinear Slosh Damping in the Stability Analysis of Liquid-propelled Space Vehicles

One of the challenges of developing flight control systems for liquid-propelled space vehicles is ensuring stability and performance in the presence of parasitic minimally damped slosh dynamics in the liquid propellants. This can be especially difficult when the fundamental frequencies of the slosh motions are in proximity to the frequency used for vehicle control. The challenge is partially alleviated since the energy dissipation and effective damping in the slosh modes increases with amplitude. However, traditional launch vehicle control design methodology is performed with linearized systems using a fixed slosh damping corresponding to a slosh motion amplitude based on heritage values. This papers presents a method for performing the control design and analysis using damping at slosh amplitudes chosen based on the resulting limit cycle amplitude of the vehicle thrust vector system due to a control-slosh interaction under degraded phase and gain margin conditions.

Ottander, John A.↗