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 829 records · Page 46
All sourcesNASA NTRSDOE OSTI
NASA NTRS1994

Global Asymptotic Behavior of Iterative Implicit Schemes

The global asymptotic nonlinear behavior of some standard iterative procedures in solving nonlinear systems of algebraic equations arising from four implicit linear multistep methods (LMMs) in discretizing three models of 2 x 2 systems of first-order autonomous nonlinear ordinary differential equations (ODEs) is analyzed using the theory of dynamical systems. The iterative procedures include simple iteration and full and modified Newton iterations. The results are compared with standard Runge-Kutta explicit methods, a noniterative implicit procedure, and the Newton method of solving the steady part of the ODEs. Studies showed that aside from exhibiting spurious asymptotes, all of the four implicit LMMs can change the type and stability of the steady states of the differential equations (DEs). They also exhibit a drastic distortion but less shrinkage of the basin of attraction of the true solution than standard nonLMM explicit methods. The simple iteration procedure exhibits behavior which is similar to standard nonLMM explicit methods except that spurious steady-state numerical solutions cannot occur. The numerical basins of attraction of the noniterative implicit procedure mimic more closely the basins of attraction of the DEs and are more efficient than the three iterative implicit procedures for the four implicit LMMs. Contrary to popular belief, the initial data using the Newton method of solving the steady part of the DEs may not have to be close to the exact steady state for convergence. These results can be used as an explanation for possible causes and cures of slow convergence and nonconvergence of steady-state numerical solutions when using an implicit LMM time-dependent approach in computational fluid dynamics.

Yee, H. C.↗
NASA NTRS2010

Analytic Development of a Reference Profile for the First Entry in a Skip Atmospheric Entry

This note shows that a feasible reference drag profile for the first entry portion of a skip entry can be generated as a polynomial expression of the velocity. The coefficients of that polynomial are found through the resolution of a system composed of m + 1 equations, where m is the degree of the drag polynomial. It has been shown that a minimum of five equations (m = 4) are required to establish the range and the initial and final conditions on velocity and flight path angle. It has been shown that at least one constraint on the trajectory can be imposed through the addition of one extra equation in the system, which must be accompanied by the increase in the degree of the drag polynomial. In order to simplify the resolution of the system of equations, the drag was considered as being a probability density function of the velocity, with the velocity as a distribution function of the drag. Combining this notion with the introduction of empirically derived constants, it has been shown that the system of equations required to generate the drag profile can be successfully reduced to a system of linear algebraic equations. For completeness, the resulting drag profiles have been flown using the feedback linearization method of differential geometric control as a guidance law with the error dynamics of a second order homogeneous equation in the form of a damped oscillator. Satisfactory results were achieved when the gains in the error dynamics were changed at a certain point along the trajectory that is dependent on the velocity and the curvature of the drag as a function of the velocity. Future work should study the capacity to update the drag profile in flight when dispersions are introduced. Also, future studies should attempt to link the first entry, as presented and controlled in this note, with a more standard control concept for the second entry, such as the Apollo entry guidance, to try to assess the overall skip entry performance. A guidance law that includes an integral feedback term, as is the case in the actual Space Shuttle entry guidance and as is proposed in Ref 29, could be tried in future studies to assess whether its use results in an improvement of the tracking performance, and to evaluate the design needs when determining the control gains.

Garcia-Llama, Eduardo↗
NASA NTRS2010

Incorporation of SemiSpan SuperSonic Transport (S4T) Aeroservoelastic Models into SAREC-ASV Simulation

The Simulink-based Simulation Architecture for Evaluating Controls for Aerospace Vehicles (SAREC-ASV) was modified to incorporate linear models representing aeroservoelastic characteristics of the SemiSpan SuperSonic Transport (S4T) wind-tunnel model. The S4T planform is for a Technology Concept Aircraft (TCA) design from the 1990s. The model has three control surfaces and is instrumented with accelerometers and strain gauges. Control laws developed for wind-tunnel testing for Ride Quality Enhancement, Gust Load Alleviation, and Flutter Suppression System functions were implemented in the simulation. The simulation models open- and closed-loop response to turbulence and to control excitation. It provides time histories for closed-loop stable conditions above the open-loop flutter boundary. The simulation is useful for assessing the potential impact of closed-loop control rate and position saturation. It also provides a means to assess fidelity of system identification procedures by providing time histories for a known plant model, with and without unmeasured turbulence as a disturbance. Sets of linear models representing different Mach number and dynamic pressure conditions were implemented as MATLAB Linear Time Invariant (LTI) objects. Configuration changes were implemented by selecting which LTI object to use in a Simulink template block. A limited comparison of simulation versus wind-tunnel results is shown.

Christhilf, David M.↗
NASA NTRSDate not supplied

Integrated Control Design for A Partially Turboelectric Aircraft Propulsion System

Electrified Aircraft Propulsion (EAP) holds great potential for reducing aviation emissions and fuel burn. A variety of EAP architectures have been proposed including partially-turboelectric configurations that combine turbofan engines with motor-driven propulsors. Such architectures exhibit coupling between subsystems and thus require an integrated control solution. To address this need, this paper presents an integrated control design strategy for a commercial single-aisle partially-turboelectric aircraft concept consisting of two wing-mounted turbofan engines and an electric motor driven tailfan propulsor. Within this architecture the turbofans serve the dual purpose of generating thrust and supplying mechanical offtake power used to generate electricity for the tailfan motor. The propulsion control system is tasked with coordinating turbofan and tailfan operation under both steady-state and transient scenarios. The paper introduces a linear state-space representation of the architecture reflecting the coupling between the turbofan and tailfan subsystems along with loop transfer functions reflecting open- and closed-loop system dynamics. Also discussed is an applied strategy for scheduling the tailfan setpoint command based on the average sensed fan speed of the two turbofans. This approach ensures synchronized operation of the turbofan and tailfan subsystems while also allowing the turbofan fuel control design to be simplified. Performance of the integrated control design is assessed through a real-time hardware-in-the-loop test conducted at the NASA Electric Aircraft Testbed. During this test a scaled version of the electrical system and turbomachinery shaft dynamics were implemented in electrical machine hardware and evaluated under closed-loop control. Results from this facility test are presented to illustrate the efficacy of the applied integrated control design approach under steady-state and transient scenarios including a full-flight mission profile.

Electrified Aircraft Propulsion↗
NASA NTRSDate not supplied

Transition Modeling Based on the Dual N-factor Method for the CRM-NLF Wind Tunnel Configuration

The dual N-factor method is used to model the boundary-layer transition over the common research model with natural laminar flow (CRM-NLF) aircraft configuration. The flow conditions match selected test conditions from a wind tunnel experiment in the National Transonic Facility at the NASA Langley Research Center. The paper presents a systematic methodology for transition prediction in the presence of a dual shock system and extends the prior capability for iteratively coupled computational fluid dynamics (CFD) predictions to incorporate three-dimensional, transonic wings. The method employs stability computations based on the linear parabolized stability equations (PSE), along with a dual N-factor criterion. The iterative process begins with the fully turbulent Reynolds-averaged-Navier-Stokes (RANS) mean flow solution. For the first iteration, a mean flow solution is calculated with an imposed transition front that aligns with the shock front from the fully turbulent solution. Subsequently, stability computations are performed along a set of streamlines across the wing to calculate the amplification of planar Tollmien-Schlichting (TS) and stationary crossflow (CF) modes. The transition criterion based on the dual N-factor method is used to infer the updated transition front and the process is successively repeated until convergence of the solution. Within three iterations, the predicted fronts for angles of attack of 1.45, 1.98, 2.46 and 2.94 degrees and a mean-aerodynamic-chord Reynolds number equal to 15 million, approach visual convergence in most regions of the studied cases, and the resulting predictions are in good agreement with the transition fronts deduced from measurements of temperature-sensitive paint. Even though surface pressure measurements based on fully-turbulent flow agree well with the measured pressure coefficient distributions, strong viscous-inviscid interaction effects cause significant shifts in the shock locations based on the imposed transition front, underscoring the intrusive nature of static pressure measurements using surface mounted ports on the CRM-NLF configuration.

Boundary Layer Transition↗
NASA NTRSDate not supplied

Integrated Control Design for A Partially Turboelectric Aircraft Propulsion System

Electrified Aircraft Propulsion (EAP) holds great potential for reducing aviation emissions and fuel burn. A variety of EAP architectures have been proposed including partially-turboelectric configurations that combine turbofan engines with motor-driven propulsors. Such architectures exhibit coupling between subsystems and thus require an integrated control solution. To address this need, this paper presents an integrated control design strategy for a commercial single-aisle partially-turboelectric aircraft concept consisting of two wing-mounted turbofan engines and an electric motor driven tailfan propulsor. Within this architecture the turbofans serve the dual purpose of generating thrust and supplying mechanical offtake power used to generate electricity for the tailfan motor. The propulsion control system is tasked with coordinating turbofan and tailfan operation under both steady-state and transient scenarios. The paper introduces a linear state-space representation of the architecture reflecting the coupling between the turbofan and tailfan subsystems along with loop transfer functions reflecting open- and closed-loop system dynamics. Also discussed is an applied strategy for scheduling the tailfan setpoint command based on the average sensed fan speed of the two turbofans. This approach ensures synchronized operation of the turbofan and tailfan subsystems while also allowing the turbofan fuel control design to be simplified. Performance of the integrated control design is assessed through a real-time hardware-in-the-loop test conducted at the NASA Electric Aircraft Testbed. During this test a scaled version of the electrical system and turbomachinery shaft dynamics were implemented in electrical machine hardware and evaluated under closed-loop control. Results from this facility test are presented to illustrate the efficacy of the applied integrated control design approach under steady-state and transient scenarios including a full-flight mission profile.

Electrified Aircraft Propulsion↗
NASA NTRS2023

Integrated Control Design for A Partially Turboelectric Aircraft Propulsion System

Electrified Aircraft Propulsion (EAP) holds great potential for reducing aviation emissions and fuel burn. A variety of EAP architectures have been proposed including partially-turboelectric configurations that combine turbofan engines with motor-driven propulsors. Such architectures exhibit coupling between subsystems and thus require an integrated control solution. To address this need, this paper presents an integrated control design strategy for a commercial single-aisle partially-turboelectric aircraft concept consisting of two wing-mounted turbofan engines and an electric motor driven tailfan propulsor. Within this architecture the turbofans serve the dual purpose of generating thrust and supplying mechanical offtake power used to generate electricity for the tailfan motor. The propulsion control system is tasked with coordinating turbofan and tailfan operation under both steady-state and transient scenarios. The paper introduces a linear state-space representation of the architecture reflecting the coupling between the turbofan and tailfan subsystems along with loop transfer functions reflecting open- and closed-loop system dynamics. Also discussed is an applied strategy for scheduling the tailfan setpoint command based on the average sensed fan speed of the two turbofans. This approach ensures synchronized operation of the turbofan and tailfan subsystems while also allowing the turbofan fuel control design to be simplified. Performance of the integrated control design is assessed through a real-time hardware-in-the-loop test conducted at the NASA Electric Aircraft Testbed. During this test a scaled version of the electrical system and turbomachinery shaft dynamics were implemented in electrical machine hardware and evaluated under closed-loop control. Results from this facility test are presented to illustrate the efficacy of the applied integrated control design approach under steady-state and transient scenarios including a full-flight mission profile.

Electrified Aircraft Propulsion↗
NASA NTRS2003

Expected Deployment Dynamics of Proseds

The control law for The Propulsive Small Expendable Deployment System (ProSEDS) deployment is a modification of the control routine that was successfully used in the flight of SEDS-II. Unlike SEDS, the tether of ProSEDS consists of different sections with different mechanical characteristics. A non-linear control trajectory in phase-space (i.e., the reference profile) is fed forward to the controller to guide the satellite, at the tether tip, to the desired final state under nominal conditions and no external perturbations. A linear feedback control is applied by the brake to keep the actual trajectory as close as possible to the reference. The paper also shows the results of simulations of deployment dynamics with and without noise. The control law has thus far been developed and tested on the ground for the original ProSEDS tether configuration of 15 km. A new reference will have to be designed and tested for other tether configurations.

Lorenzini, E. C.↗
NASA NTRS1981

Nonlinear dynamic phenomena in the space shuttle thermal protection system

The development of an analysis for examining the nonlinear dynamic phenomena arising in the space shuttle orbiter tile/pad thermal protection system is presented. The tile/pad system consists of ceramic tiles bonded to the aluminum skin of the orbiter through a thin nylon felt pad. The pads are a soft nonlinear material which permits large strains and displays both hysteretic and nonlinear viscous damping. Application of the analysis to a square tile subjected to transverse sinusoidal motion of the orbiter skin is presented and the following nonlinear dynamic phenomena are considered: highly distorted wave forms, amplitude-dependent resonant frequencies which initially decrease and then increase with increasing amplitude of motion, magnification of substrate motion which is higher than would be expected in a similarly highly damped linear system, and classical parametric resonance instability.

Housner, J. M.↗
NASA NTRS1995

Structural, dynamical and electronic properties of CaCuO2

The scalar relativistic version of an accurate first principles full potential self-consistent linearized muffin tin orbital (LMTO) method has been employed for describing the physical properties of the parent system of the high-T(sub c) oxide superconductors, i.e., CaCuO2. The presently employed modified version of the LMTO method is quite fast and goes beyond the usual LMTO ASA method in the sense that it permits a completely general shape of the potential and the charge density. Also, in contrast to LMTO ASA, the present method is also capable of treating distorted lattice structures accurately. The calculated values of the lattice parameters of pure CaCuO2 lie within 3% of the experimentally measured values for the Sr-doped system Ca(0.86)Sr(0.14)CuO(2). The computed electronic structures and the density of states is quite similar to those of the other oxide superconductors, except of their three- dimensional character because of the presence of strong coupling between the closely spaced CuO2 layers. The van Hove singularity peak appears slightly below the Fermi level and a small concentration of oxygenation /or/ substitutional doping may pin it at the Fermi level. The calculated frequencies for some symmetric frozen phonons for undoped CaCuO2 are quite near to the measured data for the Sr-doped CaCuO2.

Agrawal, Bal K.↗
NASA NTRS1974

Optimal control theory investigation of proprotor/wing response to vertical gust

Optimal control theory is used to design linear state variable feedback to improve the dynamic characteristics of a rotor and cantilever wing representing the tilting proprotor aircraft in cruise flight. The response to a vertical gust and system damping are used as criteria for the open and closed loop performance. The improvement in the dynamic characteristics achievable is examined for a gimballed rotor and for a hingeless rotor design. Several features of the design process are examined, including: (1) using only the wing or only the rotor dynamics in the control system design; (2) the use of a wing flap as well as the rotor controls for inputs; (3) and the performance of the system designed for one velocity at other forward speeds.

Frick, J. K. D.↗
NASA NTRS1990

Modeling the pressure-strain correlation of turbulence: An invariant dynamical systems approach

The modeling of the pressure-strain correlation of turbulence is examined from a basic theoretical standpoint with a view toward developing improved second-order closure models. Invariance considerations along with elementary dynamical systems theory are used in the analysis of the standard hierarchy of closure models. In these commonly used models, the pressure-strain correlation is assumed to be a linear function of the mean velocity gradients with coefficients that depend algebraically on the anisotropy tensor. It is proven that for plane homogeneous turbulent flows the equilibrium structure of this hierarchy of models is encapsulated by a relatively simple model which is only quadratically nonlinear in the anisotropy tensor. This new quadratic model - the SSG model - is shown to outperform the Launder, Reece, and Rodi model (as well as more recent models that have a considerably more complex nonlinear structure) in a variety of homogeneous turbulent flows. Some deficiencies still remain for the description of rotating turbulent shear flows that are intrinsic to this general hierarchy of models and, hence, cannot be overcome by the mere introduction of more complex nonlinearities. It is thus argued that the recent trend of adding substantially more complex nonlinear terms containing the anisotropy tensor may be of questionable value in the modeling of the pressure-strain correlation. Possible alternative approaches are discussed briefly.

Speziale, Charles G.↗
NASA NTRS1991

Nonlinear modal resonances in low-gravity slosh-spacecraft systems

Nonlinear models of low gravity slosh, when coupled to spacecraft vibrations, predict intense nonlinear eigenfrequency shifts at zero gravity. These nonlinear frequency shifts are due to internal quadratic and cubic resonances between fluid slosh modes and spacecraft vibration modes. Their existence has been verified experimentally, and they cannot be correctly modeled by approximate, uncoupled nonlinear models, such as pendulum mechanical analogs. These predictions mean that linear slosh assumptions for spacecraft vibration models can be invalid, and may lead to degraded control system stability and performance. However, a complete nonlinear modal analysis will predict the correct dynamic behavior. This paper presents the analytical basis for these results, and discusses the effect of internal resonances on the nonlinear coupled response at zero gravity.

Peterson, Lee D.↗
NASA NTRS1991

Modelling the pressure-strain correlation of turbulence - An invariant dynamical systems approach

The modeling of the pressure-strain correlation of turbulence is examined from a basic theoretical standpoint with a view toward developing improved second-order closure models. Invariance considerations along with elementary dynamical systems theory are used in the analysis of the standard hierarchy of closure models. In these commonly used models, the pressure-strain correlation is assumed to be a linear function of the mean velocity gradients with coefficients that depend algebraically on the anisotropy tensor. It is proven that for plane homogeneous turbulent flows the equilibrium structure of this hierarchy of models is encapsulated by a relatively simple model which is only quadratically nonlinear in the anisotropy tensor. This new quadratic model - the SSG model - is shown to outperform the Launder, Reece, and Rodi model (as well as more recent models that have a considerably more complex nonlinear structure) in a variety of homogeneous turbulent flows. Some deficiencies still remain for the description of rotating turbulent shear flows that are intrinsic to this general hierarchy of models and, hence, cannot be overcome by the mere introduction of more complex nonlinearities. It is thus argued that the recent trend of adding substantially more complex nonlinear terms containing the anisotropy tensor may be of questionable value in the modeling of the pressure-strain correlation. Possible alternative approaches are discussed briefly.

Speziale, Charles G.↗
NASA NTRS1995

Roll-yaw control at high angle of attack by forebody tangential blowing

The feasibility of using forebody tangential blowing to control the roll-yaw motion of a wind tunnel model is experimentally demonstrated. An unsteady model of the aerodynamics is developed based on the fundamental physics of the flow. Data from dynamic experiments is used to validate the aerodynamic model. A unique apparatus is designed and built that allows the wind tunnel model two degrees of freedom, roll and yaw. Dynamic experiments conducted at 45 degrees angle of attack reveal the system to be unstable. The natural motion is divergent. The aerodynamic model is incorporated into the equations of motion of the system and used for the design of closed loop control laws that make the system stable. These laws are proven through dynamic experiments in the wind tunnel using blowing as the only actuator. It is shown that asymmetric blowing is a highly non-linear effector that can be linearized by superimposing symmetric blowing. The effects of forebody tangential blowing and roll and yaw angles on the flow structure are determined through flow visualization experiments. The transient response of roll and yaw moments to a step input blowing are determined. Differences on the roll and yaw moment dependence on blowing are explained based on the physics of the phenomena.

Pedreiro, N.↗
NASA NTRS1995

Roll-Yaw control at high angle of attack by forebody tangential blowing

The feasibility of using forebody tangential blowing to control the roll-yaw motion of a wind tunnel model is experimentally demonstrated. An unsteady model of the aerodynamics is developed based on the fundamental physics of the flow. Data from dynamic experiments is used to validate the aerodynamic model. A unique apparatus is designed and built that allows the wind tunnel model two degrees of freedom, roll and yaw. Dynamic experiments conducted at 45 degrees angle of attack reveal the system to be unstable. The natural motion is divergent. The aerodynamic model is incorporated into the equations of motion of the system and used for the design of closed loop control laws that make the system stable. These laws are proven through dynamic experiments in the wind tunnel using blowing as the only actuator. It is shown that asymmetric blowing is a highly non-linear effector that can be linearized by superimposing symmetric blowing. The effects of forebody tangential blowing and roll and yaw angles on the flow structure are determined through flow visualization experiments. The transient response of roll and yaw moments to a step input blowing are determined. Differences on the roll and yaw moment dependence on blowing are explained based on the physics of the phenomena.

Pedreiro, N.↗
NASA NTRS2015

Advanced Computational Modeling Approaches for Shock Response Prediction

Motivation: (1) The activation of pyroshock devices such as explosives, separation nuts, pin-pullers, etc. produces high frequency transient structural response, typically from few tens of Hz to several hundreds of kHz. (2) Lack of reliable analytical tools makes the prediction of appropriate design and qualification test levels a challenge. (3) In the past few decades, several attempts have been made to develop methodologies that predict the structural responses to shock environments. (4) Currently, there is no validated approach that is viable to predict shock environments overt the full frequency range (i.e., ~100 Hz to 10 kHz). Scope: (1) Model, analyze, and interpret space structural systems with complex interfaces and discontinuities, subjected to shock loads. (2) Assess the viability of a suite of numerical tools to simulate transient, non-linear solid mechanics and structural dynamics problems, such as shock wave propagation.

Derkevorkian, Armen↗