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NASA NTRS2005

Designing Adaptive Low-Dissipative High Order Schemes for Long-Time Integrations

A general framework for the design of adaptive low-dissipative high order schemes is presented. It encompasses a rather complete treatment of the numerical approach based on four integrated design criteria: (1) For stability considerations, condition the governing equations before the application of the appropriate numerical scheme whenever it is possible. (2) For consistency, compatible schemes that possess stability properties, including physical and numerical boundary condition treatments, similar to those of the discrete analogue of the continuum are preferred. (3) For the minimization of numerical dissipation contamination, efficient and adaptive numerical dissipation control to further improve nonlinear stability and accuracy should be used. (4) For practical considerations, the numerical approach should be efficient and applicable to general geometries, and an efficient and reliable dynamic grid adaptation should be used if necessary. These design criteria are, in general, very useful to a wide spectrum of flow simulations. However, the demand on the overall numerical approach for non-linear stability and accuracy is much more stringent for long-time integration of complex multiscale viscous shock/shear/turbulence/acoustics interactions and numerical combustion. Robust classical numerical methods for less complex flow physics are not suitable or practical for such applications. The present approach is designed expressly to address such flow problems, especially unsteady flows.

Yee, H. C.↗

NASA NTRS2021

Joint cloud water path and rainwater path retrievals from airborne ORACLES observations

This study presents a new algorithm that combines W-band reflectivity measurements from the Airborne Precipitation Radar – third generation (APR-3) passive radiometric cloud optical depth and effective radius retrievals from the Research Scanning Polarimeter (RSP) to estimate total liquid water path in warm clouds and identify the contributions from cloud water path (CWP) and rainwater path (RWP). The resulting CWP estimates are primarily determined by the optical depth input, although reflectivity measurements contribute ∼10 %–50 % of the uncertainty due to attenuation through the profile. Uncertainties in CWP estimates across all conditions are 25 % to 35 %, while RWP uncertainty estimates frequently exceed 100 %. Two-thirds of all radar-detected clouds observed during the ObseRvations of Aerosols above CLouds and their intEractionS (ORACLES) campaign that took place from 2016–2018 over the southeast Atlantic Ocean have CWP between 41 and 168 g/sq. m and almost all CWPs (99 %) between 6 to 445 g/sq. m. RWP, by contrast, typically makes up a much smaller fraction of total liquid water path (LWP), with more than 70 % of raining clouds having less than 10 g/sq. m of rainwater. In heavier warm rain (i.e., rain rate exceeding 40 mm/h or 1000 mm/d), however, RWP is observed to exceed 2500 g/sq. m. CWP (RWP) is found to be approximately 30 g/sq. m (7 g/sq. m) larger in unstable environments compared to stable environments. Surface precipitation is also more than twice as likely in unstable environments. Comparisons against in situ cloud microphysical probe data spanning the range of thermodynamic stability and meteorological conditions encountered across the southeast Atlantic basin demonstrate that the combined APR-3 and RSP dataset enable a robust joint cloud–precipitation retrieval algorithm to support future ORACLES precipitation susceptibility and cloud–aerosol–precipitation interaction studies.

algorithm↗

NASA NTRSDate not supplied

Anisotropic Goal-Based Mesh Adaptation Metric Clarification and Development

Adaptive unstructured mesh techniques have a limited, but growing impact on production analysis workflows to control discretization error for reliable simulation results. Multiple independent implementations of flow solvers, anisotropic metric construction methods, and anisotropic mesh adaptation mechanics have matured. Goal-based metrics target estimated error in output functions, such as lift and drag, through the guidance of an adjoint solution. A unification of goal-based anisotropic metrics is presented for steady viscous flows, which is an active area of research. These goal-based metrics drive robust and efficient anisotropic mesh adaptation for the calculation of output functions. The super-convergent functional output error behavior of stabilized finite-element methods is exploited without a formal proof, and evidence of super-convergence is shown in numerical experiments. Mesh adapted drag and lift outputs for two simple bodies in compressible viscous flow show convergence of error to less than a single drag count. Asymptotic behavior established for relatively coarse meshes shows the efficiency of this goal-based metric when compared to solution interpolation error control and expert-guided meshing. Anisotropic mesh adaptation techniques are applied to a transport aircraft in a high-lift configuration where variation between approaches decreases with mesh refinement, but asymptotic behavior is not observed with available resources.

goal-based↗

NASA NTRS2002

Entropy Splitting for High Order Numerical Simulation of Compressible Turbulence

A stable high-order numerical scheme for direct numerical simulation (DNS) of shock-free compressible turbulence is presented. The method is applicable to general geometries. It contains no upwinding, artificial dissipation, or filtering. Instead the method relies on the stabilizing mechanisms of an appropriate conditioning of the governing equations and the use of compatible spatial difference operators for the interior points (interior scheme) as well as the boundary points (boundary scheme). An entropy-splitting approach splits the inviscid flux derivatives into conservative and nonconservative portions. The spatial difference operators satisfy a summation-by-parts condition, leading to a stable scheme (combined interior and boundary schemes) for the initial boundary value problem using a generalized energy estimate. A Laplacian formulation of the viscous and heat conduction terms on the right hand side of the Navier–Stokes equations is used to ensure that any tendency to odd–even decoupling associated with central schemes can be countered by the fluid viscosity. The resulting methods are able to minimize the spurious high-frequency oscillations associated with pure central schemes, especially for long time integration applications such as DNS. For validation purposes, the methods are tested in a DNS of compressible turbulent plane channel flow at low values of friction Mach number, where reference turbulence data bases exist. It is demonstrated that the methods are robust in terms of grid resolution, and in good agreement with published channel data. Accurate turbulence statistics can be obtained with moderate grid sizes. Stability limits on the range of the splitting parameter are determined from numerical tests.

N.D. Sandham↗

NASA NTRS1996

On longitudinal control of high speed aircraft in the presence of aeroelastic modes

Longitudinal control system design is considered for a linearized dynamic model of a supersonic transport aircraft concept characterized by relaxed static stability and significant aeroelastic interactions. Two LQG-type controllers are designed using the frequency-domain additive uncertainty formulation to ensure robustness to unmodeled flexible modes. The first controller is based on a 4th-order model containing only the rigid-body modes, while the second controller is based on an 8th-order model that additionally includes the two most prominent flexible modes. The performance obtainable from the 4th-order controller is not adequate, while the 8th-order controller is found to provide better performance. Frequency-domain and time-domain (Lyapunov) methods are subsequently used to assess the robustness of the 8th-order controller to parametric uncertainties in the design model.

Joshi, Suresh M.↗

NASA NTRS2000

Generalized Predictive and Neural Generalized Predictive Control of Aerospace Systems

The research work presented in this thesis addresses the problem of robust control of uncertain linear and nonlinear systems using Neural network-based Generalized Predictive Control (NGPC) methodology. A brief overview of predictive control and its comparison with Linear Quadratic (LQ) control is given to emphasize advantages and drawbacks of predictive control methods. It is shown that the Generalized Predictive Control (GPC) methodology overcomes the drawbacks associated with traditional LQ control as well as conventional predictive control methods. It is shown that in spite of the model-based nature of GPC it has good robustness properties being special case of receding horizon control. The conditions for choosing tuning parameters for GPC to ensure closed-loop stability are derived. A neural network-based GPC architecture is proposed for the control of linear and nonlinear uncertain systems. A methodology to account for parametric uncertainty in the system is proposed using on-line training capability of multi-layer neural network. Several simulation examples and results from real-time experiments are given to demonstrate the effectiveness of the proposed methodology.

Kelkar, Atul G.↗

NASA NTRS2003

Integration of Online Parameter Identification and Neural Network for In-Flight Adaptive Control

An indirect adaptive system has been constructed for robust control of an aircraft with uncertain aerodynamic characteristics. This system consists of a multilayer perceptron pre-trained neural network, online stability and control derivative identification, a dynamic cell structure online learning neural network, and a model following control system based on the stochastic optimal feedforward and feedback technique. The pre-trained neural network and model following control system have been flight-tested, but the online parameter identification and online learning neural network are new additions used for in-flight adaptation of the control system model. A description of the modification and integration of these two stand-alone software packages into the complete system in preparation for initial flight tests is presented. Open-loop results using both simulation and flight data, as well as closed-loop performance of the complete system in a nonlinear, six-degree-of-freedom, flight validated simulation, are analyzed. Results show that this online learning system, in contrast to the nonlearning system, has the ability to adapt to changes in aerodynamic characteristics in a real-time, closed-loop, piloted simulation, resulting in improved flying qualities.

Hageman, Jacob↗

NASA NTRS2003

Integration of Online Parameter Identification and Neural Network for In-Flight Adaptive Control

Hageman, Jacob J.↗

NASA NTRS2006

A High-Authority/Low-Authority Control Strategy for Coupled Aircraft-Style Bays

This paper presents a numerical investigation of an active structural acoustic control strategy for coupled aircraft-style bays. While structural coupling can destabilize or limit the performance of some model-based decentralized control systems, fullycoupled centralized control strategies are impractical for typical aircraft containing several hundred bays. An alternative is to use classical rate feedback with matched, collocated transducer pairs to achieve active damping. Unfortunately, due to the conservative nature of this strategy, stability is guaranteed at the expense of achievable noise reduction. Therefore, this paper describes the development of a combined control strategy using robust active damping in addition to a high-authority controller based on linear quadratic Gaussian (LQG) theory. The combined control system is evaluated on a tensioned, two-bay model using piezoceramic actuators and ideal point velocity sensors. Transducer placement on the two-bay structure is discussed, and the advantages of a combined control strategy are presented.

Schiller, N. H.↗

NASA NTRSDate not supplied

Boundary-Layer Transition Prediction Through Loose Coupling of OVERFLOW and LASTRAC

Transition prediction based on linear stability theory is expected to more accurately reflect the causality of transition onset than phenomenological transition models based on RANS-like transport equations. To help achieve the CFD vision 2030 aim of building a CFD tool chain with automated prediction of boundary layer transition, a technique to loosely tie the NASA OVERFLOW CFD solver with the LASTRAC stability analysis tool is described. The coupled solver is then used to compute transition over selected over a flat plate in a freestream with sufficiently low levels of turbulence, NLF(1)-0416 airfoil, the 6:1 prolate spheroid at an angle of attack, and a NASA juncture flow model with symmetric wing configuration. The findings show that the loosely coupled approach can reliably predict the transition location accurately in scenarios that are dominated by a single transition mechanism involving Tollmien-Schlichting instabilities, crossflow instabilities, or separation bubble-induced transition, or include a mixture of selected mechanisms. The toolset presents here appears to be robust to the prescription of the initial transition location, and it can lead to a converged solution in four or five rounds of the mean flow calculation and stability analysis, with minimal input from the user.

boundary layer transition↗

NASA NTRS1982

On current aspects of finite element computational fluid mechanics for turbulent flows

A set of nonlinear partial differential equations suitable for the description of a class of turbulent three-dimensional flow fields in select geometries is identified. On the basis of the concept of enforcing a penalty constraint to ensure accurate accounting of ordering effects, a finite element numerical solution algorithm is established for the equation set and the theoretical aspects of accuracy, convergence and stability are identified and quantized. Hypermatrix constructions are used to formulate the reduction of the computational aspects of the theory to practice. The robustness of the algorithm, and the computer program embodiment, have been verified for pertinent flow configurations.

Baker, A. J.↗

NASA NTRS1986

Control of elastic robotic systems by nonlinear inversion and modal damping

Energy efficient, lightweight robot arms for space applications have considerable structural flexibility. For large and fast motions, both the nonlinear coupled dynamics and the elastic behavior of the robots must be considered in control system designs. This paper presents an approach to the control of a class of flexible robotic systems. A control law is derived which decouples the joint-angle motion from the flexible motion and asymptotically decomposes the elastic dynamics into two subsystems, representing the transverse vibrations of the elastic link in two orthogonal planes. This decomposition allows the design of an elastic mode stabilizer independently based on lower order models representing structural flexibility. The closed-loop system is shown to be globally asymptotically stable and robust to uncertainty in system parameters. Simulation results are presented to show that large, fast control of joint angles can be performed in spite of space vehicle motion and uncertainty in the payload.

Singh, S. N.↗

NASA NTRS1989

Application of spectral collocation techniques to the stability of swirling flows

The linearized stability equations in cylindrical coordinates of a Chebyshev spectral collocation method for the temporal and spatial stability of swirling flows are presently solved with the eigenvalues obtained through the use of the QZ routine. The algorithm thus created is robust and easily adaptable to a range of flow configurations encompassing internal and external flows with minor boundary condition application modifications. Accuracy and efficiency tests of the method are made for the cases of plane Poiseulle, rotating-pipe, and trailing line vortex flows.

Khorrami, Mehdi R.↗

NASA NTRS1993

Global asymptotic stability of dynamic dissipative compensators for multibody flexible space structures

The stability characteristics of dynamic dissipative compensators are investigated for multibody flexible space structures having nonlinear dynamics. The problem addressed is that of proving asymptotic stability of dynamic dissipative compensators. The stability proof uses the Liapunov approach and exploits the inherent passivity of such systems. For such systems these compensators are shown to be robust to parametric uncertainties and unmodeled dynamics. The results are applicable to a large class of structures such as flexible space structures with articulated flexible appendages.

Kelkar, Atul G.↗

NASA NTRS1987

Robust nonlinear attitude control of flexible spacecraft

This paper presents an approach to large-angle rotational maneuvers of a spacecraft-beam-tip body configuration based on nonlinear invertibility and linear feedback stabilization. A control law u sub d is derived for the decoupled control of attitude angles, lateral elastic deflections, slopes due to bending and angular deflection due to torsion at the tip of the beam using torquers and force actuators. For the stabilization of the elastic modes, a linear feedback control law u sub s is obtained based on a linearized model augmented with a servocompensator. Simulation results are presented to show that large slewing and elastic mode stabilization can be accomplished.

Singh, Sahjendra N.↗

NASA NTRS1981

On regulators with a prescribed degree of stability

Several important aspects of the Regulator with a Prescribed Degree of Stability (RPDS) methodology and its applications are considered. The solution of the time varying RPDS problem as well as the characterization of RPDS closed loop eigenstructure properties are obtained. Based on the asymptotic behavior of RPDS root loci, a one step algorithm for designing Regulators with Prescribed Damping Ratio (RPDR) is developed. The robustness properties of RPDS are characterized in terms of the properties of the return difference and the inverse return difference matrices for the RPDS state feedback loop. This class of regulators is found to possess excellent multiloop margins with respect to stability and degree of stability properties. The ability of RPDS design to tolerate changing operating conditions and unmodelled dynamics are illustrated with a multiterminal dc/ac power system example. The output feedback realization of RPDS requires the use of Linear Quadratic Gaussian (LQG) methodology.

Ng, P. T. P.↗

NASA NTRS1994

Hypersonic vehicle model and control law development using H(infinity) and micron synthesis

The control system design for a Single Stage To Orbit (SSTO) air breathing vehicle will be central to a successful mission because a precise ascent trajectory will preserve narrow payload margins. The air breathing propulsion system requires the vehicle to fly roughly halfway around the Earth through atmospheric turbulence. The turbulence, the high sensitivity of the propulsion system to inlet flow conditions, the relatively large uncertainty of the parameters characterizing the vehicle, and continuous acceleration make the problem especially challenging. Adequate stability margins must be provided without sacrificing payload mass since payload margins are critical. Therefore, a multivariable control theory capable of explicitly including both uncertainty and performance is needed. The H(infinity) controller in general provides good robustness but can result in conservative solutions for practical problems involving structured uncertainty. Structured singular value mu framework for analysis and synthesis is potentially much less conservative and hence more appropriate for problems with tight margins. An SSTO control system requires: highly accurate tracking of velocity and altitude commands while limiting angle-of-attack oscillations, minimized control power usage, and a stabilized vehicle when atmospheric turbulence and system uncertainty are present. The controller designs using H(infinity) and mu-synthesis procedures were compared. An integrated flight/propulsion dynamic mathematical model of a conical accelerator vehicle was linearized as the vehicle accelerated through Mach 8. Vehicle acceleration through the selected flight condition gives rise to parametric variation that was modeled as a structured uncertainty. The mu-analysis approach was used in the frequency domain to conduct controller analysis and was confirmed by time history plots. Results demonstrate the inherent advantages of the mu framework for this class of problems.

Gregory, Irene M.↗

NASA NTRS1991

Sensitivity of Space Station Alpha Joint robust controller to structural modal parameter variations

The baseline design of the photovoltaic-array sun-tracking control system is presented with special attention given to the optimization of design variables related to stability and performance. The procedures utilized to attenuate control/structure interaction are described, and controller sensitivity to variations in structural modal parameters is examined. Constrained optimization techniques determine the stability margin and tracking capability, which are then tested for sensitivity to variations in natural frequency, mode-shape amplitudes, and modal-damping ratios. The effect of variations in the modal parameters of the dominant modes on performance indicators is also examined to optimize tracking-performance responsiveness and satisfy the design requirements. It is concluded that accurate on-orbit modal data are necessary to make the reoptimization procedure effective in improving the performance of the control system.

Kumar, Renjith R.↗