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NASA NTRS1990

Dynamic Analysis and Control of Lightweight Manipulators with Flexible Parallel Link Mechanisms

The objective is the theoretical analysis and the experimental verification of dynamics and control of a two link flexible manipulator with a flexible parallel link mechanism. Nonlinear equations of motion of the lightweight manipulator are derived by the Lagrangian method in symbolic form to better understand the structure of the dynamic model. The resulting equation of motion have a structure which is useful to reduce the number of terms calculated, to check correctness, or to extend the model to higher order. A manipulator with a flexible parallel link mechanism is a constrained dynamic system whose equations are sensitive to numerical integration error. This constrained system is solved using singular value decomposition of the constraint Jacobian matrix. Elastic motion is expressed by the assumed mode method. Mode shape functions of each link are chosen using the load interfaced component mode synthesis. The discrepancies between the analytical model and the experiment are explained using a simplified and a detailed finite element model.

Lee, Jeh Won↗

NASA NTRS1996

Fossilization processes in siliceous thermal springs: trends in preservation along thermal gradients

To enhance our ability to extract palaeobiological and palaeoenvironmental information from ancient thermal spring deposits, we have studied the processes responsible for the development and preservation of stromatolites in modern subaerial thermal spring systems in Yellowstone National Park (USA). We investigated specimens collected from silica-depositing thermal springs along the thermal gradient using petrographic techniques and scanning electron microscopy. Although it is known that thermophilic cyanobacteria control the morphogenesis of thermal spring stromatolites below 73 degrees C, we have found that biofilms which contain filamentous thermophiles contribute to the microstructural development of subaerial geyserites that occur along the inner rims of thermal spring pools and geyser effluents. Biofilms intermittently colonize the surfaces of subaerial geyserites and provide a favoured substrate for opaline silica precipitation. We have also found that the preservation of biotically produced microfabrics of thermal spring sinters reflects dynamic balances between rates of population growth, decomposition of organic matter, silica deposition and early diagenesis. Major trends in preservation of thermophilic organisms along the thermal gradient are defined by differences in the mode of fossilization, including replacement, encrustation and permineralization.

NASA Discipline Exobiology↗

NASA NTRS1971

Users manual for the Variable dimension Automatic Synthesis Program (VASP)

A dictionary and some problems for the Variable Automatic Synthesis Program VASP are submitted. The dictionary contains a description of each subroutine and instructions on its use. The example problems give the user a better perspective on the use of VASP for solving problems in modern control theory. These example problems include dynamic response, optimal control gain, solution of the sampled data matrix Ricatti equation, matrix decomposition, and pseudo inverse of a matrix. Listings of all subroutines are also included. The VASP program has been adapted to run in the conversational mode on the Ames 360/67 computer.

White, J. S.↗

NASA NTRS1980

Handling Qualities of Large Flexible Aircraft

The effects on handling qualities of elastic modes interaction with the rigid body dynamics of a large flexible aircraft are studied by a mathematical computer simulation. An analytical method to predict the pilot ratings when there is a severe modes interactions is developed. This is done by extending the optimal control model of the human pilot response to include the mode decomposition mechanism into the model. The handling qualities are determined for a longitudinal tracking task using a large flexible aircraft with parametric variations in the undamped natural frequencies of the two lowest frequency, symmetric elastic modes made to induce varying amounts of mode interaction.

Poopaka, S.↗

NASA NTRS1988

An application of eigenspace methods to symmetric flutter suppression

An eigenspace assignment approach to the design of parameter insensitive control laws for linear multivariable systems is presented. The control design scheme utilizes flexibility in eigenvector assignments to reduce control system sensitivity to changes in system parameters. The methods involve use of the singular value decomposition to provide an exact description of allowable eigenvectors in terms of a minimum number of design parameters. In a design example, the methods are applied to the problem of symmetric flutter suppression in an aeroelastic vehicle. In this example the flutter mode is sensitive to changes in dynamic pressure and eigenspace methods are used to enhance the performance of a stabilizing minimum energy/linear quadratic regulator controller and associated observer. Results indicate that the methods provide feedback control laws that make stability of the nominal closed loop systems insensitive to changes in dynamic pressure.

Fennell, Robert E.↗

NASA NTRS1988

An application of eigenspace methods to symmetric flutter suppression

An eigenspace assignment approach to the design of parameter insensitive control laws for linear multivariable systems is presented. The control design scheme utilizes constrained optimization techniques to exploit the flexibility in eigenvector assignments to reduce control system sensitivity to changes in system parameters while maintaining performance requirements; it thus provides a systematic approach for choosing values for eigensystem design variables. The methods involve use of the singular value decomposition to provide an exact description of allowable eigenvectors in terms of a minimum number of design parameters. In a design example, the methods are applied to the problem of symmetric flutter suppression in an aeroelastic vehicle. In this example the flutter mode is sensitive to changes in dynamic pressure and eigenspace methods are used to enhance the performance of a stabilizing minimum energy/linear quadratic regulator controller and associated observer. Numerical results indicate that the methods provide feedback control laws that make the stability of the nominal closed loop systems less sensitive to changes in dynamic pressure, while maintaining acceptable control power and robustness constraints.

Fennell, Robert E.↗

NASA NTRS1985

Large eddy interactions in a turbulent channel flow

The dynamic processes of large eddies in a turbulent channel flow have been examined by utilizing an orthogonal expansion of the velocity fluctuation, known in the literature as the Proper Orthogonal Decomposition Theorem. The mathematical form of these functions is unknown in contrast to the Fourier analysis. Attention is focused on the nonlinear, turbulence-turbulence interaction process in the dynamical equation for large eddies (the first term in the expansion). The nonlinear interactions of the components of the first mode are treated exactly, but influences of higher modes are modeled. This requires adjustment of both the skewness and the effective Reynolds number so that the energy equilibrium of the large eddies is ensured when the mean velocity distribution is assumed known for experiments. Computational results show that the first mode contributes significantly to turbulent intensities and possesses a structural and statistical character similar to that of the entire flow.

Hong, S. K.↗

NASA NTRS1987

A low dimensional dynamical system for the wall layer

Low dimensional dynamical systems which model a fully developed turbulent wall layer were derived.The model is based on the optimally fast convergent proper orthogonal decomposition, or Karhunen-Loeve expansion. This decomposition provides a set of eigenfunctions which are derived from the autocorrelation tensor at zero time lag. Via Galerkin projection, low dimensional sets of ordinary differential equations in time, for the coefficients of the expansion, were derived from the Navier-Stokes equations. The energy loss to the unresolved modes was modeled by an eddy viscosity representation, analogous to Heisenberg's spectral model. A set of eigenfunctions and eigenvalues were obtained from direct numerical simulation of a plane channel at a Reynolds number of 6600, based on the mean centerline velocity and the channel width flow and compared with previous work done by Herzog. Using the new eigenvalues and eigenfunctions, a new ten dimensional set of ordinary differential equations were derived using five non-zero cross-stream Fourier modes with a periodic length of 377 wall units. The dynamical system was integrated for a range of the eddy viscosity prameter alpha. This work is encouraging.

Aubry, N.↗

NASA NTRS2001

System Identification and POD Method Applied to Unsteady Aerodynamics

The representation of unsteady aerodynamic flow fields in terms of global aerodynamic modes has proven to be a useful method for reducing the size of the aerodynamic model over those representations that use local variables at discrete grid points in the flow field. Eigenmodes and Proper Orthogonal Decomposition (POD) modes have been used for this purpose with good effect. This suggests that system identification models may also be used to represent the aerodynamic flow field. Implicit in the use of a systems identification technique is the notion that a relative small state space model can be useful in describing a dynamical system. The POD model is first used to show that indeed a reduced order model can be obtained from a much larger numerical aerodynamical model (the vortex lattice method is used for illustrative purposes) and the results from the POD and the system identification methods are then compared. For the example considered, the two methods are shown to give comparable results in terms of accuracy and reduced model size. The advantages and limitations of each approach are briefly discussed. Both appear promising and complementary in their characteristics.

Tang, Deman↗

NASA NTRS1992

A hybrid formulation of a component mode synthesis method

Component mode synthesis is a substructuring technique frequently employed in structural dynamics. In this method, a given structure is subdivided into components or substructures, each of which is analyzed independently for natural frequencies and for mode shapes. The substructure mode shapes are then assembled to give displacement shapes or load patterns of the original structure. An analytical justification of the basic concept is presented using spectral decompositions, and a variant substructuring approach where intersubstructure continuity is enforced in a weak form is derived. This leads to a hybrid formulation of the basic method which is particularly suitable for assembling heterogeneous substructures and analyzing nonconforming and incompatible finite element substructure models. For problems where both the basic and hybrid methods are applicable, the hybrid variant can be computationally more advantageous.

Farhat, Charbel↗

NASA NTRS2001

Dynamic modeling of gene expression data

We describe the time evolution of gene expression levels by using a time translational matrix to predict future expression levels of genes based on their expression levels at some initial time. We deduce the time translational matrix for previously published DNA microarray gene expression data sets by modeling them within a linear framework by using the characteristic modes obtained by singular value decomposition. The resulting time translation matrix provides a measure of the relationships among the modes and governs their time evolution. We show that a truncated matrix linking just a few modes is a good approximation of the full time translation matrix. This finding suggests that the number of essential connections among the genes is small.

NASA Discipline Plant Biology↗

DOE OSTI2026

Comparison between explicit and implicit discretization strategies for a dissipative thermal environment

We investigate strategies for simulating open quantum systems coupled to dissipative baths by comparing explicit wave function-based discretization [via multi-layer multi-configuration time-dependent Hartree (ML-MCTDH)] and the implicit density matrix-based master equation method [via tree tensor network hierarchical equations of motion (TTN-HEOM)]. For dissipative baths characterized by exponentially decaying bath correlation functions, the implicit discretization approach of HEOM—rooted in bath correlation function decompositions—proves significantly more efficient than explicit discretization of the bath into discrete harmonic modes. Explicit methods, like ML-MCTDH, require extensive mode discretization to approximate continuum baths, leading to computational bottlenecks. Case studies for two-level systems and a Fenna–Matthews–Olson complex model highlight TTN-HEOM’s superiority in capturing dissipative dynamics with relaxations with a minimal number of auxiliary modes, while the explicit methods are as exact as the HEOM in pure dephasing regimes. This comparison is enabled by the TENSO package, which has both ML-MCTDH and TTN-HEOM implemented using the same computational structure and propagation strategy.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1985

Decomposition and state variable feedback control of elastic robotic systems

Energy-efficient, lightweight robot arms for space applications have considerable structural flexibility. An approach to control of a class of flexible robotic systems is presented. A control law is derived which decouples the joint-angle motion from the flexible motion and, in addition, asymptotically decomposes the elastic dynamics into two subsystems. This 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 uncertaintly in system parameters. Simulation results show that the combination of nonlinear decoupling and elastic stabilization permits rapid, accurate tracking of large joint angle commands with well damped elastic response, in spite of space vehicle motion and payload uncertainty.

Singh, S. N.↗

NASA NTRS2003

Non-Linear Structural Dynamics Characterization using a Scanning Laser Vibrometer

This paper presents the use of a scanning laser vibrometer and a signal decomposition method to characterize non-linear dynamics of highly flexible structures. A Polytec PI PSV-200 scanning laser vibrometer is used to measure transverse velocities of points on a structure subjected to a harmonic excitation. Velocity profiles at different times are constructed using the measured velocities, and then each velocity profile is decomposed using the first four linear mode shapes and a least-squares curve-fitting method. From the variations of the obtained modal \ielocities with time we search for possible non-linear phenomena. A cantilevered titanium alloy beam subjected to harmonic base-excitations around the second. third, and fourth natural frequencies are examined in detail. Influences of the fixture mass. gravity. mass centers of mode shapes. and non-linearities are evaluated. Geometrically exact equations governing the planar, harmonic large-amplitude vibrations of beams are solved for operational deflection shapes using the multiple shooting method. Experimental results show the existence of 1:3 and 1:2:3 external and internal resonances. energy transfer from high-frequency modes to the first mode. and amplitude- and phase- modulation among several modes. Moreover, the existence of non-linear normal modes is found to be questionable.

Pai, P. F.↗

NASA NTRS2007

Wavefront Control Toolbox for James Webb Space Telescope Testbed

We have developed a Matlab toolbox for wavefront control of optical systems. We have applied this toolbox to the optical models of James Webb Space Telescope (JWST) in general and to the JWST Testbed Telescope (TBT) in particular, implementing both unconstrained and constrained wavefront optimization to correct for possible misalignments present on the segmented primary mirror or the monolithic secondary mirror. The optical models implemented in Zemax optical design program and information is exchanged between Matlab and Zemax via the Dynamic Data Exchange (DDE) interface. The model configuration is managed using the XML protocol. The optimization algorithm uses influence functions for each adjustable degree of freedom of the optical mode. The iterative and non-iterative algorithms have been developed to converge to a local minimum of the root-mean-square (rms) of wavefront error using singular value decomposition technique of the control matrix of influence functions. The toolkit is highly modular and allows the user to choose control strategies for the degrees of freedom to be adjusted on a given iteration and wavefront convergence criterion. As the influence functions are nonlinear over the control parameter space, the toolkit also allows for trade-offs between frequency of updating the local influence functions and execution speed. The functionality of the toolbox and the validity of the underlying algorithms have been verified through extensive simulations.

Shiri, Ron↗

NASA NTRS1985

An Eigensystem Realization Algorithm (ERA) for modal parameter identification and model reduction

A method, called the Eigensystem Realization Algorithm (ERA), is developed for modal parameter identification and model reduction of dynamic systems from test data. A new approach is introduced in conjunction with the singular value decomposition technique to derive the basic formulation of minimum order realization which is an extended version of the Ho-Kalman algorithm. The basic formulation is then transformed into modal space for modal parameter identification. Two accuracy indicators are developed to quantitatively identify the system modes and noise modes. For illustration of the algorithm, examples are shown using simulation data and experimental data for a rectangular grid structure.

Juang, J. N.↗

NASA NTRS1988

Flexible spacecraft maneuver - Inverse attitude control and modal stabilization

A control law is presented for three-axis rotational maneuvers of a spacecraft (orbiter)-beam-tip body (antenna or a reflector) configuration based on nonlinear inversion and modal velocity feedback. Using invertibility and functional reproducibility results, a decoupling attitude control law is presented such that, in the closed-loop system, the attitude angles of the spacecraft are independently controlled using the control moments acting on the space vehicle. This controller asymptotically decouples the flexible dynamics from the rigid one and also allows the decomposition of the elastic dynamics into two subsystems representing the transverse deflections of the beam in two orthogonal planes. These low-order subsystems are used for derivation of a modal velocity feedback stabilizer using the force and moment actuators at the end body. Simulation results are presented to show that, in the closed-loop system, attitude control and elastic mode stabilization are accomplished in spite of the parameter uncertainty and disturbance torque input in the system.

Singh, Sahjendra N.↗

NASA NTRS2011

High Frequency Acoustic Response Characterization and Analysis of the Deep Throttling Common Extensible Cryogenic Engine

The Common Extensive Cryogenic Engine program demonstrated the operation of a deep throttling engine design. The program, spanning five years from August 2005 to July 2010, funded testing through four separate engine demonstration test series. Along with successful completion of multiple objectives, a discrete response of approximately 4000 Hz was discovered and explored throughout the program. The typical low-amplitude acoustic response was evident in the chamber measurement through almost every operating condition; however, at certain off-nominal operating conditions, the response became discrete with higher amplitude. This paper summarizes the data reduction, characterization, and analysis of the 4,000 Hz response for the entire program duration, using the large amount of data collected. Upon first encountering the response, new objectives and instrumentation were incorporated in future test series to specifically collect 4,000 Hz data. The 4,000 Hz response was identified as being related to the first tangential acoustic mode by means of frequency estimation and spatial decomposition. The latter approach showed that the effective node line of the mode was aligned with the manifold propellant inlets with standing waves and quasi-standing waves present at various times. Contour maps that contain instantaneous frequency and amplitude trackings of the response were generated as a significant improvement to historical manual approaches of data reduction presentation. Signal analysis and dynamic data reduction also uncovered several other features of the response including a stable limit cycle, the progressive engagement of subsequent harmonics, the U-shaped time history, an intermittent response near the test-based neutral stability region, other acoustic modes, and indications of modulation with a separate subsynchronous response. Although no engine damage related to the acoustic mode was noted, the peak-to-peak fluctuating pressure amplitude achieved 12.1% of the mean chamber pressure at its highest. The identification of this response in terms of an instability is also discussed.

Casiano, M. J.↗