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NASA NTRS1989

Accurate calculation of control-augmented structural eigenvalue sensitivities using reduced-order models

A method is presented for generating mode shapes for model order reduction in a way that leads to accurate calculation of eigenvalue derivatives and eigenvalues for a class of control augmented structures. The method is based on treating degrees of freedom where control forces act or masses are changed in a manner analogous to that used for boundary degrees of freedom in component mode synthesis. It is especially suited for structures controlled by a small number of actuators and/or tuned by a small number of concentrated masses whose positions are predetermined. A control augmented multispan beam with closely spaced natural frequencies is used for numerical experimentation. A comparison with reduced-order eigenvalue sensitivity calculations based on the normal modes of the structure shows that the method presented produces significant improvements in accuracy.

Livne, Eli↗

NASA NTRS2017

LPV Modeling of a Flexible Wing Aircraft Using Modal Alignment and Adaptive Gridding Methods

One of the earliest approaches in gain-scheduling control is the gridding based approach, in which a set of local linear time-invariant models are obtained at various gridded points corresponding to the varying parameters within the flight envelop. In order to ensure smooth and effective Linear Parameter-Varying control, aligning all the flexible modes within each local model and maintaining small number of representative local models over the gridded parameter space are crucial. In addition, since the flexible structural models tend to have large dimensions, a tractable model reduction process is necessary. In this paper, the notion of s-shifted H2- and H Infinity-norm are introduced and used as a metric to measure the model mismatch. A new modal alignment algorithm is developed which utilizes the defined metric for aligning all the local models over the entire gridded parameter space. Furthermore, an Adaptive Grid Step Size Determination algorithm is developed to minimize the number of local models required to represent the gridded parameter space. For model reduction, we propose to utilize the concept of Composite Modal Cost Analysis, through which the collective contribution of each flexible mode is computed and ranked. Therefore, a reduced-order model is constructed by retaining only those modes with significant contribution. The NASA Generic Transport Model operating at various flight speeds is studied for verification purpose, and the analysis and simulation results demonstrate the effectiveness of the proposed modeling approach.

LPV Modeling↗

NASA NTRS1985

Interactive software for spectral assignment

A new interactive computer software package for eigenvalue/eigenvector assignment using constant state feedback is described. The package consists of ten subprograms, each associated with a specific design objective, accessible from a main control program. Using this package, primary design objectives of assigning eigenvalues and approximating eigenvectors are first achieved. Then secondary design objectives, including modification of specific eigenvector components, reduction in specified elements of the feedback gain matrix, and reduction in eigensystem sensitivity to changes in plant parameters, are addressed. These secondary objectives are achieved by a systematic modification of the assigned eigenvectors in a small region about the initial assignment. In addition, the program implements the use of spectral assignment procedures with reduced-order system models. Program modes are described and illustrated by numerical examples.

Mielke, R. R.↗

NASA NTRS1992

Enhanced Method Of Reduction Of Dynamical Models

Enhanced projection-and-assembly method is recent product of efforts to model mathematically dynamics of vibrations of large, flexible structures. In projection-and-assembly method modes contributing significantly to control input and output points selected at system (overall structure) level, then projected (in abstract mathematical sense) onto components of system. In enhanced version, static correction modes capture static contributions of those modes neglected in reduced-order model. Reduced models for suppressing vibrations of structures made more accurate.

Lee, Allan Y.↗

NASA NTRS1989

CSI compensation for reduced-order model based control of a flexible robot manipulator

In controller design for flexible structures, certain system modes are extremely important for the overall performance of the structure. A reduced-order model (ROM) based control focuses on these modes, providing a viable, active control algorithm for large systems. Unfortunately, unmodeled structure dynamics can interact with the ROM controller (CSI) and cause crippling deterioration of system performance, possibly to the point that system stability is lost. A residual model filter (RMF) eliminates one channel of control structure interaction (CSI), while adding only a simple, second-order filter to the control loop. Thus, the ROM controller can be designed independently, based strictly on performance criteria, and residual mode filters can then be selected to compensate for CSI. A flexible robot manipulator is used for preliminary experimentation with the ROM/RMF design methodology. Since the controller was to be implemented both with, and without compensation for CSI, the ROM control gains are carefully chosen such that closed loop stability is never compromised. In this way, RMF effectiveness is easily evaluated in terms of the improvement in system performance resulting from CSI compensation.

Reisenauer, Brian T.↗

NASA NTRS1984

Design of multivariable feedback control systems via spectral assignment using reduced-order models and reduced-order observers

The feasibility of using reduced order models and reduced order observers with eigenvalue/eigenvector assignment procedures is investigated. A review of spectral assignment synthesis procedures is presented. Then, a reduced order model which retains essential system characteristics is formulated. A constant state feedback matrix which assigns desired closed loop eigenvalues and approximates specified closed loop eigenvectors is calculated for the reduced order model. It is shown that the eigenvalue and eigenvector assignments made in the reduced order system are retained when the feedback matrix is implemented about the full order system. In addition, those modes and associated eigenvectors which are not included in the reduced order model remain unchanged in the closed loop full order system. The full state feedback design is then implemented by using a reduced order observer. It is shown that the eigenvalue and eigenvector assignments of the closed loop full order system rmain unchanged when a reduced order observer is used. The design procedure is illustrated by an actual design problem.

Mielke, R. R.↗

NASA NTRS1985

Design of multivariable feedback control systems via spectral assignment using reduced-order models and reduced-order observers

The feasibility of using reduced order models and reduced order observers with eigenvalue/eigenvector assignment procedures is investigated. A review of spectral assignment synthesis procedures is presented. Then, a reduced order model which retains essential system characteristics is formulated. A constant state feedback matrix which assigns desired closed loop eigenvalues and approximates specified closed loop eigenvectors is calculated for the reduced order model. It is shown that the eigenvalue and eigenvector assignments made in the reduced order system are retained when the feedback matrix is implemented about the full order system. In addition, those modes and associated eigenvectors which are not included in the reduced order model remain unchanged in the closed loop full order system. The fulll state feedback design is then implemented by using a reduced order observer. It is shown that the eigenvalue and eigenvector assignments of the closed loop full order system remain unchanged when a reduced order observer is used. The design procedure is illustrated by an actual design problem.

Mielke, R. R.↗

NASA NTRS2004

Reduced-Order Blade Mistuning Analysis Techniques Developed for the Robust Design of Engine Rotors

The primary objective of this research program is to develop vibration analysis tools, design tools, and design strategies to significantly improve the safety and robustness of turbine engine rotors. Bladed disks in turbine engines always feature small, random blade-to-blade differences, or mistuning. Mistuning can lead to a dramatic increase in blade forced-response amplitudes and stresses. Ultimately, this results in high-cycle fatigue, which is a major safety and cost concern. In this research program, the necessary steps will be taken to transform a state-of-the-art vibration analysis tool, the Turbo-Reduce forced-response prediction code, into an effective design tool by enhancing and extending the underlying modeling and analysis methods. Furthermore, novel techniques will be developed to assess the safety of a given design. In particular, a procedure will be established for using eigenfrequency curve veerings to identify "danger zones" in the operating conditions--ranges of rotational speeds and engine orders in which there is a great risk that the rotor blades will suffer high stresses. This work also will aid statistical studies of the forced response by reducing the necessary number of simulations. Finally, new strategies for improving the design of rotors will be pursued. Several methods will be investigated, including the use of intentional mistuning patterns to mitigate the harmful effects of random mistuning, and the modification of disk stiffness to avoid reaching critical values of interblade coupling in the desired operating range. Recent research progress is summarized in the following paragraphs. First, significant progress was made in the development of the component mode mistuning (CMM) and static mode compensation (SMC) methods for reduced-order modeling of mistuned bladed disks (see the following figure). The CMM method has been formalized and extended to allow a general treatment of mistuning. In addition, CMM allows individual mode mistuning, which accounts for the realistic effects of local variations in blade properties that lead to different mistuning values for different mode types (e.g., mistuning of the first torsion mode versus the second flexural mode). The accuracy and efficiency of the CMM method and the corresponding Turbo-Reduce code were validated for an example finite element model of a bladed disk.

Min, James B.↗

NASA NTRS1985

Normal modes in an overmoded circular waveguide coated with lossy material

The normal modes in an overmoded waveguide coated with a lossy material are analyzed, particularly for their attenuation properties as a function of coating material, layer thickness, and frequency. When the coating material is not too lossy, the low-order modes are highly attenuated even with a thin layer of coating. This coated guide serves as a mode suppressor of the low-order modes, which can be particularly useful for reducing the radar cross section (RCS) of a cavity structure such as a jet inlet. When the coating material is very lossy, low-order modes fall into two distinct groups: highly and lowly attenuated modes. However, as a/lambda (a = radius of the cylinder; lambda = the free-space wavelength) increases, the separation between these two groups becomes less distinctive. The attenuation constants of most of the low-order modes become small, and decrease as a function of lambda sup 2/a sup 3.

Lee, C. S.↗

NASA NTRS1986

Normal modes in an overmoded circular waveguide coated with lossy material

The normal modes in an overmoded waveguide coated with a lossy material are analyzed, particularly for their attenuation properties as a function of coating material, layer thickness, and frequency. When the coating material is not too lossy, the low-order modes are highly attenuated even with a thin layer of coating. This coated guide serves as a mode suppressor of the low-order modes, which can be particularly useful for reducing the radar cross section of a cavity structure such as a jet engine inlet. When the coating material is very lossy, low-order modes fall into two distinct groups: highly and lowly attenuated modes. However, as a/lambda (a = radius of the cylinder; lambda = the free-space wavelength) increases, the separation between these two groups becomes less distinctive. The attenuation constants of most of the low-order modes become small and decrease as a function of lambda-squared/a-cubed.

Lee, C. S.↗

NASA NTRS1999

Acoustic Reflection and Transmission of 2-Dimensional Rotors and Stators, Including Mode and Frequency Scattering Effects

A reduced order modeling scheme has been developed for the unsteady acoustic and vortical coupling between blade rows of a turbomachine. The essential behavior of the system is governed by modal scattering coefficients (i.e., reflection and transmission coefficients) of the rotor, stator, inlet and nozzle, which are calculated as if they were connected to non-reflecting ducts. The objective of this report is to identify fundamental behavior of these scattering coefficients for a better understanding of the role of blade row reflection and transmission in noise generation. A 2D flat plate unsteady cascade model is used for the analysis with the expectation that the general behavior presented herein will carry over to models that include more realistic flow and geometry. It is shown that stators scatter input waves into many modes at the same frequency whereas rotors scatter on frequency, or harmonic order. Important cases are shown here the rotor reflection coefficient is greater than unity; a mode at blade passing frequency (BPF) traveling from the stator with unit sound power is reflected by the rotor with more than unit power at 2xBPF and 3xBPE Analysis is presented to explain this unexpected phenomenon. Scattering curves are presented in a format chosen for design use and for physical interpretation. To aid in interpretation of the curves, formulas are derived for special condition where waveforms are parallel to perpendicular to the rotor.

Hanson, Donald B.↗

NASA NTRS1993

Component modes damping assignment methodology for articulated, multiflexible body structures

To simulate the dynamical motion of articulated, multiflexible body structures, one can use multibody simulation packages such as DISCOS. To this end, one must supply appropriate reduced-order models for all of the flexible components involved. The component modes projection and assembly model reduction (COMPARE) methodology is one way to construct these reduced-order component models, which when reassembled capture important system input-to-output mapping of the full-order model at multiple system configurations of interest. In conjunction, we must also supply component damping matrices which when reassembled generate a system damping matrix that has certain desirable properties. The problem of determining the damping factors of components' modes to achieve a given system damping matrix is addressed here. To this end, we must establish from first principles a matrix-algebraic relation between the system's modal damping matrix and the components' modal damping matrices. An unconstrained/constrained optimization problem can then be formulated to determine the component modes' damping factors that best satisfy that matrix-algebraic relation. The effectiveness of the developed methodology, called ModeDamp, has been successfully demonstrated on a high-order, finite element model of the Galileo spacecraft.

Lee, Allan Y.↗

NASA NTRS1987

Modeling and control of beam-like structures

The most popular finite element codes are based upon appealing theories of convergence of modal frequencies. For example, the popularity of cubic elements for beam-like structures is due to the rapid convergence of modal frequencies and stiffness properties. However, for those problems in which the primary consideration is the accuracy of response of the structure at specified locations it is more important to obtain accuracy in the modal costs than in the modal frequencies. The modal cost represents the contribution of a mode in the norm of the response vector. This paper provides a complete modal cost analysis for beam-like continua. Upper bounds are developed for mode truncation errors in the model reduction process and modal cost analysis dictates which modes to retain in order to reduce the model for control design purposes.

Hu, A.↗

NASA NTRS1988

Modal cost analysis for simple continua

The most popular finite element codes are based upon appealing theories of convergence of modal frequencies. For example, the popularity of cubic elements for beam-like structures is due to the rapid convergence of modal frequencies and stiffness properties. However, for those problems in which the primary consideration is the accuracy of response of the structure at specified locations, it is more important to obtain accuracy in the modal costs than in the modal frequencies. The modal cost represents the contribution of a mode in the norm of the response vector. This paper provides a complete modal cost analysis for simple continua such as beam-like structures. Upper bounds are developed for mode truncation errors in the model reduction process and modal cost analysis dictates which modes to retain in order to reduce the model for control design purposes.

Hu, A.↗

NASA NTRS2020

Multiple Shaker Placement for Ground Vibration Test of X-59 Aircraft Using Topology Optimization

A multiple shaker placement methodology is developed and tested using a topology optimization technique. Current multiple shaker placement methodology requires optimum accelerometer placement and optimum single-shaker placement techniques. The proposed methodology is tested using a finite element model of the X-59 Low Boom Flight Demonstrator aircraft. The effective independence and the driving point acceleration transfer function (DPATF) methods are used for the accelerometer placement study. In this study, four shakers are used to excite each mode more effectively during the ground vibration test; all the modes of interest thus are separated into four groups. Each shaker takes care of a separate group of modes. Grouping the modes of interest is performed utilizing topology optimization. The number of modes for each group therefore will be automatically decided during grouping. For each group of modes, perform the following two steps to determine optimal location of four shakers: 1) At each accelerometer location, compare the magnitude of DPATF values at natural frequencies, select the minimum value, and make a vector with these minimum values of the DPATF magnitudes for each group; and 2) Select the degrees of freedom corresponding to the maximum value of this vector. The objective function value is the maximum value of the vector with minimum value of the magnitude of the superposed acceleration transfer function. This objective function value is maximized by changing the modes for each group. Forty accelerometers are enough to have good correlation between mode shapes obtained from the reduced order model and the simulated ground vibration test.

Optimization Analysis↗

NASA NTRS2010

Reduced Order Modeling Incompressible Flows

The details: a) Need stable numerical methods; b) Round off error can be considerable; c) Not convinced modes are correct for incompressible flow. Nonetheless, can derive compact and accurate reduced-order models. Can be used to generate actuator models or full flow-field models

Helenbrook, B. T.↗

NASA NTRS2019

Few-Mode Fiber Coupled Superconducting Nanowire Single-Photon Detectors for Photon Efficient Optical Communications

The NASA Glenn Research Center's development of a high-photon efficiency real-time optical communications ground receiver has added superconducting nanowire single-photon detectors (SNSPDs) coupled with few-mode fibers (FMF). High data rate space-to-ground optical communication links require enhanced ground receiver sensitivity to reduce spacecraft transmitter constraints, and therefore require highly efficient coupling from fiber to detector. In the presence of atmospheric turbulence the received optical wave front can be severely distorted introducing higher-order spatial mode components to the received signal. To reduce mode filtering and mismatch loss and the resulting degradations to detector coupling efficiency, we explore the use of few-mode fiber coupling to commercial single-pixel SNSPDs. Graded index 20-µm few-mode fibers allow the commercial single pixel SNSPD's active area to couple with equal efficiency as single mode fibers. Here we determine detector characteristics such as count rate, detection efficiency, dark counts, and jitter, as well as detection efficiencies for higher-order fiber spatial modes. Additionally, we assess the laboratory performance of the detectors in an optical system which emulates future deep space optical communications links.

Vyhnalek, Brian E.↗

NASA NTRS1990

Selection of component modes

Structural dynamic models of complex spacecraft are often assembled from a number of component models. In this paper, three methods for reducing the order of these component models are presented by selecting 'important' fixed interface component modes. These methods are applied to two component structures of the Space Station Freedom: a photovoltaic (PV) array and a solar dynamic collector. The reduced order models of these components retain a small fraction of the number of modes in the original models while accurately representing a set of outputs chosen by the user.

Blelloch, Paul A.↗