Matching Items (7)

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Reduced order modeling with variable spatial fidelity for the linear and nonlinear dynamics of multi-bay structures

Description

This investigation develops small-size reduced order models (ROMs) that provide an accurate prediction of the response of only part of a structure, referred to as component-centric ROMs. Four strategies to

This investigation develops small-size reduced order models (ROMs) that provide an accurate prediction of the response of only part of a structure, referred to as component-centric ROMs. Four strategies to construct such ROMs are presented, the first two of which are based on the Craig-Bampton Method and start with a set of modes for the component of interest (the β component). The response in the rest of the structure (the α component) induced by these modes is then determined and optimally represented by applying a Proper Orthogonal Decomposition strategy using Singular Value Decomposition. These first two methods are effectively basis reductions techniques of the CB basis. An approach based on the “Global - Local” Method generates the “global” modes by “averaging” the mass property over α and β comp., respectively (to extract a “coarse” model of α and β) and the “local” modes orthogonal to the “global” modes to add back necessary “information” for β. The last approach adopts as basis for the entire structure its linear modes which are dominant in the β component response. Then, the contributions of other modes in this part of the structure are approximated in terms of those of the dominant modes with close natural frequencies and similar mode shapes in the β component. In this manner, the non-dominant modal contributions are “lumped” onto the dominant ones, to reduce the number of modes for a prescribed accuracy. The four approaches are critically assessed on the structural finite element model of a 9-bay panel with the modal lumping-based method leading to the smallest sized ROMs. Therefore, it is extended to the nonlinear geometric situation and first recast as a rotation of the modal basis to achieve unobservable modes. In the linear case, these modes completely disappear from the formulation owing to orthogonality. In the nonlinear case, however, the generalized coordinates of these modes are still present in the nonlinear terms of the observable modes. A closure-type algorithm is then proposed to eliminate the unobserved generalized coordinates. This approach, its accuracy and computational savings, was demonstrated on a simple beam model and the 9-bay panel model.

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Date Created
  • 2017

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Reduced order model-based prediction of the nonlinear geometric response of a panel under thermal, aerodynamic, and acoustic loads

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This paper addresses some aspects of the development of fully coupled thermal-structural reduced order modeling of planned hypersonic vehicles. A general framework for the construction of the structural and thermal

This paper addresses some aspects of the development of fully coupled thermal-structural reduced order modeling of planned hypersonic vehicles. A general framework for the construction of the structural and thermal basis is presented and demonstrated on a representative panel considered in prior investigations. The thermal reduced order model is first developed using basis functions derived from appropriate conduction eigenvalue problems. The modal amplitudes are the solution of the governing equation, which is nonlinear due to the presence of radiation and temperature dependent capacitance and conductance matrices, and the predicted displacement field is validated using published data. A structural reduced order model was developed by first selecting normal modes of the system and then constructing associated dual modes for the capturing of nonlinear inplane displacements. This isothermal model was validated by comparison with full finite element results (Nastran) in static and dynamic loading environments. The coupling of this nonlinear structural reduced order model with the thermal reduced order model is next considered. Displacement-induced thermal modes are constructed in order to account for the effect that structural deflections will have on the thermal problem. This coupling also requires the enrichment of the structural basis to model the elastic deformations that may be produced consistently with the thermal reduced order model. The validation of the combined structural-thermal reduced order model is carried out with pure mechanical loads, pure thermal loads, and combined mechanical-thermal excitations. Such comparisons are performed here on static solutions with temperature increases up to 2200F and pressures up to 3 psi for which the maximum displacements are of the order of 3 thicknesses. The reduced order model predicted results agree well with the full order finite element predictions in all of these various cases. A fully coupled analysis was performed in which the solution of the structural-thermal-aerodynamic reduced order model was carried out for 300 seconds and validated against a full order model. Finally, a reduced order model of a thin, aluminum beam is extended to include linear variations with local temperature of the elasticity tensor and coefficients of thermal expansion.

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Date Created
  • 2014

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Modeling, analysis, and control of a hypersonic vehicle with significant aero-thermo-elastic-propulsion interactions: elastic, thermal and mass uncertainty

Description

This thesis examines themodeling, analysis, and control system design issues for scramjet powered hypersonic vehicles. A nonlinear three degrees of freedom longitudinal model which includes aero-propulsion-elasticity effects was used for

This thesis examines themodeling, analysis, and control system design issues for scramjet powered hypersonic vehicles. A nonlinear three degrees of freedom longitudinal model which includes aero-propulsion-elasticity effects was used for all analyses. This model is based upon classical compressible flow and Euler-Bernouli structural concepts. Higher fidelity computational fluid dynamics and finite element methods are needed for more precise intermediate and final evaluations. The methods presented within this thesis were shown to be useful for guiding initial control relevant design. The model was used to examine the vehicle's static and dynamic characteristics over the vehicle's trimmable region. The vehicle has significant longitudinal coupling between the fuel equivalency ratio (FER) and the flight path angle (FPA). For control system design, a two-input two-output plant (FER - elevator to speed-FPA) with 11 states (including 3 flexible modes) was used. Velocity, FPA, and pitch were assumed to be available for feedback. Aerodynamic heat modeling and design for the assumed TPS was incorporated to original Bolender's model to study the change in static and dynamic properties. De-centralized control stability, feasibility and limitations issues were dealt with the change in TPS elasticity, mass and physical dimension. The impact of elasticity due to TPS mass, TPS physical dimension as well as prolonged heating was also analyzed to understand performance limitations of de-centralized control designed for nominal model.

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Date Created
  • 2011

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Multidisciplinary optimization for the design and control of uncertain dynamical systems

Description

This dissertation considers an integrated approach to system design and controller design based on analyzing limits of system performance. Historically, plant design methodologies have not incorporated control relevant considerations. Such

This dissertation considers an integrated approach to system design and controller design based on analyzing limits of system performance. Historically, plant design methodologies have not incorporated control relevant considerations. Such an approach could result in a system that might not meet its specifications (or one that requires a complex control architecture to do so). System and controller designers often go through several iterations in order to converge to an acceptable plant and controller design. The focus of this dissertation is on the design and control an air-breathing hypersonic vehicle using such an integrated system-control design framework. The goal is to reduce the number of system-control design iterations (by explicitly incorporate control considerations in the system design process), as well as to influence the guidance/trajectory specifications for the system. Due to the high computational costs associated with obtaining a dynamic model for each plant configuration considered, approximations to the system dynamics are used in the control design process. By formulating the control design problem using bilinear and polynomial matrix inequalities, several common control and system design constraints can be simultaneously incorporated into a vehicle design optimization. Several design problems are examined to illustrate the effectiveness of this approach (and to compare the computational burden of this methodology against more traditional approaches).

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Date Created
  • 2014

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Thermoelastodynamic responses of panels through reduced order modeling: oscillating flux and temperature dependent properties

Description

This thesis focuses on the continued extension, validation, and application of combined thermal-structural reduced order models for nonlinear geometric problems. The first part of the thesis focuses on the determination

This thesis focuses on the continued extension, validation, and application of combined thermal-structural reduced order models for nonlinear geometric problems. The first part of the thesis focuses on the determination of the temperature distribution and structural response induced by an oscillating flux on the top surface of a flat panel. This flux is introduced here as a simplified representation of the thermal effects of an oscillating shock on a panel of a supersonic/hypersonic vehicle. Accordingly, a random acoustic excitation is also considered to act on the panel and the level of the thermo-acoustic excitation is assumed to be large enough to induce a nonlinear geometric response of the panel. Both temperature distribution and structural response are determined using recently proposed reduced order models and a complete one way, thermal-structural, coupling is enforced. A steady-state analysis of the thermal problem is first carried out that is then utilized in the structural reduced order model governing equations with and without the acoustic excitation. A detailed validation of the reduced order models is carried out by comparison with a few full finite element (Nastran) computations. The computational expedience of the reduced order models allows a detailed parametric study of the response as a function of the frequency of the oscillating flux. The nature of the corresponding structural ROM equations is seen to be of a Mathieu-type with Duffing nonlinearity (originating from the nonlinear geometric effects) with external harmonic excitation (associated with the thermal moments terms on the panel). A dominant resonance is observed and explained. The second part of the thesis is focused on extending the formulation of the combined thermal-structural reduced order modeling method to include temperature dependent structural properties, more specifically of the elasticity tensor and the coefficient of thermal expansion. These properties were assumed to vary linearly with local temperature and it was found that the linear stiffness coefficients and the "thermal moment" terms then are cubic functions of the temperature generalized coordinates while the quadratic and cubic stiffness coefficients were only linear functions of these coordinates. A first validation of this reduced order modeling strategy was successfully carried out.

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Date Created
  • 2011

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Control relevant modeling and design of scramjet-powered hypersonic vehicles

Description

This report provides an overview of scramjet-powered hypersonic vehicle modeling and control challenges. Such vehicles are characterized by unstable non-minimum phase dynamics with significant coupling and low thrust margins. Recent

This report provides an overview of scramjet-powered hypersonic vehicle modeling and control challenges. Such vehicles are characterized by unstable non-minimum phase dynamics with significant coupling and low thrust margins. Recent trends in hypersonic vehicle research are summarized. To illustrate control relevant design issues and tradeoffs, a generic nonlinear 3DOF longitudinal dynamics model capturing aero-elastic-propulsive interactions for wedge-shaped vehicle is used. Limitations of the model are discussed and numerous modifications have been made to address control relevant needs. Two different baseline configurations are examined over a two-stage to orbit ascent trajectory. The report highlights how vehicle level-flight static (trim) and dynamic properties change over the trajectory. Thermal choking constraints are imposed on control system design as a direct consequence of having a finite FER margin. The implication of this state-dependent nonlinear FER margin constraint, the right half plane (RHP) zero, and lightly damped flexible modes, on control system bandwidth (BW) and FPA tracking has been discussed. A control methodology has been proposed that addresses the above dynamics while providing some robustness to modeling uncertainty. Vehicle closure (the ability to fly a trajectory segment subject to constraints) is provided through a proposed vehicle design methodology. The design method attempts to use open loop metrics whenever possible to design the vehicle. The design method is applied to a vehicle/control law closed loop nonlinear simulation for validation. The 3DOF longitudinal modeling results are validated against a newly released NASA 6DOF code.

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Date Created
  • 2012

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Modeling, analysis, and control of a hypersonic vehicle with significant aero-thermo-elastic-propulsion interactions, and propulsive uncertainty

Description

This thesis examines the modeling, analysis, and control system design issues for scramjet powered hypersonic vehicles. A nonlinear three degrees of freedom longitudinal model which includes aero-propulsion-elasticity effects was used

This thesis examines the modeling, analysis, and control system design issues for scramjet powered hypersonic vehicles. A nonlinear three degrees of freedom longitudinal model which includes aero-propulsion-elasticity effects was used for all analysis. This model is based upon classical compressible flow and Euler-Bernouli structural concepts. Higher fidelity computational fluid dynamics and finite elementmethods are needed formore precise intermediate and final evaluations. The methods presented within this thesis were shown to be useful for guiding initial control relevant design. The model was used to examine the vehicles static and dynamic characteristics over the vehicles trimmable region. The vehicle has significant longitudinal coupling between the fuel equivalency ratio (FER) and the flight path angle (FPA). For control system design, a two-input two-output plant (FER - elevator to speed-FPA) with 11 states (including 3 flexible modes) was used. Velocity, FPA, and pitch were assumed to be available for feedback. Propulsion system design issues were given special consideration. The impact of engine characteristics (design) and plume model on control system design were addressed.Various engine designs were considered for comparison purpose. With accurate plume modeling, effective coupling from the FER to the FPA was increased, which made the peak frequency-dependent (singular value) conditioning of the two-input two-output plant (FER-elevator to speed-FPA) worse. This forced the control designer to trade off desirable (performance/robustness) properties between the plant input and output. For the vehicle under consideration (with a very aggressive engine and significant coupling), it has been observed that a large FPA settling time is needed in order to obtain reasonable (performance/ robustness) properties at the plant input. Ideas for alleviating this fundamental tradeoff were presented. Plume modeling was also found to be particularly significant. Controllers based on plants with insufficient plume fidelity did not work well with the higher fidelity plants. Given the above, the thesismakes significant contributions to control relevant hypersonic vehicle modeling, analysis, and design.

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Date Created
  • 2010