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Results for “balanced truncation model reduction”

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.

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NASA NTRS1990

A decentralized linear quadratic control design method for flexible structures

A decentralized suboptimal linear quadratic control design procedure which combines substructural synthesis, model reduction, decentralized control design, subcontroller synthesis, and controller reduction is proposed for the design of reduced-order controllers for flexible structures. The procedure starts with a definition of the continuum structure to be controlled. An evaluation model of finite dimension is obtained by the finite element method. Then, the finite element model is decomposed into several substructures by using a natural decomposition called substructuring decomposition. Each substructure, at this point, still has too large a dimension and must be reduced to a size that is Riccati-solvable. Model reduction of each substructure can be performed by using any existing model reduction method, e.g., modal truncation, balanced reduction, Krylov model reduction, or mixed-mode method. Then, based on the reduced substructure model, a subcontroller is designed by an LQ optimal control method for each substructure independently. After all subcontrollers are designed, a controller synthesis method called substructural controller synthesis is employed to synthesize all subcontrollers into a global controller. The assembling scheme used is the same as that employed for the structure matrices. Finally, a controller reduction scheme, called the equivalent impulse response energy controller (EIREC) reduction algorithm, is used to reduce the global controller to a reasonable size for implementation. The EIREC reduced controller preserves the impulse response energy of the full-order controller and has the property of matching low-frequency moments and low-frequency power moments. An advantage of the substructural controller synthesis method is that it relieves the computational burden associated with dimensionality. Besides that, the SCS design scheme is also a highly adaptable controller synthesis method for structures with varying configuration, or varying mass and stiffness properties.

Su, Tzu-Jeng↗
NASA NTRS1989

Modern CACSD using the Robust-Control Toolbox

The Robust-Control Toolbox is a collection of 40 M-files which extend the capability of PC/PRO-MATLAB to do modern multivariable robust control system design. Included are robust analysis tools like singular values and structured singular values, robust synthesis tools like continuous/discrete H(exp 2)/H infinity synthesis and Linear Quadratic Gaussian Loop Transfer Recovery methods and a variety of robust model reduction tools such as Hankel approximation, balanced truncation and balanced stochastic truncation, etc. The capabilities of the toolbox are described and illustated with examples to show how easily they can be used in practice. Examples include structured singular value analysis, H infinity loop-shaping and large space structure model reduction.

Chiang, Richard Y.↗
NASA NTRS1989

Model reduction for flexible spacecraft with clustered natural frequencies

Two approaches to the problem of model reduction for flexible spacecraft that have proved very useful are balancing and model truncation. Furthermore, it is well known that a model representation of a lightly damped flexible structure with widely spaced natural frequencies is approximately balanced. Consequently, reduction in either coordinate system gives similar results for this case. It is important to note, however, that flexible space structures typically have clusters of closely spaced frequencies. In such cases, reduction in model coordinates can give large errors, while the error obtained using balancing is generally much smaller. A new reduction procedure which combines the best features of model and balanced reduction is therefore developed. It is more efficient than balanced reduction of the full system, as it only involves balancing those subsystems of close modes that are highly correlated, yet is shown to yield results which are essentially as good.

Williams, T. W. C.↗
NASA NTRS2016

Model Order Reduction of Aeroservoelastic Model of Flexible Aircraft

This paper presents a holistic model order reduction (MOR) methodology and framework that integrates key technological elements of sequential model reduction, consistent model representation, and model interpolation for constructing high-quality linear parameter-varying (LPV) aeroservoelastic (ASE) reduced order models (ROMs) of flexible aircraft. The sequential MOR encapsulates a suite of reduction techniques, such as truncation and residualization, modal reduction, and balanced realization and truncation to achieve optimal ROMs at grid points across the flight envelope. The consistence in state representation among local ROMs is obtained by the novel method of common subspace reprojection. Model interpolation is then exploited to stitch ROMs at grid points to build a global LPV ASE ROM feasible to arbitrary flight condition. The MOR method is applied to the X-56A MUTT vehicle with flexible wing being tested at NASA/AFRC for flutter suppression and gust load alleviation. Our studies demonstrated that relative to the fullorder model, our X-56A ROM can accurately and reliably capture vehicles dynamics at various flight conditions in the target frequency regime while the number of states in ROM can be reduced by 10X (from 180 to 19), and hence, holds great promise for robust ASE controller synthesis and novel vehicle design.

aeroelasticity↗
NASA NTRS2017

Genetic Algorithm-Guided, Adaptive Model Order Reduction of Flexible Aircrafts

This paper presents a methodology for automated model order reduction (MOR) of flexible aircrafts to construct linear parameter-varying (LPV) reduced order models (ROM) for aeroservoelasticity (ASE) analysis and control synthesis in broad flight parameter space. The novelty includes utilization of genetic algorithms (GAs) to automatically determine the states for reduction while minimizing the trial-and-error process and heuristics requirement to perform MOR; balanced truncation for unstable systems to achieve locally optimal realization of the full model; congruence transformation for "weak" fulfillment of state consistency across the entire flight parameter space; and ROM interpolation based on adaptive grid refinement to generate a globally functional LPV ASE ROM. The methodology is applied to the X-56A MUTT model currently being tested at NASA/AFRC for flutter suppression and gust load alleviation. Our studies indicate that X-56A ROM with less than one-seventh the number of states relative to the original model is able to accurately predict system response among all input-output channels for pitch, roll, and ASE control at various flight conditions. The GA-guided approach exceeds manual and empirical state selection in terms of efficiency and accuracy. The adaptive refinement allows selective addition of the grid points in the parameter space where flight dynamics varies dramatically to enhance interpolation accuracy without over-burdening controller synthesis and onboard memory efforts downstream. The present MOR framework can be used by control engineers for robust ASE controller synthesis and novel vehicle design.

Numerical Analysi↗
NASA NTRS1992

Model reduction for Space Station Freedom

Model reduction is an important practical problem in the control of flexible spacecraft, and a considerable amount of work has been carried out on this topic. Two of the best known methods developed are modal truncation and internal balancing. Modal truncation is simple to implement but can give poor results when the structure possesses clustered natural frequencies, as often occurs in practice. Balancing avoids this problem but has the disadvantages of high computational cost, possible numerical sensitivity problems, and no physical interpretation for the resulting balanced 'modes'. The purpose of this work is to examine the performance of the subsystem balancing technique developed by the investigator when tested on a realistic flexible space structure, in this case a model of the Permanently Manned Configuration (PMC) of Space Station Freedom. This method retains the desirable properties of standard balancing while overcoming the three difficulties listed above. It achieves this by first decomposing the structural model into subsystems of highly correlated modes. Each subsystem is approximately uncorrelated from all others, so balancing them separately and then combining yields comparable results to balancing the entire structure directly. The operation count reduction obtained by the new technique is considerable: a factor of roughly r(exp 2) if the system decomposes into r equal subsystems. Numerical accuracy is also improved significantly, as the matrices being operated on are of reduced dimension, and the modes of the reduced-order model now have a clear physical interpretation; they are, to first order, linear combinations of repeated-frequency modes.

Williams, Trevor↗
NASA NTRS1993

Model reduction results for flexible space structures

This paper describes the novel subsystem balancing technique for obtaining reduced-order models of flexible structures, and investigates its properties fully. This method can be regarded as a combination of the best features of modal truncation (efficiency) and internal balancing (accuracy); it is particularly well suited to the typical practical case of structures which possess clusters of close modes. Numerical results are then presented demonstrating the results obtained by applying subsystem balancing to the Air Force Phillips Laboratory ASTREX testbed, the Jet Propulsion Laboratory antenna facility, and the NASA Marshall Space Flight Center ACES structure.

Williams, Trevor↗
NASA NTRS1991

Discrete-time model reduction in limited frequency ranges

A mathematical formulation for model reduction of discrete time systems such that the reduced order model represents the system in a particular frequency range is discussed. The algorithm transforms the full order system into balanced coordinates using frequency weighted discrete controllability and observability grammians. In this form a criterion is derived to guide truncation of states based on their contribution to the frequency range of interest. Minimization of the criterion is accomplished without need for numerical optimization. Balancing requires the computation of discrete frequency weighted grammians. Close form solutions for the computation of frequency weighted grammians are developed. Numerical examples are discussed to demonstrate the algorithm.

Horta, Lucas G.↗
NASA NTRS1993

Space Station flexible dynamics under plume impingement

Assembly of the Space Station requires numerous construction flights by the Space Shuttle. A particularly challenging problem is that of control of each intermediate station configuration when the shuttle orbiter is approaching it to deliver the next component. The necessary braking maneuvers cause orbiter thruster plumes to impinge on the station, especially its solar arrays. This in turn causes both overall attitude errors and excitation of flexible-body vibration modes. These plume loads are predicted to lead to CMG saturation during the approach of the orbiter to the SC-5 station configuration, necessitating the use of the station RCS jets for desaturation. They are also expected to lead to significant excitation of solar array vibrations. It is therefore of great practical importance to investigate the effects of plume loads on the flexible dynamics of station configuration SC-5 as accurately as possible. However, this system possesses a great many flexible modes (89 below 5 rad/s), making analysis time-consuming and complicated. Model reduction techniques can be used to overcome this problem, reducing the system model to one which retains only the significant dynamics, i.e. those which are strongly excited by the control inputs or plume disturbance forces and which strongly couple with the measured outputs. The particular technique to be used in this study is the subsystem balancing approach which was previously developed by the present investigator. This method is very efficient computationally. Furthermore, it gives accurate results even for the difficult case where the structure has many closed-spaced natural frequencies, when standard modal truncation can give misleading results. Station configuration SC-5 is a good example of such a structure.

Williams, Trevor↗