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NASA NTRS1989

Model reduction in the physical coordinate system

In the dynamics modeling of a flexible structure, finite element analysis employs reduction techniques, such as Guyan's reduction, to remove some of the insignificant physical coordinates, thus producing a dynamics model that has smaller mass and stiffness matrices. But this reduction is limited in the sense that it removes certain degrees of freedom at a node points themselves in the model. From the standpoint of linear control design, the resultant model is still too large despite the reduction. Thus, some form of the model reduction is frequently used in control design by approximating a large dynamical system with a fewer number of state variables. However, a problem arises from the placement of sensors and actuators in the reduced model, because a model usually undergoes, before being reduced, some form of coordinate transformations that do not preserve the physical meanings of the states. To correct such a problem, a method is developed that expresses a reduced model in terms of a subset of the original states. The proposed method starts with a dynamic model that is originated and reduced in finite element analysis. Then the model is converted to the state space form, and reduced again by the internal balancing method. At this point, being in the balanced coordinate system, the states in the reduced model have no apparent resemblance to those of the original model. Through another coordinate transformation that is developed, however, this reduced model is expressed by a subset of the original states.

Yae, K. Harold↗

NASA NTRS1991

Unsymmetric Lanczos model reduction and linear state function observer for flexible structures

This report summarizes part of the research work accomplished during the second year of a two-year grant. The research, entitled 'Application of Lanczos Vectors to Control Design of Flexible Structures' concerns various ways to use Lanczos vectors and Krylov vectors to obtain reduced-order mathematical models for use in the dynamic response analyses and in control design studies. This report presents a one-sided, unsymmetric block Lanczos algorithm for model reduction of structural dynamics systems with unsymmetric damping matrix, and a control design procedure based on the theory of linear state function observers to design low-order controllers for flexible structures.

Su, Tzu-Jeng↗

NASA NTRS1991

Hybrid CMS methods with model reduction for assembly of structures

Future on-orbit structures will be designed and built in several stages, each with specific control requirements. Therefore there must be a methodology which can predict the dynamic characteristics of the assembled structure, based on the dynamic characteristics of the subassemblies and their interfaces. The methodology developed by CSC to address this issue is Hybrid Component Mode Synthesis (HCMS). HCMS distinguishes itself from standard component mode synthesis algorithms in the following features: (1) it does not require the subcomponents to have displacement compatible models, which makes it ideal for analyzing the deployment of heterogeneous flexible multibody systems, (2) it incorporates a second-level model reduction scheme at the interface, which makes it much faster than other algorithms and therefore suitable for control purposes, and (3) it does answer specific questions such as 'how does the global fundamental frequency vary if I change the physical parameters of substructure k by a specified amount?'. Because it is based on an energy principle rather than displacement compatibility, this methodology can also help the designer to define an assembly process. Current and future efforts are devoted to applying the HCMS method to design and analyze docking and berthing procedures in orbital construction.

Farhat, Charbel↗

NASA NTRS1993

Model reduction of mechanical systems

A reduced model of a stable mechanical system with proportional damping represented in modal coordinates is developed, based on a procedure reported by Commault and Guerin (1978). In this model, model error is calculated a priori and is used to determine the dominant modes. Two examples are presented showing that reduced models generated as described will be better or at least as good as those produced by the popular modal cost analysis scheme of Skelton and Hughes (1980).

Yousuff, Ajmal↗

NASA NTRS1992

Simulation and model reduction for the AFW program

The simulation methodology used in the Active Flexible Wing wind-tunnel test program is described. An overview of the aeroservoelastic modeling used in building the required batch and hot-bench simulations is presented. Successful hot-bench implementation required that the full mathematical model be significantly reduced while assuring that accuracy be maintained for all combinations of 10 inputs and 56 outputs. The reduction was accomplished by using a method based on internally balanced realizations and focussing on the linear, aeroelastic portion of the full mathematical model. The error-bound properties of the internally balanced realization significantly contribute to its utility in the model reduction process. The reduction method and the results achieved are described.

Buttrill, Carey↗

DOE OSTI2025

Nitrate Reduction Modeling under Acidic Conditions with Late Transition Metals

The electrochemical reduction of nitrate (NO 3 R) to ammonia is a bold yet conceivable way of producing ammonia using renewable electricity. However, serious challenges remain in finding optimal electrocatalysts for the process. An atomistic understanding of the surface energetics behind the NO 3 R is needed in order to design an efficient catalyst. Herein, we combine energetics from density functional theory and microkinetic modeling to demonstrate how surface descriptors can help simplify the search for efficient NO 3 R electrocatalysts. We illustrate the strong correlations between transition-state energetics and O* binding energies for adsorbed nitrate and nitrite on transition metals. For intermediates from NO* and beyond, we compare the benefits of using either the N* or H* binding energies to predict reduction onset potentials. These insights enable us to develop a simple microkinetic model that elucidates the surface coverages of intermediates and the product selectivity of NO 3 R across a range of potentials and transition metals. As a result, we show that the model adequately corroborates with quasi-steady-state rates observed experimentally.

ammonia↗

NASA NTRS1985

Residue-Measure Model-Reduction Technique

New residue-measure criterion simplifies mathematical models of feedback-control systems. Although originally developed for flight control, approach applied to any flexible structural system involving dominantly linear dynamics.

Gluch, D. P.↗

NASA NTRS1989

Model reduction for flexible structures - Test data approach

A reduced model of a system is obtained by truncating part of its state variables. Hankel singular values and component costs determine which component is deleted or retained in the reduced model. In this paper Hankel singular values and component costs of a flexible structure are obtained from the resonance test data, rather than from the system matrices. Test data, besides system dynamics, include also actuators and sensors dynamics. For this reason, the reduced model obtained from test data can be far from the optimal one. In this paper the reconstruction of the flexible structure indices from the joint actuator-sensor-flexible structure indices is discussed.

Gawronski, Wodek↗

NASA NTRS1979

Flexible space structure model reduction by modal cost analysis

It is noted that reduced models and reduced controllers for flexible space structures are obtained by retaining those modes which make the greatest contribution to quadratic control objectives. Attention is given to the relative importance of damping, frequency and mode shapes in the mode truncation decisions for the following control objectives: attitude control, vibration suppression and figure control. It is also shown that using Modal Cost Analysis (MCA) on the closed loop modes of the optimally controlled system allows the construction of reduced control policies which feedback only those closed loop coordinates which are most critical to the quadratic control performance criterion. In this manner, the modes which need to be controlled are deduced from truncations of the optimal controller.

Skelton, R. E.↗

NASA NTRS1990

Practical model reduction for flexible structures

The most accepted methods for developing models of flexible structures for the analysis, design and simulation of control systems are finite element methods and extraction from experimental data. Using either of these methods, models are often produced with modes that do not significantly add to the fidelity of the model. This paper presents techniques for eliminating these modes. Particular attention is paid to multiple-input, multiple-output systems. First, control system models developed for flexible structures, using finite element methods and experimental data, are briefly discussed. the shortcomings of using models with unnecessary and/or residual modes are delineated. Then, two techniques for reducing the order of models are presented; the first is applicable to single-input, single-output systems and the second for multiple-input, multiple-output systems. Finally, both are illustrated using model data from the proposed NASA Shuttle-C.

Mitchell, Jerrel R.↗

DOE OSTI2025

Block-Structured Operator Inference for Coupled Multiphysics Model Reduction

This work presents a block-structured formulation of Operator Inference as a way to learn structured reduced-order models for multiphysics systems. The approach specifies the governing equation structure for each physics component and the structure of the coupling terms. Once the multiphysics structure is specified, the reduced-order model is learned from snapshot data following the nonintrusive Operator Inference methodology. In addition to preserving physical system structure, which in turn permits preservation of system properties such as stability and second-order structure, the block-structured approach has the advantages of reducing the overall dimensionality of the learning problem and admitting tailored regularization for each physics component. The numerical advantages of the block-structured formulation over a monolithic Operator Inference formulation are demonstrated for aeroelastic analysis, which couples aerodynamic and structural models. For the benchmark test case of the AGARD 445.6 wing, block-structured Operator Inference provides an average 20% online prediction speedup over monolithic Operator Inference across subsonic and supersonic flow conditions in both the stable and fluttering parameter regimes while preserving the accuracy achieved with monolithic Operator Inference.

42 ENGINEERING↗

NASA NTRS1992

Model reduction for systems with integrators

The reduction algorithm for systems with integrators is derived. The algorithm is based on balancing the antigrammians and has the same computational effectiveness as the regular balancing procedure. It was applied to the reduction of the NASA Deep Space Network antenna model. As a result, the 90-state model has been reduced to a 27-state model, which preserves the full-model properties.

Gawronski, Wodek↗

NASA NTRS1991

A Markov model reduction technique for fault tolerant processor reliability analysis

A fault tolerant processor (FTP) plays a key role in many high performance, safety-critical control system applications. Realistic modeling of an FTP is crucial to gaining a high degree of confidence in the reliability and safety analysis of such a system. While fidelity is clearly a major consideration, a practical model must also be kept to a moderate size to allow its incorporation into the overall system model. This paper presents a systematic reduction technique that starts from a complex, detailed model of a triple, redundant FTP and produces a low order approximation of very high accuracy. The existence of two distinct time scales represents the key to the success of the technique. No eigenvalue solution or coordinate transformation are needed. The reduced model captures all the important features of the detailed model, is amenable to an analytical solution and provides insight into the reconfiguration behavior of an FTP.

Schor, Andrei L.↗

NASA NTRS1989

Fatigue strength reduction model: RANDOM3 and RANDOM4 user manual, appendix 2

The FORTRAN programs RANDOM3 and RANDOM4 are documented. They are based on fatigue strength reduction, using a probabilistic constitutive model. They predict the random lifetime of an engine component to reach a given fatigue strength. Included in this user manual are details regarding the theoretical backgrounds of RANDOM3 and RANDOM4. Appendix A gives information on the physical quantities, their symbols, FORTRAN names, and both SI and U.S. Customary units. Appendix B and C include photocopies of the actual computer printout corresponding to the sample problems. Appendices D and E detail the IMSL, Version 10(1), subroutines and functions called by RANDOM3 and RANDOM4 and SAS/GRAPH(2) programs that can be used to plot both the probability density functions (p.d.f.) and the cumulative distribution functions (c.d.f.).

Boyce, Lola↗

NASA NTRS1989

Fatigue strength reduction model: RANDOM3 and RANDOM4 user manual. Appendix 2: Development of advanced methodologies for probabilistic constitutive relationships of material strength models

FORTRAN programs RANDOM3 and RANDOM4 are documented in the form of a user's manual. Both programs are based on fatigue strength reduction, using a probabilistic constitutive model. The programs predict the random lifetime of an engine component to reach a given fatigue strength. The theoretical backgrounds, input data instructions, and sample problems illustrating the use of the programs are included.

Boyce, Lola↗

NASA NTRS1991

Numerical and literal aeroelastic-vehicle-model reduction for feedback control synthesis

The simplification of a high-order, literal model for large flexible aircraft is discussed. Areas of model fidelity that are critical if the model is to be used for control law synthesis are presented. Several simplification techniques, some new and some widely available, that can deliver the necessary model fidelity are presented and applied to a model from the literature. The techniques include both numerical and analytical approaches. An analytical approach, based on first-order sensitivity theory, is shown to lead not only to excellent numerical results, but also to closed-form analytical expressions for key system dynamic properties such as the pole/zero factors of the vehicle transfer-function matrix. The analytical results are expressed in terms of vehicle vibrational characteristics and rigid-body and aeroelastic stability derivatives, thus providing insight into the underlying causes for critical dynamic characteristics.

Newman, Brett↗

NASA NTRS1988

Closed-form Grammians and model reduction for flexible space structures

Analytical expression are derived for the Grammians of a model in modal coordinates for the dynamics of a flexible space structure (FSS). These exact results provide insight into the dynamics of such systems and reduce the known approximate expressions in the case of lightly damped, widely separated modes. A novel algorithm is outlined that uses these to compute a dominant reduced-order model for such a system in an efficient manner.

Williams, Trevor↗

NASA NTRS1985

An Overview of Latest Model Reduction and Control Methods of Large Flexible Space Structures

The latest trends and theoretical developments involved with the modeling and control of Large Flexible Space Structures (LFSS) are described. The paper addresses first the basic problems, characteristics, and difficulties inherent in modeling and control of LFSS. Major sources of difficulties and errors are the stiffness and damping operators of the dynamic model. Extensions of Linear Quadratic Gaussian (LQG) theory as applied to LFSS are presented, including frequency-shaped cost functionals and perturbation methods. The minimum data/maximum entropy approach which uses a stochastic design model to overcome difficulties found in the LQG-based methods is described. Latest trends in system theory including balanced realization and singular-value analysis are used to determine reduced order controllers and models. Ad hoc methods such as component cost analysis and modal cost analysis are discussed in context with the closed-loop reduction problem of controller order versus performance. The minimum data/maximum entropy approach also addresses controller order versus performance. Those areas of control science and large scale systems that appear to have an important role in understanding and solving LFSS modeling and control are also identified.

Santiago, J. M.↗