Showing papers on "Model order reduction published in 1991"

Model reduction and control of flexible structures using Krylov vectors

Abstract: Krylov vectors and the concept of parameter matching are combined together to develop a model reduction algorithm for a damped structural dynamics system. The obtained reduced-order model matches a certain number of low-frequency moments of the full-order system. The major application of the present method is to the control of flexible structures. It is shown that, in the control of flexible structures, three types of control energy spillover generally exist: control, observation, and dynamic. The formulation based on Krylov vectors can eliminate both the control and observation spillovers while leaving only the dynamic spillover to be considered. Two examples are used to illustrate the efficacy of the Krylov method. I. Introduction A MAJOR difficulty in the control of flexible structures or any other large-scale system is, in the words of Bellman, the "curse of dimensionality." A flexible structure is, by nature, a distributed-pa rameter system, and, hence, it has infinitely many degrees of freedom. Even approximate structural models obtained by some discretization approach are generally still too large for use in control design applications. Therefore, model order reduction plays an indispensable role in the control of flexible structures. Usually, model reduction of a structural dynamics system is performed by the RayleighRitz method, which transforms the system equation to a smaller scale by using a projection subspace. It is indisputable that the choice of projection subspace is important to the accuracy of the reduced model. The eigensubspace, or the normal mode subspace, is frequently used for projection because it has a clear physical meaning and can preserve the system natural frequencies. However, with regard to the accuracy of system response, numerical experience has shown that preservation of the natural frequencies is usually not the only • concern. Other than normal modes, there are other static modes, e.g., constraint modes, attachment modes, and inertiarelief modes, which are frequently used in component mode synthesis.1 In this paper, Krylov vectors, which can be considered as static modes, are used for model reduction. There has been quite a bit of research concerning the convergence and efficiency of Krylov vectors in application to eigenvalue analysis and to the structural dynamics model reduction problem.2'5 Krylov vectors are also efficient when employed in general linear system and controller reduction problems.6'7 The major purpose of this paper is to discuss the possible application of Krylov vectors to controller design for flexible structures. The structural dynamics system studied here is described by a second-order matrix differential equation together with an output measurement equation. To perform model reduction to a structural dynamics system in this input-output configuration, the concept of parameter matching for general linear system model reduction is adopted. Parameter matching constitutes a class of efficient methods for model order reduction

Model order reduction via real Schur-form decomposition

Abstract: A new algorithm is presented for computing Moore's reduced-order transfer-function matrix without calculating the balancing transformation, which tends to be ill-conditioned, especially when the original system is non-minimal or when it has very nearly uncontrollable or unobservable modes. The algorithm is based on finding the eigenspaces associated with large eigenvalues of the cross-gramian matrix Wco using the real Schur-form decomposition. The algorithm does not require a minimal model to start with. The state-space realization obtained by this method is related to the balanced realization by a non-singular matrix. An example is presented to illustrate the proposed algorithm

Model order reduction applied to a hot-bench simulation of an aeroelastic wind-tunnel model

Abstract: Simulations of an aeroelastically scaled wind-tunnel model were developed for hot-bench testing of a digital controller. The digital controller provided active flutter-suppression, rolling-maneuver-load alleviation, and plant estimation. To achieve an acceptable time scale for the hot-bench application, the mathematical model of the wind-tunnel model was reduced from 220 states to approximately 130 states while assuring that the required accuracy was preserved for all combinations of 10 inputs and 56 outputs. The reduction was achieved by focussing on a linear, aeroelastic submodel of the full mathematical model and by applying a method based on the internally balanced realization of a dynamic system. 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.

PDEMOD: Software for control/structures optimization

Abstract: Because of the possibility of adverse interaction between the control system and the structural dynamics of large, flexible spacecraft, great care must be taken to ensure stability and system performance. Because of the high cost of insertion of mass into low earth orbit, it is prudent to optimize the roles of structure and control systems simultaneously. Because of the difficulty and the computational burden in modeling and analyzing the control structure system dynamics, the total problem is often split and treated iteratively. It would aid design if the control structure system dynamics could be represented in a single system of equations. With the use of the software PDEMOD (Partial Differential Equation Model), it is now possible to optimize structure and control systems simultaneously. The distributed parameter modeling approach enables embedding the control system dynamics into the same equations for the structural dynamics model. By doing this, the current difficulties involved in model order reduction are avoided. The NASA Mini-MAST truss is used an an example for studying integrated control structure design.

Discrete-time frequency weighted model order reduction

Abstract: The problem of frequency-weighted optimal model order reduction for discrete-time systems is considered. Necessary conditions completely characterizing the reduced-order model are given. The solution consists of a set of one generalized Riccati equation and two generalized Lyapunov equations all coupled by a projection. In the case when the frequency-weighting transfer function is strictly proper an additional projection appears in the solution. >