Showing papers on "Model order reduction published in 1993"

On the Hankel-norm approximation of upper-triangular operators and matrices

Abstract: A matrix T = Tij ∞=-∞ , which consists of a doubly indexed collection Tij of operators, is said to be upper when Tij = 0 for i > j. We consider the case where the Tij are finite matrices and the operator T is bounded, and such that the Tij are generated by a strictly stable, non-stationary but linear dynamical state space model or colligation. For such a model, we consider model reduction, which is a procedure to obtain optimal approximating models of lower system order. Our approximation theory uses a norm which generalizes the Hankel norm of classical stationary linear dynamical systems. We obtain a parametrization of all solutions of the model order reduction problem in terms of a fractional representation based on a non-stationary J-unitary operator constructed from the data. In addition, we derive a state space model for the so-called maximum entropy approximant. In the stationary case, the problem was solved by Adamyan, Arov and Krein in their paper on Schur-Takagi interpolation. Our approach extends that theory to cover general, non-Toeplitz upper operators.

Controllability and observability of flexible structures with proof-mass actuators

Abstract: Relationships between Hankel singular values of a structure with a proof-mass actuator to those of a structure with an ideal actuator are analyzed. They indicate that the proof-mass actuator has little influence on Hankel singular values of a structure if the natural frequency of the actuator is much lower than the structural frequencies. This fact significantly simplifies controllability/observability analysis and model reduction of flexible structures. Results from numerical simulations verify the conclusions.

Least-squares model order reduction enhancements

Abstract: Two enhancements to the least-squares (LS) discrete-time model order reduction (MOR) method are presented: scaling and frequency response matching. Scaling generally improves the low-frequency fit between the reduced-order model (ROM) and the original model. For exact gains at specific frequencies, optional frequency response constraints can easily be added to the LS MOR method. An example is presented that illustrates these enhancements. The example model is reduced with the Hankel norm, weighted impulse response gramian, and LS MOR methods. Plots of error versus frequency are given for each of the three MOR methods. >

ANDECS Model Order Reduction Modules

Abstract: The report is a comprehensive documentation of 17 new ANDECS modules for model reduction. Based on balancity related methods implemented in the RASP-MODRED subroutines library.

Dynamic Analysis of Space Station Freedom Assembly via Continuum Modeling

Abstract: The initial assembly of Space Station Freedom involves the Space Shuttle and its remote manipulating system (RMS), modeling and analysis of which is made formidable by kinematic and joint nonlinearities. In this paper, continuum models are used instead of finite element models because of the improved accuracy, reduced number of system parameters, the avoidance of the model order reduction and the ability to represent the structural dynamics and control system dynamics in the same system of equations. The continuum modeling approah is seen to offer an alternative to finite element modeling.

Computationally Efficient Homotopies for the H 2 Model order Reduction Problem

Abstract: The H 2 optimal model reduction problem, i.e., the problem of approximating a higher order dynamical system by a lower order one so that a model reduction criterion is minimized, is of significant importance and is under intense study. Several earlier attempts to apply homotopy methods to the H 2 optimal model order reduction problem were not entirely satisfactory. Richter devised a homotopy approach which only estimated certain crucial partial derivatives and employed relatively crude curve tracking techniques. Žigic, Bernstein, Collins, Richter, and Watson formulated the problem so that numerical linear algebra techniques could be used to explicitly calculate partial derivatives, and employed sophisticated homotopy curve tracking algorithms, but the number of variables made large problems intractable. We propose here several ways to reduce the dimension of the homotopy map so that large problems are computationally feasible.

Analysis of circuits with lossy transmission lines via approximated state-space models

Abstract: In this work a new method for the analysis of circuits interconnected with lossy transmission lines, is presented. At first a lumped model is obtained by adopting suitable approximation techniques. Then classical model order reduction algorithms are applied to obtain a low order model of the circuit, suitable for computing a time domain response to arbitrary input signals. An example is reported, showing the suitability of the proposed approach. >