Showing papers on "Model order reduction published in 1994"

Efficient frequency-domain modeling and circuit simulation of transmission lines

Abstract: In this paper we describe an algorithm for efficient SPICE-level simulation of transmission lines with arbitrary scattering parameter descriptions. That is, the line can be represented in the form of a frequency-domain model or a table of measured frequency-domain data. Our approach initially uses a forced stable decade-by-decade l/sub 2/ minimization approach to construct a sum of rational functions approximation, but the approximation has dozens of poles and zeros. This unnecessarily high-order model is then reduced using a guaranteed stable model order reduction scheme based on balanced realizations. Once the reduced-order model is derived, it can be combined with the transmission line's inherent delay to generate an impulse response. Finally, following what is now a standard approach, the impulse response can be efficiently incorporated in a circuit simulator using recursive convolution. An example of a transmission line with skin-effect is examined to both demonstrate the effectiveness of the approach and to show its generality. >

An input normal form homotopy for the L/sup 2/ optimal model order reduction problem

Abstract: In control system analysis and design, finding a reduced-order model, optimal in the L/sup 2/ sense, to a given system model is a fundamental problem. The problem is very difficult without the global convergence of homotopy methods, and a homotopy based approach has been proposed. The issues are the number of degrees of freedom, the well posedness of the finite dimensional optimization problem, and the numerical robustness of the resulting homotopy algorithm. A homotopy algorithm based on the input normal form characterization of the reduced-order model is developed here and is compared with the homotopy algorithms based on Hyland and Bernstein's optimal projection equations. The main conclusions are that the input normal form algorithm can be very efficient, but can also be very ill conditioned or even fail. >

Model order reduction techniques for circuit simulation

Abstract: Theoretical and practical aspects of model order reduction techniques for use in the context of circuit simulation are investigated, with particular attention to problems involving clocked analog circuitry and to interconnect and packaging applications. First, an algorithm for the efficient simulation of clocked analog circuits is described and simulation results are presented. Traditional simulation programs, which must accurately solve the associated differential equations with a time discretization method become extraordinarily computationally expensive when applied to simulating the transient behavior of clocked analog circuits. These circuits are clocked at a frequency whose period is typically orders of magnitude smaller than the time interval of interest to the designer. The nature of the calculations requires that in order to construct the solution over the time interval of interest, an accurate solution must be computed for every cycle of the high frequency clock in the interval, and this can involve thousands of cycles. The algorithm to be described substantially reduces the simulation time without compromising accuracy by exploiting the property that the behavior of such a circuits in a given high frequency clock cycle is similar, but not identical, to the behavior in the preceding and following cycles. This algorithm is in itself a model order reduction technique, since it simplifies the understanding of the problem and reduces its computational cost. Further model order reduction is possible which allows for significant speedups in circuits containing digital control circuitry. Next, we describe an algorithm for efficient SPICE-level simulation of frequencydependent elements, such as transmission lines with arbitrary scattering parameter descriptions, or complicated 3-D interconnect with nonlinear transistor drivers and receivers. The elements can be represented in the form of a frequency-domain model or a table of measured frequency-domain data. Our approach initially uses a forced stable decade-by-decade £2 minimization approach to construct a sum of rational functions approximation, which may have dozens of poles and zeros. This unnecessarily high-order model is then reduced using a guaranteed stable model order reduction scheme based on balanced realizations. Once the reduced-order model is derived, an impulse response can easily be generated. Finally, the impulse response can be efficiently incorporated into a circuit simulator using recursive convolution. Examples including a transmission line

On the /spl sigma/-reciprocal system for model order reduction

Abstract: In this paper the definition of the /spl sigma/-reciprocal system is introduced. This allow one to show that the generalized singular perturbation approximation method for model reduction is related to the direct truncation of the /spl sigma/-reciprocal system. Based on this definition two new model order reduction algorithms are presented. The suitability of the proposed reduction methods is illustrated by means of two numerical examples. >

Orthogonal sets for efficient model-order reduction via a Gauss-Newton method

Abstract: Continuous or discrete time orthogonal sets easily extracted from a Routh-type stability array are extended with a view to constructing optimal models via explicit relations, without computing or inverting Gram matrices.

Model order reduction of multichannel stable systems

Abstract: This paper addresses the problem of approximating multichannel stable systems by lower order stable system transfer functions that interpolate the partial impulse response matrix sequence of the original system. This is achieved by making use of the left- and right-Schur (1918) recursion algorithms, and in this context, the classical Pade approximations that are also stable are shown to be a special case of this general formulation. >

Dynamic analysis of Space Shuttle/RMS configuration using continuum approach

Abstract: The initial assembly of Space Station Freedom involves the Space Shuttle, its Remote Manipulation System (RMS) and the evolving Space Station Freedom. The dynamics of this coupled system involves both the structural and the control system dynamics of each of these components. The modeling and analysis of such an assembly is made even more formidable by kinematic and joint nonlinearities. The current practice of modeling such flexible structures is to use finite element modeling in which the mass and interior dynamics is ignored between thousands of nodes, for each major component. The model characteristics of only tens of modes are kept out of thousands which are calculated. The components are then connected by approximating the boundary conditions and inserting the control system dynamics. In this paper continuum models are used instead of finite element models because of the improved accuracy, reduced number of model parameters, the avoidance of model order reduction, and the ability to represent the structural and control system dynamics in the same system of equations. Dynamic analysis of linear versions of the model is performed and compared with finite element model results. Additionally, the transfer matrix to continuum modeling is presented.