Back to results
US 6,188,974 B1Granted
Method for constructing reduced-order models of systems
AssigneeInternational Business Machines Corporation
InventorsJane Grace Kehoe Cullum, Albert Emil Ruehli
Life of this patent
Estimating the term…
Abstract
A method comprising a computational procedure for obtaining reduced-order models of partial element equivalent circuit (PEEC) models of very large scale integrated (VLSI) interconnects. The methodology is not limited to PEEC applications, and can be used for generating reduced-order models of other systems which can be modeled with linear, time-invariant systems of ordinary differential equations with time delays.
Claims18
A computer implemented method comprising:
- representing an original physical system comprising time delays as an original linear circuit model having a time domain formulation of C x . ( t ) + ∑ k , m = 1 M C ~ k , m x . ( t - τ k , m L ) = Gx ( t ) + ∑ i , j = 1 J G ~ i , j x ( t - τ i , j P ) + Bu ( t ) y = Ex ( t )
- where C, Ck,m and G, Gi,j are n×n where n is the order of the system, B is n×q where q is the number of variables and E is o×n where o is the number of output variables;
- transforming the original linear circuit model into a corresponding original transform domain circuit model having a transfer function represented by the formula
- y(s)/u(s)=H(s)=E(s)(A(s))−1B(s)
- where A ( s ) = sC + ∑ k , m = 1 M C k , m ( s ) - G - ∑ i , j = 1 J G i , j ( s ) .
- B(s)=B and E(s)=E, and H(s) is a matrix of rational functions of s;
- locally approximating the original transform circuit model by a system without time delays, thereby generating at least one localized representation of the original system;
- applying an iterative method to each localized representation of the original system, for identifying local characteristics of the original system;
- and
- combining the identified local characteristics to obtain a reduced order model for the original system.
7 more elements
A computer implemented method comprising:
- representing an original physical system formed of elements, having time delays as an original linear circuit model having a time domain formulation of C x . ( t ) + ∑ k , m = 1 M C ~ k , m x . ( t - τ k , m L ) = Gx ( t ) + ∑ i , j = 1 J G ~ i , j x ( t - τ i , j P ) + Bu ( t )
- where C, Ck,m and G, Gi,j are n×n, where n is the order of the system, B is n×q where q is the number of variables and E is o×n where o is the number of output variables;
- transforming the original linear circuit model into a corresponding original transform domain circuit model having a transfer function represented by the formula
- y(s)/u(s)=H(s)=E(s)(A(s))−1B(s)
- where A ( s ) = sC + ∑ k , m = 1 M C k , m ( s ) - G - ∑ i , j = 1 J G i , j ( s ) .
- B(s)=B and E(s)=E and H(s) is a matrix of rational functions of s;
- locally approximating the original transform circuit model by a system without time delays, thereby generating at least one localized representation of the original system;
- applying an iterative method to each localized representation of the original system, for identifying local characteristics of the original physical system;
- and
- combining the identified local characteristics to obtain a reduced order model for the original physical system.
7 more elements
Dependencies are inferred from the claim text.