Eigenvalue and Eigenvector Analysis of Dynamic Systems
Posted: Wed Mar 03, 2010 7:38 am
Lately, I have had a little time to catch up on some SD reading!
It seems there are two interesting methods out there for calculating dominant feedback loops in a system; David N. Ford's is the first, in which changes in the behavior of a loop's "atomic" pattern (calculated by observing the change of pattern of a target variable's second derivative) indicates loop dominance; but from my trials this method doesn't seem to be robust or clear when the model is large and there are many complementary feedback loops.
The other method, which I find really fascinating is that of Paulo Goncalves's, (adapted from Nathan Forrester's work); this requires us to linearize the system, calculate eigenvalues from link gains of the system, accordingly calculate eigenevectors and form a resulting system of time varying equations. By taking the derivatives of the eigenvalues and vectors with respect to the loop gains we can calculate the impact of levels by changes in gain over time. Phase shift and gain of key state variables can also be calculated at specific times from the analytic equation.
With reference to this method:
- I have seen this analysis used in a few papers in past SD conferences; has anyone written a MATLAB or excel program to aid in such an analysis?
- Would anyone care to share some of their insights using either method?
Attached are the articles (published by the SDS, but they seem to be in circulation in the public domain)
Best Wishes,
Karan
It seems there are two interesting methods out there for calculating dominant feedback loops in a system; David N. Ford's is the first, in which changes in the behavior of a loop's "atomic" pattern (calculated by observing the change of pattern of a target variable's second derivative) indicates loop dominance; but from my trials this method doesn't seem to be robust or clear when the model is large and there are many complementary feedback loops.
The other method, which I find really fascinating is that of Paulo Goncalves's, (adapted from Nathan Forrester's work); this requires us to linearize the system, calculate eigenvalues from link gains of the system, accordingly calculate eigenevectors and form a resulting system of time varying equations. By taking the derivatives of the eigenvalues and vectors with respect to the loop gains we can calculate the impact of levels by changes in gain over time. Phase shift and gain of key state variables can also be calculated at specific times from the analytic equation.
With reference to this method:
- I have seen this analysis used in a few papers in past SD conferences; has anyone written a MATLAB or excel program to aid in such an analysis?
- Would anyone care to share some of their insights using either method?
Attached are the articles (published by the SDS, but they seem to be in circulation in the public domain)
Best Wishes,
Karan