Ventana software support forum

In Michael R. Goodman's book "Study Notes in System Dynamics", a fair amount of attention is paid to understanding input/output gain and phase relationships of closed loop systems.

One interesting method to understanding these relationships is to:
1) initialize the system in steady state;
2) break any one link in the system such that the closed loop system becomes an open system;
3) introduce a sinusoidal pulse with an a determined period;
4) if necessary, rewrite any feedback structures as delays in the system;

Once these steps are completed one can go component by component relating the delay (TC or Time Constant) across those components to the original input period (P), ratio = (TC/P); depending on the type of delay (material, information, order of delay), this ratio yields corresponding gain and phase values from a chart.

Any suggestions as to where can I find out how they came up with the relationship of (TC/P) to phase and gain for various types of delays? Where can I find higher resolution charts (since the ones in the book are barely readable, P.232 "Study Notes in SD" ) or even the formula's themselves?

From my research, Bode Plots are as close to this as I can get but I don't see how I can modify them to match SD delay and feedback structures.

Are there more direct and less time consuming ways of determining phase and gain relationships across a closed loop system with delays?

Best

Karan

The appendix of Industrial Dynamics does in fact give the formula for calculating phase and gain from input period and delay period across system components; however, it doesn't explain the necessity for making the system open loop, nor does it explain why feedback structures have to represented as simple delays? Any thoughts?