Understanding Delays. 2.2 Studying the First Order Negative Feedback System with Excel I program the system in Excel and carry out further experiments.

I also notice the programming task becomes much easier. 2.2.1 First Order Negative Feedback Loop Responseto a Step in the The first driver function I use for the First Order Negative Feedback model is the Step. First Order Negative Feedback System Structure I formulate the model in the spreadsheet as per the below. System Response to Step in the Inflow Rate Note: the Level increases until the outflow rate rises to equal the inflow rate.

This test confirms my sketch. 2.2.2 First Order Negative Feedback Loop Responseto a Step in the Target I continue to experiment with the Step function. Target as Driver System Response to Step in the Target Note: the Level increases by the value of the Target i.e. 5 cups. The Gap decreases from a value of 8 cups to 3 cups at time = 2 seconds and then grows asymptotically by 5 cups to its initial value of 8 cups. Inflow Rate as Driver. 4.5 - Exponential and Logarithmic Models. Exponential Growth Function y = C ekt, k > 0 Features Asymptotic to y = 0 to left Passes through (0,C) C is the initial value Increases without bound to right Notes Some of the things that exponential growth is used to model include population growth, bacterial growth, and compound interest.

If you are lucky enough to be given the initial value, that is the value when x = 0, then you already know the value of the constant C. Alternatively, almost like cheating, you can put the x-values into List 1, the y-values into List 2, and choose the ExpReg option on the TI-82 calculator. Exponential Decay (decreasing form) y = C e-kt, k > 0 Asymptotic to y = 0 to right Passes through (0,C) C is the initial value Decreasing, but bounded below by y=0 Exponential decay and be used to model radioactive decay and depreciation. Exponential decay models decrease very rapidly, and then level off to become asymptotic towards the x-axis. Exponential Decay (increasing form) y = C ( 1 - e-kt ), k > 0 Gaussian Model. U.S. Department of Energy's Introduction to System Dynamics. Road Maps: Table of Contents. Road Maps: A Guide to Learning System Dynamics Table of Contents Introduction to Road Maps To start learning more about Road Maps, please see the introduction to Road maps (D-4500-3).

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Road Maps Help While we have the webmasters@sysdyn.mit.edu email address available for any technical questions regarding the downloading of Road Maps, there is also a help email for questions and comments about the exercises and examples in Road Maps itself. Road Maps Glossary Books You will need several books to complete Road Maps. Downloading Go to a Chapter:1 | 2 | 3 | 4 | 5 | 6 | 7. Thwink.org - An analytical approach to solving the sustainability problem.