First Order Systems
First-order systems are those which can be described by first-order differential equations. A common example is the RC circuit.
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The files listed below are a combination of PDF tutorial documents, voice annotated tutorial documents (FLASH and AVI), MATLAB Graphical User Interfaces (GUIs), and LabVIEW GUIs. The MATLAB GUIs are available for both MATLAB 6.5 and 7.0. In addition, MATLAB .exe files are also available for those without MATLAB and can be used with the MATLAB Runtime Engine.
See the general MATLAB GUI instruction file below for more information on system requirements and how to run the GUIs. The LabVIEW GUI .zip files contain a stand-alone version which does not require LabVIEW to run. See the readme in the .zip file for more information. Each GUI .zip file contains a document of suggested exercises to be performed with the GUI.
| First-Order Theory | View File |
|---|---|
| First-Order Theory Overview of the theory of first-order systems: ODE and homogeneous and particular solutions | First-Order Theory (pdf) |
| First-Order Block Diagram Modeling How to model a first-order system using a block diagram. An example is constructed using Simulink, and a sample response is shown. | First-Order Block Diagram Modeling (pdf) |
| Project | View File |
|---|---|
| RC Circuit Project for Differential Equations Class This project, developed by Stephen Pennell, was given in a differential equations class. It asks students to develop and analyze a mathematical model of an RC circuit. | RC Circuit Project (pdf) |
| First-Order RC Circuit as Low-Pass Filter | View File |
|---|---|
| Filtering with RC Circuits Use of an RC circuit as a low-pass filter, including system model description, filtering characteristics, discussion of cut-off frequency, and examples of use for filtering sinusoidal signals. | Filtering with RC Circuits (pdf) |
| Cut-off Frequency Discussion of Cut-off Frequency, which is an important characteristic of filtering devices such as RC Circuits. | Cut-off Frequency (pdf) |
| MATLAB GUI Download
M6.5 and M7.0 open in MATLAB, EXE is a stand-alone GUI Allows the user to explore the behavior of an RC circuit low-pass filter. Vary the R and C values of the circuit, view the Bode plot of the filter response, and the effect of the filter on a sinusoidal signal in the time domain. | MATLAB GUI M6.5 MATLAB GUI M7.0 MATLAB GUI EXE |
| GUI Overview | GUI Overview (pdf) |
| GUI Assignment | GUI Assignment (pdf) |
| LabVIEW GUI Download LabVIEW not needed, zip file contains set-up for stand-alone GUI This GUI allows the user to examine the effects of an RC circuit, low-pass filter on a sinusoidal signal. The R and C values and the input frequency can be adjusted independently. | LabVIEW GUI |
| GUI Overview | GUI Overview (pdf) |
| GUI Assignment | GUI Assignment (pdf) |
| First-Order RC Circuit Step Response | View File |
|---|---|
| First-Order Systems Step Response Overview Description of first-order system model and discussion of the response to a step function, the effect of varying the time constant of the system, and how to find the step response in MATLAB. | First-Order Systems Response (pdf) |
| MATLAB GUI Download M6.5 and M7.0 open in MATLAB The user can vary the R and C values of the circuit, and see the response of the circuit to a step function, the time constant, and the settling time. | MATLAB GUI M6.5 MATLAB GUI M7.0 |
| GUI Overview | GUI Overview (pdf) |
| GUI Assignment | GUI Assignment (pdf) |
| LabVIEW GUI Download LabVIEW not needed, zip file contains set-up for stand-alone GUI This GUI shows the response of a first-order, RC circuit to a unit step input. The R and C values can be adjusted to change the time constant of the system. | LabVIEW GUI |
| GUI Overview | GUI Overview (pdf) |
| GUI Assignment | GUI Assignment (pdf) |
| Gravity Driven Flow (GDF) in a Tank | View File |
|---|---|
| MATLAB GUI Download M7.0 opens in MATLAB This GUI Simulates the draining of a tank under various conditions in order to address the dynamics of gravity driven flows. | MATLAB GUI M7.0 |
| GUI Overview | GUI Overview (pdf) |
| GUI Assignment | GUI Assignment (pdf) |