Second Order Systems
A second-order system is one which can be described by a second-order differential equation.
The files listed below are a combination of PDF tutorial documents, 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.
You will need Adobe Acrobat Reader to view any pdf files. It can be downloaded for free from the Adobe website.
| Second-Order Theory | View File |
|---|---|
| Second-Order System Theory Discussion of the system equation, homogeneous, and particular solutions for varying amounts of damping. | System Theory (pdf) |
| Second-Order Block Diagram Modeling Construction of a block diagram of a second-order system, with an example model and response shown in Simulink. | Diagram Modeling (pdf) |
| Second-Order Initial Condition Response | View File |
|---|---|
| Second-Order Initial Condition Response Equations for and plots of system response to initial displacement, initial velocity, and combination, for various amounts of damping. | Initial Condition Response (pdf) |
| MATLAB GUI Download M6.5 and M7.0 open in MATLAB, EXE is a stand-alone GUI The user may input m, c, and k values for a second-order system and view the time response of the system to an initial displacement of -1, the frequency response, and the root-locus. | M6.5 Download M7.0 Download EXE Download |
| 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 simulate the free response of a single-degree-of-freedom (SDOF), second-order system. Mass, damping, and stiffness are adjustable along with the initial conditions necessary to provide the response. The time response, frequency response, and root locus can be viewed. | LabVIEW |
| GUI Overview | GUI Overview (pdf) |
| GUI Assignment | GUI Assignment (pdf) |
| Second-Order Step Response | View File |
|---|---|
| Second-Order Step Response Definition of step function, equations for and plots of system response for varying amounts of damping, how to calculate step response in MATLAB and Simulink. | Step Response (pdf) |
| MATLAB GUI Download M6.5 and M7.0 open in MATLAB, EXE is a stand-alone GUI The user may input m, c, and k values of a second-order system, and view the response of the system to a unit step, along with the frequency response and the root locus. | M6.5 Download M7.0 Download EXE Download |
| 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 simulate the step response of a single-degree-of-freedom (SDOF), second-order system. Mass, damping, and stiffness are adjustable along with the initial conditions and step magnitude. The time response, frequency response, and root locus can be viewed. | LabVIEW |
| GUI Overview | GUI Overview (pdf) |
| GUI Assignment | GUI Assignment (pdf) |
| Second-Order Impulse Response | View File |
|---|---|
| Second-Order Impulse Response Definition of impulse, equations for and plots of system response for various levels of damping, calculating impulse response in Simulink and MATLAB. | Impulse Response (pdf) |
| MATLAB GUI Download M6.5 and M7.0 open in MATLAB, EXE is a stand-alone GUI The user may input m, c, and k values for a second-order system, and then view the impulse response in the time domain, frequency domain, and root locus. | M6.5 Download M7.0 Download EXE Download |
| 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 simulate the impulse response of a single-degree-of-freedom (SDOF), second-order system. Mass, damping, and stiffness are adjustable, along with the initial conditions and impulse magnitude. The time response, frequency response, and root locus can be viewed. | LabVIEW |
| GUI Overview | GUI Download (pdf) |
| GUI Assignment | GUI Assignment (pdf) |
| General Second-Order System Response | View File |
|---|---|
| LabVIEW GUI Download LabVIEW not needed, zip file contains set-up for stand-alone GUI This GUI allows the user to simulate three different responses of a single-degree-of-freedom (SDOF), second-order system. Mass, damping, and stiffness are adjustable, along with the initial conditions and step or impulse magnitude. The time response, frequency response, and root can be viewed. | LabVIEW |
| GUI Overview | GUI Overview (pdf) |
| GUI Assignment | GUI Assignment (pdf) |
| Second-Order Complex Frequency Response | View File |
|---|---|
| MATLAB GUIDownload M6.5 and M7.0 open in MATLAB, EXE is a stand-alone GUI The user can input m, c, and k values for a second-order system, and view 5 plots describing the system: real and imaginary components of the FRF, magnitude, phase, and Nyquist. | M6.5 Download M7.0 Download EXE Download |
| GUI Overview | GUI Overview (pdf) |
| GUI Assignment | GUI Assignment (pdf) |
| S-Plane Surface | View File |
|---|---|
| MATLAB GUI Download M6.5 and M7.0 open in MATLAB, EXE is a stand-alone GUI The user may input m, c, and k values for a second-order system, and choose to view one of 6 different plot types: 3D s-plane, phase plane, real plane, or imaginary plane, or 2D magnitude / phase or root locus. | M6.5 Download M7.0 Download EXE Download |
| GUI Overview | GUI Overview (pdf) |
| GUI Assignment | GUI Assignment (pdf) |
| Two Degree of Freedom System Response | View File |
|---|---|
| Two Degree of Freedom Forced Vibration Theory Discusses the theory behind modeling two degree of freedom systems | Theory (pdf) |
| LabVIEW GUI Download LabVIEW not needed, zip file contains set-up for stand-alone GUI This GUI presents the response of a two degree of freedom system to various inputs through the example of a unbalanced motor attached to either degree of freedom. | LabVIEW |
| GUI Overview and Assignment | GUI Overview & Assignment (pdf) |
| Convolution Integral | View File |
|---|---|
| Convolution Theory Discusses the theory behind the convolution integral | Convolution Theory (pdf) |
| LabVIEW GUI Download LabVIEW not needed, zip file contains set-up for stand-alone GUI Two GUIs which present the convolution integral using both two arbitrary signals and a SDOF system | LabVIEW |
| GUI Overview and Assignment | GUI Overview & Assignment (pdf) |