Thursday, December 22, 2011

Transient Response Analysis using Matlab Part 2

In previous posts I've described how to determine the mathematical equations of electrical circuit system, a mathematical equation in the domain s (Laplace), and block diagram of input-output relationship of the system, on this occasion I will describe how to display the input-output relationship graphs to analyze transient response of the system using MATLAB. Here's the description :

1. Open Matlab program, here I am using Matlab version 7:11 (R2010b)
For those of you who do not have the Matlab program, following the download link for 7:11 Matlab version (R2010b)

2. Open the application provided by Matlab Simulink, click the "Simulink" on matlab toolbar
If matlab toolbar is missing, we can find with right-clicking the bar under the file menu and select matlab toolbar. After clicking the Simulink it will appear as follows, and then select a new model to get started.

3. Input Components to Workspace
To analyze a system, either an electrical circuit or mechanical systems, we need a few components that needed to analyze, to use these components we only need to drag them from Libraries to the workspace. Here are some of the necessary components :
  • Sources that will be tested on the system, are in librarie: Simulink> Sources,
  • Sum (Simulink> Commonly Used Block),
  • Transfer fcn (Simulink> Continuous),
  • Scope (Simulinks> Sinks),
  • Mux - required only if you want to display the signal source to scope (Simulink> Signal Routing).

5. Choose the Sources
Because we are here to analyze the system of unit-step signal, then we choose the Sources "Step"

6. Connect the component parts of each other, as shown below :

7. After that, doblle-click on the source (step)
 it will show a dialog box as follows :

Step time : serves as the time interval from the beginning to the end.
Initial value : initial value
Final value : the value of final

Here we will use the test signal, the unit-step amplitude 1 from time 0 seconds. Then fill in,
Step time: 0
Initial value: 1
Final value: 1

Then click OK

8. Double-click on the Sum, and fill dialogbox appears with | + -
So that the process looping / process control will reduce the value of the system.

9. Double-click on the transfer fcn, then fill in appropriate transfer function of the system
Because we have a transfer function of the system we just change the column numerator coefficients and denominator coefficients. Change to:
numerator coefficients: [1]
denominator coefficients: [1 1]
space as a separator between the rank values ​​of s, for example if we want to make the equation s4+s2-3s+21 then we fill in with [1 0 1 -3 21]

10. Next, click start simulator 'icon play' on the toolbar
Double click Scope on the workspace. Then it will appear as follows :

Purple line: The input signal
Yellow line: The output signal from the system.
To clarify we can click on the autoscale 'icon binoculars'.

Or we can set by right-clicking on the graph and select axes properties (to set the charts on the Y axis). As for the X axis we can set the toolbar to the workspace by fill rate simulation stop time (right side start the simulator).

From the graphic we can analyze the characteristics of the system against the response signal which tested. And to test with another test signal, we only need to replace the sources.

From this graph we can see the characteristics of the system, both the delay time, steady state error, etc.

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