BodePlotGui is a graphical user interface written in the MATLAB® programming language. It takes a transfer function and splits it into its constituent elements, then draws the piecewise linear asymptotic approximation for each element. It is hoped that the BodePlotGui program will be a versatile program for teaching and learning the construction of Bode diagrams from piecewise linear approximations.
Files for the program are found here
Consider the transfer function:
This function has three terms to be considered when constructing a Bode diagram, a constant (100), a pole at ω=10 rad/sec, and a zero at the origin. The following MATLAB® commands begin execution of the GUI:
>>MySys=tf(1000*[1 0],[1 10]); %define Xfer function >>BodePlotGui(MySys) %Invoke GUI
The GUI generates a window as shown below.
Starting in the upper left and going counterclockwise, the windows show:
Also shown in the upper right hand corner is the transfer function, H(s).
The function displayed can be manipulated term by term to illustrate the effect of each term. For example, the zero at the origin can be excluded simply by clicking on it in the lower left hand box. The figure below shows the result.
Note that the zero at the origin is no longer included in the plot. Each term can be likewise included or excluded by simply clicking on it.
The next plot shows the plot modified to have thicker lines, a grid, phase in radians and with the asymptotic plot of the complete transfer function. In the previous graph, the phase of the asymptotic plot obscured that of the real pole; this is an example when it might be convenient not to show the asymptotic approximation.
Underdamped poles (and zeros) present a difficulty because they cause a peak (dip) in the magnitude plot. The program show this with a simple circle showing the peak height. For example the transfer function
yields the output shown below. The peak due to the underdamped pole is clearly shown.
The example below is more complicated. It shows underdamped terms, repeated poles, and a pole at the origin.
The software has known limitations. It does not calculate the phase associate with a time delay. It only decomposes transfer functions with up to 20 separate terms (a limit only of the number of colors used). Repeated poles and zeros are treated as a single term (i.e., it is not possible to move only one pole of a repeated pair from the “Elements included in plot” window to the “Elements excluded from plot” window of the GUI).
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