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These are answers submitted by jan

This sounds like you need the expectation maximization algorithm.

Here is a link:




It turns out that I was wrong.  The two techniques do not produce mathematically equal results.

Case 1: Add the outputs of the BodePlot

In this case we take the individual transfer functions and calcuate the Bode plot for each and sum them together.  While calculating the Bode plot, we take an absoute value of the transfer function.  So mathematically, we have something like this:

abs(sys[1,1]) + abs(sys[1,4]) + abs(sys[1,5])

Case 2: Add the systems

In this case we sum the transfer functions together and then calculate the Bode plot from the combined system.  This would correspond to a new system that looks something like this:


          +---| sys[1,1]  |-----+
          |   +-----------+     |
          |   |                 |
          |   +-----------+    /-\
     -----+---| sys[1,1]  |---| + |--->
          |   +-----------+    \-/
          |   |                 |
          |   +-----------+     |
          +---| sys[1,1]  |-----+

Or mathematically

abs(sys[1,1] + sys[1,4] + sys[1,5])

Since the abs function in the BodePlot is non-linear the two cases are not the same.  Which case you would want to use depends on what you are trying to do.


PS: I would also increase the precision of the caculations using the Digits variable, for example if you do

Digits := 30

at the begining of the worksheet.






You can also add up the three transfer functions and create another systme object.  Then you can plot the bode plot using htis new object.

sys2 := TransferFunction(sys:-tf[1, 1] + sys:-tf[1, 4] + sys:-tf[1, 5]);

And then

BodePlot(sys2, decibels = false, numpoints=1000, range=10..1000);

In this example, you may want to increase the number of points you are plotting (with the numpoints option) and zoom in a bit (with the range option).




PS: Here is Maple's best kept secret.  You can use the legend option in the BodePlot command to label the three curves in the original bode plot, i.e.

BodePlot(sys, decibels = false, subsystem = [[1, 1], [1, 4], [1, 5]], legend=["Output 1", "Output 4", "Output 5"])

And if you want to get really fancy, then you can also change the color, thickness, and linestyle, i.e.

BodePlot(sys, decibels = false, subsystem = [[1, 1], [1, 4], [1, 5]], legend=["Output 1", "Output 4", "Output 5"], thickness=[1,2,3], color=[red, green, blue], linestyle=[solid, dash, dashdot]);


If you are using standard Maple, you can just drag the file onto the worksheet. This will open the file in another tab of the same instance. Jan
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If all you want is to be able to load and save matrices, you should have a look at MatrixImport and MatrixExport. These procedures can read and write data files directly to matrices. The files can be in different formats, and one of the formats is also MATLAB. To do a low level I/O, you should have a look at fopen and fclose to open and close the files. To read and write text you may want to look at fscanf, fprintf, readline and writeline. To read and write binary data, have a look at readdata and writedata. There is also a FileTools package that contains a collection of file manipulation utilities. All of these procedures have help pages with examples. Hope this helps, Jan Bakus Applications Engineer, Maplesoft
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