Higher order transfer function precision issue

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Steven
Steven 2014-3-3
评论： Paul 2024-7-24
Hi,
I'm creating a transfer function at higher order (to the degree of 80) by multiplication of many 2nd order transfer function. However, when I get this final transfer function, the result returned is NaN.
I suspect it is due to the precision error in MATLAB, and tried to use vpa commend. It didn't solve the problem by giving errors.
Could anyone advise me a solution please? thank you.
Steven
num_bnotch=vpa([1 4*0.20*pi*19.5 (2*pi*20.04)^2]); den_bnotch=vpa([1 4900.88 1.5855e+004]); bnotch=tf(num_bnotch,den_bnotch)
??? Error using ==> tf.tf at 251 The values of the "num" and "den" properties must be row vectors or cell arrays of row vectors, where each vector is nonempty and containing numeric data. Type "ltiprops tf" for more information.
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Landon Beutler
Landon Beutler 2024-7-24
I had the same issue with high order numeric transfer functions, but got around it by transforming models to space state form, combining them, and then converting the combined model back to a transfer function.
sys_combined = tf(ss(sys_1)*ss(sys_2))
Paul
Paul 2024-7-24
Hi Landon,
Converting from state space to transfer function isn't the right way to go (maybe there's an exception I'm not aware of?). Of the various model representations in the Control System Toolbox, the tf is probably the worst to deal with from a computational perspective, particuarly for high order models. Check out Using the Right Model Representation.

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Walter Roberson
Walter Roberson 2014-3-3
vpa() does not return numeric values: it returns symbolic numbers. tf() is complaining because you are passing it symbolic values.
You might be out of luck with trying to get a symbolic transfer function; see http://www.mathworks.com/matlabcentral/answers/48958-how-can-i-get-symbolic-transfer-function-from-block-diagram
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Walter Roberson
Walter Roberson 2014-3-4
NaN would not usually be directly due to a precision problem. You could, though, somehow end up getting 0 divided by 0 through underflow of both the numerator and denominator.
If you are multiplying transfer functions, perhaps you could instead add their logs ?

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