Normalize function at an exact value

Question

Michael Brehmer 2021-2-16

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https://ww2.mathworks.cn/matlabcentral/answers/746937-normalize-function-at-an-exact-value

回答： arushi 2024-5-28

Hello,

I need to normalize 3 different systems, so that all of them let frequencies at 0.1 Hz through without filtering them.

To make it clear I have a picture of some bode plots of the systems:

As you can see, the 3 plots have different heights and filter different frequencies.

I now want to normalize each system, so that they let all frequencies at 10^(-1) (0.1) Hz through. I already tried the h_2 norm and the h_inf norm, but none of them seem to work as I need it. Is there a way to achieve this? My goal is that I normalize those systems, so that I can evaluate the results correctly (after I filtered an optimization problem with those systems).

Thank you

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Answer 1

arushi 2024-5-28

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Hi Michael,

To normalize the systems so that they all let frequencies at 0.1 Hz through without filtering them, you want to ensure that the gain at 0.1 Hz is the same for all systems.You may achieve this by adjusting the gain of each subsytem at the specified frequency.First, you need to find out the current gain of each system at 0.1 Hz. Decide on a target gain at 0.1 Hz that you want for all systems. This could be the gain of one of the systems, or another value that suits your requirements. Then, for each system, calculate a normalization factor.Lastly,Multiply the transfer function of each system by its corresponding normalization factor. This will adjust the gain of each system at 0.1 Hz to match the target gain.

Hope this helps.