Consider this image of a loop shaping design:

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here which is the bandwidth of the system? I have a doubt because until now I have considered as bandwidth to the system the one of the complementary sensitivity function, but I heard someone sayong that it is not a good measure for the bandwidth, so it is better to consider as bandwidth the one of the sensitivity function.

Can somebody clarify this?


1 Answer 1


There are many definitions of bandwidth. Typically it is determined from the open loop transfer function and not from the sensitivity or complementary sensitivity functions.

Assuming a SISO feedback loop, with plant $P$ and controller $C$, a common definition of bandwidth is the 0 dB crossover frequency of the open loop transfer function $PC$. Assuming that the sensitivity can be written as $\frac{1}{1 + PC}$ this is also (roughly) the frequency where the sensitivity peaks.


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