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I have a doubt concerning the closed loop frequency responce of a control system.

Suppose I have the following situation:

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in which is plotted the frequency response of a system with different badwidths. In this case I know that in generale the performances are good as the bandwidth of the closed loop increases and I know that the price to pay to increase the bandwidth is a high control effort, but is there some other drawbacks in increasing the bandwidth of a system?

I was thinking abouth the noises, which are at high frequencies, this if the bandwidth is at high frequencies, and the system does not roll off fast, the noises enter into the system.

But I am not sure about what I said.

I know that as the badwidth increases, also the reference tracking gets better, but I also see that the roll off is not smooth, I so I was interpreting also this as a fact that there are worse performances with respect to the noise rejection.

Also, I know that there are some limitation of increasing the bandwidth of a system. So, considering a stable and minimum phase system, I know that the limit in bandwidth ig given by the hardware.

But if I increase the bandwidth is there some other limitation? By doing some experimentaition I have see that the disturbance rejection gets worse after a certain frequency, is it due to noise?

Can somebody please help me?

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    $\begingroup$ Both points you bring up are valid arguments, the only thing I think I would add is robustness to system uncertainty. For example one might apply the same controller to many similar systems, but for example their masses might differ slightly. $\endgroup$
    – fibonatic
    Feb 10, 2020 at 15:58

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The three main drawbacks for a high bandwidth are:

  1. Noise amplification. The higher the bandwidth, the more you are going to act on high frequent stuff in your error signal. Noise typically dominates at the higher frequency and therefore the system will start reacting to it. Therefore, the noise will not be rejected / ignored but amplified.

  2. Robustness. In general, a high closed loop bandwidth will reduce the robustness margins (e.g. phase margin, modulus margin and gain margin). If you have tight margins, you can increase them with some advanced filtering (e.g. notch filter). However, the accuracy of how 'good' you can tune these filters depends on the model accuracy. Thus, if there is a mismatch between your model and the setup, or the setup changes over time, this can have a negative effect on your robustness margins and can even cause instability.

  3. Large control signals. In general, a high bandwidth requires a high gain. When the error is relatively large, this results in large control signals. Then the input signal may be saturated, resulting in nonlinear plant behavior, which may be undesired.

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