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Anti aliasing in the real world?

Discussion in 'Electronic Design' started by mikem, Nov 13, 2003.

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  1. mikem

    mikem Guest

    I am experimenting with a PID controller which will be implemented in
    a microcontroller. The inputs come from gyroscopes and navigation
    equipment. The rate of change of these signals is instrisically slow,
    i. e. milliHz to 1Hz. Even without low pass filtering, these signals
    naturally exhibit at least a 20db per decade rolloff above 1Hz.

    AFIK, the update rate for the outputs can be as low as 10Hz (10x the
    fastest input) without compromising stability. This would dictate that
    the inputs should be sampled once per 100ms, fed through the control
    law, which then updates the outputs at 10Hz.

    If you have a signal with a natural cutoff frequency (-3db) of 1Hz
    (above which the signal exhibits a -20db/decade rolloff), and you want
    to sample that signal at 10Hz, how much additional anti-alias low-pass
    filtering needs to added before a 10bit A/D?

    Computationally, the microcontroller probably can sample and update at
    100Hz. If I turn up the compute rate to 100Hz, is the natural rolloff
    of the input signals sufficient to provide anti-aliasing without
    adding additional filtering?

    MikeM
     
  2. Bill Sloman

    Bill Sloman Guest

    The more important question is how do your output effectors react to
    high frequency quantisation noise on their inputs? If you feed the
    input of bipolar op amp more than about 20mV of high frequency noise -
    that is noise too fast for the feedback path to track it - the input
    tracks the peaks of the signal, not the average. This sort of effect
    can be a real problem.
     
  3. Strangely, anti-alias filters may cause more trouble than they are
    worth. I am working on some servos sampled at 50kHz. It is tempting to
    roll off the input to the controller at 25kHz. When I do that, the loss
    of phase margin is not very nice. It turns out that I have no unmodeled
    dynamics at embarrassing frequencies so I have removed my software notch
    filters as well as the analog anti-alias filters.

    Chuck
     
  4. Mac

    Mac Guest

    I think this question can be answered only when the power spectral density
    of the signal is known. If most of the power is in the alias free range,
    and the rest of the power is gaussian or otherwise diffusely distributed,
    then I don't see why you'd need a filter. But you better be sure this
    holds true under all possible operating conditions.

    If there is some way to make the filter optional, then experiment later,
    that would be ideal. In any event, I don't see how the filter could hurt.
    At least add an extra RC with a -3dB point at 5Hz. This will make the
    rolloff that much steeper.
    Well, in a sense you'd be getting an extra 20dB of filtering, according to
    your 20dB/decade rollof. I don't see how it could hurt, but I don't have a
    good understanding of your system, or control systems in general.

    ;-)
     
  5. Typically, if your feedback is too rapid, you can induce unexpected
    oscillations and control issues in a servo system. I would take the samples at
    10 hertz, but I would also filter the output to something more in the range of a
    hertz. Then you can be pretty close to what you want without getting ringing in
    your servo loop.

    Cheers!

    Chip Shults
    My robotics, space and CGI web page - http://home.cfl.rr.com/aichip
     
  6. Bill Sloman

    Bill Sloman Guest

    Designing filters that work inside a feedback loop requires fairly
    careful attention to the phase excursions and overall delays in the
    filters.

    Most electronic engineers don't run into this as a problem until they
    have to design a phase-locked loop, and it generally seems to come as
    a painful surprise.
     
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