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A few control system questions:

  1. I have a few Control System questions:

    I'm looking for a simple explanation of when each of these are used... whenever I read about them, I just can't remember which is used for what; this is probably because the book I'm using explains it in hard to understand terms.

    1) When do you use a Phase-Lead Compensator?

    2) When do you use a Phase-Lag Compensator?

    I understand each is used to shift the frequency responses in a certain direction, but I can't seen to figure out a good way to remember which does what. Maybe I'm missing the idea behind the terms "Lead" and "Lag"? In fact, what are the reasonings behind the Lag and Lead terms? What exactly is being lagged or lead?

    PS - I know these questions are painfully obvious, but I'm so burdened by work that I can barely think. I just can't seem to get the concepts right.

    Thank you.
     
  2. jcsd
  3. berkeman

    Staff: Mentor

    They're not obvious, so no worries about asking. Are you familiar with a gain-phase plot? What is special about the unity gain crossover frequency? What is phase margin, and why is it important?

    I don't know if your text discusses stability and compensation in terms of the gain-phase plot, but that's the easiest way I know of to visualize it.
     
  4. Yeah, it's all introduced in the frequency domain design unit. I acutally apent the night just researching and figured out the answers to my questions. This sort of stuff needs to be introduced very clearly - which was not done for me.

    Thanks.
     
  5. phase Lead:
    1) Pass low freq & Attenuate higher one.
    2)Shift the gain crossover frquency to a higher value.
    3)Bandwidth increase.
    4)Overshoot dec
    5)Steady state error not much affected.

    Phase-lag:
    1)1) Pass High freq & Attenuate lower one
    2)Shift the gain crossover frquency to a lower value.
    3)Bandwidth dec.
    4)Overshoot inc
    5)Steady state error improve.
     
  6. Phase lead moves the dominant poles to the left, making the system faster. Phase lag in general maintains the position of the dominant poles, but increases gain.
    If the system has poor transient response, you should use phase lead compensation to reduce settling time. If the system has excessive steady state error, you should use phase lag, since increased gain reduces the error.
     
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