I am studying control systems, and have encountered the definition of a slow zero. I am searching on internet and in books, but I don't understand the meaning this. I know that if a zero is too slow, it introduces a resonance peak and an overshoot in the step response, but what is a slow zero?

I thought it was a zero close to the imaginary axis in the root locus, so a zero at low frequencies, but I am not sure, since I cannot find a definition.

I know that a pole that is close from the imaginary axis settles quicker than a pole far from the imaginary axis. But I did some simulations in Matlab, and using a lead compensator, I have seen that if I decrease frequency of the zero in the lead compensator, the overshoot in the step response increases.

enter image description here

Here, the lead compensators I have used are as below.

lead = (1+10*0.05*s)/((1+0.05*s));          %red line
lead_2 = (1+30*0.083*s)/((1+0.083*s));      %blu line
lead_3 = (1+50*0.083*s)/((1+0.083*s));      %green line

Can somebody help me?


1 Answer 1


Again I refer you to the Murray's book. Which is free by the way


From the book "Furthermore a zero is said to be “slow” if its magnitude is smaller than the intended closed loop bandwidth."

  • 2
    $\begingroup$ wow. i thought a zero is "slow" for the same reason a pole is "slow". a slow pole is one associated with an impulse response that is a decaying exponential having a long time constant. longer time constant means lower corner frequency of the associated frequency response. so for the corner frequency associated with a zero (that would be a + 6 dB/oct corner), the association between the corner frequency and the speed of the zero is the same relationship as with poles. $$ $$ it's an interesting article, though, and i found the references. $\endgroup$ Feb 12, 2020 at 20:33

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