# Lead/Lag compensator - lead and lag time to pole and zero locations

Tags: compensator, control, lag, lead, time
 P: 4 Hi, I am having difficulty understanding how to convert pole and zero locations of a lead lag compensator into lead and lag time and vise versa. I have a digital lead and lag compensator which requests: gain, lead time (min) and lag time (min). However i have the gain zeros and poles of the compensator. If someone can tell me how to do this i would be most grateful. Adam
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P: 40,649
 Quote by adamkse Hi, I am having difficulty understanding how to convert pole and zero locations of a lead lag compensator into lead and lag time and vise versa. I have a digital lead and lag compensator which requests: gain, lead time (min) and lag time (min). However i have the gain zeros and poles of the compensator. If someone can tell me how to do this i would be most grateful. Adam
Given the DC gain and poles and zeros of the transfer function, you should be able to make a Bode Plot that will show you your gain and phase margin. A pole gives you lead, and a zero gives you lag. You can adjust the position of the poles and zeros to ensure that you have adequate phase margin to ensure stability.

http://en.wikipedia.org/wiki/Bode_plot

Although I notice that the concept of lead-lag compensation may be treated a bit differently in control theory, compared to the circuit design context that I'm familiar with: