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# Compensators with imaginary components-what's their utility?

## Compensators with imaginary components-what's their utility?

(OP)
Hello All,
I'm trying to understand what situations would compel you to use a compensator with imaginary components (that is s = x+jy). Such a compensator would have some oscillatory component about it, but that doesn't seem useful. Because they come in pairs, is it when you need 2 poles or zeros? Thanks!
Replies continue below

### RE: Compensators with imaginary components-what's their utility?

Think of it from a closed loop perspective.

Ultimately you are trying to get your plant to respond a certain way. You do this by setting the closed loop poles to where you want them. In order to do this you must add a compensator with the poles/zeros necessary to do this, and sometimes those poles/zeros are complex (have imaginary component). So, in theory, you could have a compensator with complex roots, but the output of the closed system could have an over-damped response (no oscillation) if you design it that way.

Best!

### RE: Compensators with imaginary components-what's their utility?

One of the most common uses of complex pole or zero pairs in a control compensator is to deal with oscillatory modes in the plant under control. A typical early controls lab is designing a compensator to control two masses connected by a spring. The required compensator will have a complex zero pair.

This feature of a compensator is often called a "notch" filter, or a "band-reject" filter, because it does not pass through signal energy in a specific small frequency band, while allowing both lower and higher frequency components through.

Remember that the actual implementation of the filter in execution does not use imaginary values at all.

Curt Wilson
Omron Delta Tau

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