# What does having complex conjugate zeros implies?

I am studying control systems, and I have found a system which has two complex conjugate zeros.

I know that if I had two complex conjugate poles in the system, this implies having some damping in the frequency response, but what does having complex conjugate zeros implies?

Moreover, I have found them in the RHP, so they have positive real part, what does this implies?

By plotting the frequency response of my system I have this:

I know that if I had two complex conjugate poles in the system, this implies having some damping in the frequency response, but what does having complex conjugate zeros implies?

Possibly a simple way of looking at this is to imagine that you have a low pass filter with a damping ratio ($$\\zeta\$$) less than 1 (complex poles) and you used it in a negative feedback branch of a regular amplifier you will get zeros replacing the poles.

Assume that K = $$\\dfrac{\omega_n^2}{s^2+2\zeta\omega_n s + \omega_n^2}\$$

After it is used in the feedback loop you get: -

$$H(s) = \dfrac{s^2+2\zeta\omega_n s + \omega_n^2}{s^2+2\zeta\omega_n s + 2\omega_n^2}$$.

Notice the $$\2\omega_n^2\$$ in the denominator (in case you missed it) and also notice that you have conjugate zeros in the numerator.

• Could you elaborate on the time signature of such zeros? Commented Jul 4, 2023 at 0:17
• Not really because poles and zeros don't have time signatures. Commented Jul 4, 2023 at 6:49
• I'm afraid they do. Examples include the feedforward nature of zeros and the exponential/ringing nature of poles. Of course, these are rough statements and rigor must be exercised when computing the exact step response. Commented Jul 5, 2023 at 7:03
• Poles and zeros don't have a step response inherently. I think you should formally ask a brand-new site-wide question. Commented Jul 5, 2023 at 7:16