control question about root locus plotting?

Question

what is the physical meaning of poles and zeroes 4 characteristic equationof transfer function?what the change happens after a change in poles or zeroes?

Answer 1

They determine the frequency and phase response of the system.

Think of a sheet of rubber that represents the complex plane. Zeros tack that rubber sheet down at zero amplitude (for the frequency response), while poles stretch the rubber to points at infinity (the rubber is very stretchy). When all the poles and zeros are plotted, the rubber sheet is like a tent with tent stakes at zeros and tent poles at the poles. I

Now, if you take the cross section of this tent, cutting down through the imaginary axis, and if you graph the edge of the tent (as it intersects the plane) you will have a frequency response curve of the system.

(To get the phase response is a little more difficult.)

If you have no zeros (but at least one pole), then there will be some value at s=(0,0), meaning the system will pass DC. If there are zeros present, then the system will not pass DC (it is AC coupled).

Think of a single real pole moving along the real axis (left side of the plane). If it is close to the imaginary axis it will tend to raise the amplitude of the frequency response at low frequencies, even peaking them at some low frequency while the response drops at higher frequencies. As you move that real pole away from the imaginary axis, the frequency response curve drops and smooths out.

Complex pole-pairs raise the amplitudes of the frequency response curve to higher frequencies. Multiple sets of pole-pairs can shape the frequency response curve to be almost anything you want, depending on how they are arranged in different patterns.

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