What is difference between repeated poles and distinct poles? [duplicate]

Repeated poles simply means there are more than one pole at the same location. If a pole is not repeated then it is a Distinct Pole.

1. Why are repeated poles on imaginary axis unstable?
2. How do poles affect settling time?
3. What are the poles of a transfer function?
4. What do the poles and zeros of a system tell us?

Why are repeated poles on imaginary axis unstable?

If there is any pole on the imaginary axis which is repeated (multiplicity > 1), then the linear system is unstable. This can be established by expressing the system in a partial fraction expansion and calculating the inverse Laplace transform. The repeated poles on the imaginary axis cause a stability problem.

How do poles affect settling time?

LHP Poles: Increase settling time. The effects are small if the pole is far in the LHP. LHP Zeros: Increase overshoot, decrease rise time, and have no effect on settling time. The effects are small if the zero is far in the LHP.

What are the poles of a transfer function?

The transfer function poles are the roots of the characteristic equation, and also the eigenvalues of the system A matrix. location; poles far from the origin in the left-half plane correspond to components that decay rapidly, while poles near the origin correspond to slowly decaying components. 2.

What do the poles and zeros of a system tell us?

Poles and Zeros of a transfer function are the frequencies for which the value of the denominator and numerator of transfer function becomes zero respectively. The values of the poles and the zeros of a system determine whether the system is stable, and how well the system performs.