Difference between repeated poles and distinct poles?

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 unstable?
2. Are poles the same as roots?
3. What will happen to the stability of the system if closed loop poles moves in the left half way from imaginary axis?

Why are repeated poles unstable?

In simple way, inverse laplace of A/s^2 terms is ramp function. So if there is any s^n term in s domain, its inverse will give ramp, parabola or higher order functions in time domain,these functions are unbounded. So multiple poles on origin implies an unstable system.

Are poles the same as roots?

Poles are the roots of the denominator of a transfer function. Let us take a simple transfer function as an example: Here Poles are the roots of D(s) and can be evaluated by taking D(s) = 0 and is solved for s. Generally, the number of Poles is equal or greater than Zeros.

What will happen to the stability of the system if closed loop poles moves in the left half way from imaginary axis?

Closed-Loop Stability

Hence, any poles moving toward the left-hand side in the pole-zero map will contribute to faster system response.