Number of Poles in a System with Transfer Function C(s) = 1/(s-1)^3

Definition of Poles

In control systems engineering, poles are the points in the complex plane where the transfer function of a system becomes infinite. Poles are also known as singularities or resonant frequencies. They are critical to the stability and performance of a control system.

Finding the Number of Poles

The transfer function of the system is given as:

C(s) = 1/(s-1)^3

This transfer function has a pole at s=1. To find the total number of poles, we need to look at the highest power of (s-a) in the denominator of the transfer function, where a is the location of the pole. In this case, the highest power of (s-1) is 3.

Therefore, the transfer function has 3 poles at s=1.

Answer

The number of poles in the system with transfer function C(s) = 1/(s-1)^3 is 3.

Explanation

The transfer function of the system is given by C(s) = 1/(s-1)^3. This transfer function has a pole at s=1. The highest power of (s-1) in the denominator is 3, which means that there are 3 poles at s=1. Poles are critical to the stability and performance of a control system, and it is important to know how many poles a system has in order to analyze its behavior.