What do we know about the transfer function away from its zeros?

1. What do the zeros of a transfer function tell you?
2. Can a transfer function have no zeros?
3. How do you identify poles and zeros of a transfer function?
4. What does a transfer function tell us about a system?

What do the zeros of a transfer function tell you?

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.

Can a transfer function have no zeros?

First-Order System

The transfer function has no finite zeros and a single pole located at s=−1τ in the complex plane. The reduced-order model of a DC motor with voltage input and angular velocity output (Example 1.4. 3) is described by the differential equation: τ˙ω(t)+ω(t)=Va(t).

How do you identify poles and zeros of a transfer function?

The z_i terms are the zeros of the transfer function; as s→z_i the numerator polynomial goes to zero, so the transfer function also goes to zero. The p_i terms are the poles of the transfer function; as s→p_i the denominator polynomial is zero, so the transfer function goes to infinity.

What does a transfer function tell us about a system?

In engineering, a transfer function (also known as system function or network function) of a system, sub-system, or component is a mathematical function that theoretically models the system's output for each possible input. They are widely used in electronics and control systems.