Control System

Bode Diagram [Part 2]

Numeric Analysis (Minimum Phase System)

Example 1

To create a Bode diagram of a transfer function, we have to break it down into simpler components and plot each component on a Bode diagram.

The transfer function can be broken down into the following components:

Constant Gain Component:

Constant gain is 10. In decibels (dB), this is:

Component Integrator (1 / s):

This component provides a slope contribution of -20 dB/decade starting from a frequency of 1 rad/s. So, at low frequencies, the magnitude will decrease by 20 dB/decade.

Pole Components on (𝑠 = 1):

This component provides a slope contribution of -20 dB/decade starting from a frequency of 1 rad/s. So, at a frequency of 1 rad/s, the slope will change to -40 dB/decade.

Pole Components on (s = 10):

This component contributes a slope of -20 dB/decade starting from a frequency of 10 rad/s. So, at a frequency of 10 rad/s, the slope will change to -60 dB/decade.

Magnitude Bode Plot:

• At a frequency of 0.1 rad/s: Initial results are 20 dB of constant gain.
• At a frequency of 1 rad/s: Additional -20 dB/decade from the integrator, so…