1. Definitions:
- The phase crossover frequency, w_{pc }, is the frequency where phase shift is equal to -180^{o}.
- The gain crossover frequency, w_{gc}, is the frequency where the amplittude ratio is 1, or when log modulus is equal to 0.
Example 1: Given the following Bode plots,
Example 2: Given the following Bode plots,
The phase crossover frequency is at 1.43 rad/sec, while the gain crossover frequency is at 1.06 rad/sec. The system is closed loop stable with the following stability margins:
PM= 180^{o }+ (-142^{o}) = 38^{o}
20 log(1/GM) = -17 or GM = 10^{(17/20) }= 7.08
The Nyquist plot is shown below:
This page is maintained by Tomas B. Co (tbco@mtu.edu).
Last revised 2/13/2000.
Tomas B. Co
Associate Professor
Department of Chemical Engineering
Michigan Technological University
1400 Townsend Avenue
Houghton, MI 49931-1295