Bode, Nyquist, and Nichols Diagrams of Second-Order Systems

Bode diagram

Nyquist diagram

Nichols diagram

process gain K

1

response time τ

1

damping coefficient ζ

1

Consider a second-order system given by the transfer function:

G(s)=

K

p

2

τ

2

s

+2ζτs+1

,

where

ζ

is the damping coefficient,

τ

is the response time, and

K

p

is the process steady-state gain.

This Demonstration plots the Bode, Nyquist, and Nichols diagrams for user-set values of the parameters

ζ

,

K

p

, and

τ

. Different behaviors are observed for

0≤ζ<1

(underdamped or oscillating system),

ζ=1

(critically damped system), and

ζ>1

(overdamped system).