Page 41 - Servo Motors and Industrial Control Theory -

2.6 Nyquist Plot 33

Fig. 2.11 Nyquist plot for 1 1
first order lag open loop
transfer function
0.5

Imag
–1 –0.5 0 0.5 1

–0.5

–1 –1

–1 Real 1

Fig. 2.12 A unity feedback
control system with second 1
order Lag open loop transfer x + 1 ξ y
2
function s – 2 s + 1
(ω ) 2 ω n
– n

−
1
ϕ =− tan (τω ) (2.16)
The plot of frequency response of open loop transfer function, which is known as
Nyquist plot is shown in Fig. 2.11. It can be seen that for first order lag transfer
function the locus is a semi-circle. When ω = 0 the plot starts at point 1 and for
frequency of large value the plot ends at zero indicating that this type of transfer
function the system remains stable. The response to a unit step input is always over-
damped. This is shown in Fig. 2.11.
The Nyquist plot is located in the first quadrant measuring from the real axis
clockwise showing that this kind of system is always stable.
A system with a second order lag open loop transfer function is shown in
Fig. 2.12. It is assumed a unity gain and unity feedback.
It was shown that the amplitude ratio and phase angle are given as
1
M = 2 2
2 ) +
(1 − ω 2 2 4ζω (2.17)
ω n ω 2
n