Page 24 - Servo Motors and Industrial Control Theory

16 1 Feedback Control Theory

Fig. 1.15 Phase angle 0.0 0
response of a second order
Phase angel (deg) ψ3 (ω) 100
system for ς = 0.1, ς = 0.5, ψ1 (ω)
ς = 1, ς = 2 ψ2 (ω)

ψ4 (ω)
180
0.1 1 10 100
0.1 ω 100
frequency w/wn (rad/sec)

quency. The phase angle changes from 0° to − 180° at high frequency. If ω , ς are
n
known, the frequency response can be calculated. If the experimental frequency
response is obtained, then the natural frequency and damping ratio can be obtained
from the result. Once natural frequency and damping ratio are known, the transfer
function can be determined.

1.11 Conclusion

In this chapter, it was shown that by taking Laplace Transform from governing dif-
ferential equations, the concept of transfer function can be introduced. Block dia-
gram can then be used to represent the system. The standard first and second order
transfer functions were studied. Negative and positive feedback was introduced.
And some procedure was used to reduce the block diagram to a single block. In gen-
eral, any system with any complexity can be reduced to a single block. The problem
is then to study the stability, transient response, and steady state error.