Page 480 - Mechanical Engineers' Handbook (Volume 2)

5 Closed-Loop Representation 471

Figure 22 Impulse responses associated with pole locations. LHP, RHP: left- and right-half plane.

t
The fundamental responses that can be obtained are of the form e t and e sin t with
0. It should be noted that for a real pole its location completely characterizes the
resulting impulse response. When a transfer function has complex-conjugate poles, the im-
pulse response is more complicated.

5.4 Standard Second-Order Transfer Function
A standard second-order transfer function takes the form
2 1
G(s) n (67)
2
2
2
s 2 s 2 n s / 2 (s/ ) 1
n
n
n
Parameter is called the damping ratio, and is called the undamped natural frequency.
n
The poles of the transfer function given by Eq. (67) can be determined by solving its char-
acteristic equation: