Page 829 - The Mechatronics Handbook

066_Frame_C26 Page 14 Wednesday, January 9, 2002 1:59 PM

4
3
2
1
Imag Axis 0
−1
−2
−3
−4
−6 −5 −4 −3 −2 −1 0 1
Real Axis

FIGURE 26.13 Root locus for Example 3(b).

6

4
2
Imag Axis 0

−2
−4

−6
−16 −14 −12 −10 −8 −6 −4 −2 0 2
Real Axis

FIGURE 26.14 Root locus for Example 3(c).
(b) p m = −0.5, p 1 = −1, p 2 = −2, p 3 = −3 ⇒

K = 8.25, p = −5.50, z = −0.73
c
c
(c) p m = −5, p 1 = −11, p 2 = −4 + j1, p 3 = −4 − j1 ⇒
K = 35, p = −14, z = −5.343
c
c
Example 4
Consider the open-loop transfer function

( s – 3s + 3) sz c )
(
2
–
P s()Cs() = K c -------------------------------------------------
(
ss +( 2 3s + 3) sp c )
–
where K c is the controller gain to be adjusted, and z c and p c are the controller zero and pole, respectively.
Observe that the root locus has four branches except for the non-generic case z c = p c . Let the desired
dominant closed-loop poles be r 1,2 = −0.4. The steady state error for unit ramp reference input is
e ss = ---------
p c
K c z c

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