Modern Control Engineering

384 Chapter 6 / Control Systems Analysis and Design by the Root-Locus Method

Real Axis

• 20 – 15 – 10 – 5 0 5 10

(a)

Imag Axis

• 5

5

15

0

10

• 10


• 15

Root-Locus Plot of Compensated System

Real Axis

• 10 – 0.5 0.5 1

(b)

Imag Axis

• 0.6

0

0.6

• 0.2

0.2

• 1

1

0.8

0.4

• 0.8


• 0.4

Root-Locus Plot of Compensated System near the Origin

Figure 6–91

(a) Root-locus plot

of compensated

system; (b) root-

locus plot near the

origin.

Figures 6–92(a) and (b) show the unit-step response and unit-ramp response of the designed

system, respectively. Note that the closed-loop pole at s=–0.1684almost cancels the zero at

s=–0.16025.However, this pair of closed-loop pole and zero located near the origin pro-

duces a long tail of small amplitude. Since the closed-loop pole at s=–17.205is located very

much farther to the left compared to the closed-loop poles at the effect

of this real pole on the system response is very small. Therefore, the closed-loop poles at

are indeed dominant closed-loop poles that determine the response

characteristics of the closed-loop system. In the unit-ramp response, the steady-state error in

following the unit-ramp input eventually becomes 1 Kv= 501 =0.02.

s=-1.8308;j3.2359

s=-1.8308;j3.2359,

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