Modern Control Engineering

Section 10–6 / Design of Regulator Systems with Observers 785

Finally, we shall compare the root-locus plots of the first system with L=[–10 –10]

and the second system with L=[–4.5 –4.5].The plot for the first system given in

Figure 10–24(a) shows that the system is unstable for small dc gain and becomes stable

for large dc gain. The plot for the second system given in Figure 10–24(b), on the other

hand, shows that the system is stable for any positive dc gain.

Frequency (rad/sec)

Bode Diagram of System 2 — Closed Loop

− 200

− 50

− 100

− 150

0

− 60

− 40

Phase (deg); Magnitude (dB)

20

− 20

0

10 −^1100101102

Figure 10–23
Bode diagram for the
closed-loop transfer
function of System 2.

Root-Locus Plot of (91s^3 + 917s^2 + 2720s + 2500)/

(s^5 + 27s^4 + 164s^3 + 108s^2 − 720 s)

Real Axis

Imag Axis

2

− 4

− 6

− 8

− 14 − 12 − 10 − 8 − 6 − 4 −20 2

4

− 2

0

6

8

(a)

Root-Locus Plot of (12.109s^3 + 136.343s^2 + 477.375s + 506.25)/

(s^5 + 16s^4 + 86.1406s^3 + 165.406s^2 + 51.3744s)

Real Axis

Imag Axis

2

− 3

− 4

− (^5) − 8 − 7 − 6 − 5 − 4 − 3 − 2 −10 1 2
3
− 2
− 1
0
1
4
5
(b)
Figure 10–24
(a) Root-locus plot of the system with observer poles at s=–10ands=–10;(b) root-locus plot of the
system with observer poles at s=–4.5ands=–4.5.