Modern Control Engineering

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

Thus

Next we determine the value of Kcfrom the magnitude condition:

Hence,

The phase-lag portion of the compensator can be designed as follows: First the value of bis

determined to satisfy the requirement on the static velocity error constant:

Hence,bis determined as

Finally, we choose the value such that the following two conditions are satisfied:

We may choose several values for T 2 and check if the magnitude and angle conditions are satis-

fied. After simple calculations we find for T 2 = 5

SinceT 2 = 5 satisfies the two conditions, we may choose

Now the transfer function of the designed lag–lead compensator is given by

=

10(2s+1)(5s+1)

(0.1992s+1)(80.19s+1)

=6.26a

s+0.5

s+5.02

ba

s+0.2

s+0.01247

b

Gc(s)=(6.26)±

s+

1

2

s+

10.04

2

≤±

s+

1

5

s+

1

16.04* 5

≤

T 2 = 5

17 magnitude 7 0.98, -2.10° 6 angle 60 °

• 5 ° (^6) n
  s+

1

T 2

s+

1

16.04T 2

4

s=-2.5+j4.33

4 60 °

s+

1

T 2

s+

1

16.04T 2

4

s=-2.5+j4.33

1,

T 2

b=16.04

=limsS 0 s(6.26)

b

10.04

4

s(s+0.5)

=4.988b= 80

Kv=limsS 0 sGc(s)G(s)=slimS 0 sKc

b

g

G(s)

Kc=^2

(s+5.02)s

4

2

s=-2.5+j4.33

=6.26

(^2) Kcs+0.5
s+5.02

4

s(s+0.5)

2

s=-2.5+j4.33

= 1

T 1 =2, g=

5.02

0.5

=10.04

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