Section 6–8 / Lag-Lead Compensation 333
is approximately unity, where is one of the dominant closed-loop poles,
choose the values of and gfrom the requirement that
The choice of and gis not unique. (Infinitely many sets of and gare possible.)
Then determine the value of Kcfrom the magnitude condition:
4.If the static velocity error constant Kvis specified, determine the value of bto
satisfy the requirement for Kv. The static velocity error constant Kvis given by
whereKcandgare already determined in step 3. Hence, given the value of Kv, the value
ofbcan be determined from this last equation. Then, using the value of bthus deter-
mined, choose the value of such that
(The preceding design procedure is illustrated in Example 6–8.)
Case 2. Ifg=bis required in Equation (6–23), then the preceeding design
procedure for the lag–lead compensator may be modified as follows:
1.From the given performance specifications, determine the desired location for the
dominant closed-loop poles.
g=b.
- 5 ° 6
n
s 1 +
1
T 2
s 1 +
1
bT 2
60 °
4
s 1 +
1
T 2
s 1 +
1
bT 2
4 1
T 2
=slimS 0 sKc
b
g
G(s)
=slimS 0 sKc±
s+
1
T 1
s+
g
T 1
≤±s+
1
T 2
s+
1
bT 2
≤G(s)
Kv=slimS 0 sGc(s)G(s)
4 Kc
s 1 +
1
T 1
s 1 +
g
T 1
GAs 1 B 4 = 1