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340 CHAPTER 10 Scalar and Vector Control of Induction Motor

4.2 SELECTION OF THE REGULATORS
The regulators used are PI type whose transfer functions are given by:
K p ð1 þ s p sÞ
RðsÞ¼ (10.12)
s p s
For the selection of the regulator parameters, the method of zeros compensation
is adopted [24]. The flux regulator output allows the direct stator current i sd to be
generated, using Eq. (10.10). The transfer function relating the current to the voltage
of the direct stator component is given by Eq. (10.13). The regulation scheme is
given by Fig. 10.3.
1

m 2
r s þ
i sd ðsÞ l r s r
H 1 ðsÞ¼ ¼ (10.13)
v sd ðsÞ k s

s
1 þ
m 2
r s þ
l r s r
Using Eq. (10.11), the torque regulation ensures the regulation of the quadrature
stator current i sq . The transfer function relating the current to the voltage of the quad-
rature stator component is given by Eq. (10.14) with its principle described by
Fig. 10.4:
1

m 2
r s þ
i sq ðsÞ l r s r
H 2 ðsÞ¼ ¼ (10.14)
v sq ðsÞ k s
s
1 þ
m 2
r s þ
l r s r
Flux m
+ —
- regulator 1 + τ s
r
FIGURE 10.3
Principle of flux regulation.

i
PI sq m
+ C em = p — ϕ r i sq
- l r

FIGURE 10.4
Principle of the torque regulation.