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va

ce

ia

T m = J m/F m

T a = la/ra

T m ∼= 150s T a ∼= 30ms

ω∗

m ωm

i∗a

ia

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va = raia + ladiadt

+ ea

ea = keλeωm

ea

va = va − ea

va = raia + ladiadt

I a(s) = 1/raT as + 1 V a(s) = G1(s)V a(s)

T v

V a(s) = 1

T vs + 1V ∗a (s) = Gv(s)V ∗a (s)

va = va − ea

V a(s) = V ∗a (s)Gv(s) − E a(s)

V ∗a (s) = V ∗a (s) + E ∗a(s)Ge(s)

V a(s) = V ∗a (s)Gv(s) + E ∗a(s)Ge(s)Gv(s) − E a(s)

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ea

Ge(s) = 1/Gv(s) E ∗a(s) = E a(s)

V a(s) = V ∗a (s)Gv(s)

V a(s)

I a(s) = 1/ra

(T as + 1)(T vs + 1) V ∗

a (s) = Gi(s)V ∗

a (s)

T v

G pii(s) = k pi + kii

s =

kii(sk pi/kii + 1)

s

Goi = G pii(s)Gi(s) = (kii/ra)(sk pi/kii + 1)

s(T as + 1)(T vs + 1)

T a = k pi/kii

Goi

Goi(s) = kia

s(T vs + 1)

kia = kii/ra.

Gfi

Gfi(s) = kia

s(T vs + 1) + kia=

kia

T vs2 + s + kia

kii

kii = ra/(4T v)

I a(s) = Gfi(s)I ∗a(s) = 1

(2T vs + 1)2I ∗a(s)

I a(s) = Gfi(s)I ∗a(s) ∼= 1

T vs + 1I ∗a(s)

T v = 4T v

ea

Ge(s) = 1/Gv(s)

ea

ea

ea

= 0

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ce − cm = J mdω

dt + F mωm

ce = ce − cm = J mdω

dt + F mωm

Ωm(s) = (1/F m)

T ms + 1

C e(s) = G2C e(s)

cm

C m = 0 C e(s) =

C e(s) = keλeI a(s)

Ωm(s) = keλe/F m

(1 + sT m)(T vs + 1)I ∗a(s) = GωI ∗a(s)

T v

G piω(s) = k pω + kiω

s =

kiω(sk pω/kiω + 1)

s

Goω(s)

Goω(s) = G piω(s)Gω(s) = kim(sk pω/kiω + 1)

s(1 + sT m)(T vs + 1)

kim = kiωkeλe/F m.

T m = k pω/kiω)

Goω(s) = kim

s(T vs + 1)

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Gfω

Gfω(s) = kim

s(T vs + 1) + kim

= kim

T vs2 + s + kim

kiω = F m/(16keλeT v)

Ωm(s) = Gfω(s)Ω∗

m(s) = 1

(2T vs + 1)2Ω∗

m(s)

dx(t)/dt = Ax(t) + Bu(t)

t

x(t)

to

x(to)

x(t) = eA(t−to)x(to) +

tto

eA(t−τ )Bu(τ )dτ

eAt

t + h, x(t + h),

t

x(t)

x(t + h) = eAhx(t) +

t+h

t

eA(t+h−τ )Bu(τ )dτ

h

u(t)

B

x(t + h) = F x(t) + Hu(t)

F = eAh

H = [

h0

eAν dν ]B

eAh

F = eAh =∞

j=0

(Ah) j

j! = I + Ah +

(Ah)2

2! +

(Ah)3

3! + ....

H

H = [∞

j=0

Aih j+1

( j + 1)!]B = [I +

Ah

2! +

(Ah)2

3! +

(Ah)3

4! + ....]Bh

x(t)

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ea

cm ω∗

m

t = 0

cm t = tmax/2

tmax

1s

ea

Ge = 1

|i∗a| < 1.5

|v∗a| < 1.5

ea

Ge(s) = 1/Gv(s)

Ge(s)