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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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