3
d
3
t
T
T
T
T
d 0
d 0
d 0
d 0
(29)
d
1
d t
2
d
T
1
c
E U
U X X
2
1
q
1
d
q
b
1
c
L
sin
sin 2
d t T
T
T
T X
T 2
a 0
a 0
a 0
a 0
d
a 0
XdXq
We select the error of voltage U
as state varible, The relation between U and U
is
U
U U 0
(30)
In the equation: U 0 is initial value of stator winding terminal voltage, its value is 1.
2
E U
U X X
We use
q
d
q
e
P repalce
sin
sin 2 , regarding
X
2
e
P as external disturbance,
d
XdXq
substituting Eq.(30) into Eq.(29), we get
d Efd
Efd K 2
u
dt
2
2
T
2
T
d U
1
1
c
1
3
Xd Xd
E
fd
U
c 3
( c 3
)
Id
d t
d
T 0
d
T 0
d
T 0
d
T 0
d
T 0
(31)
d 1
d t
d T
1
b
c 2
1
1
c
L
P
d
e
t
a
T 0
a
T 0
a
T 0
a
T 0
Eq.(31) can be written as matrix form
x A x
1
B w
2
B 2
u
(32)
1
0
0
0
T
E
2
fd
1
1
c
3
c
In the equation:
U
x
,
3
,
A T
T
T
d 0
d 0
d 0
0
0
0
1
T
0
0
0
b
a
T 0
70
Applications of Nonlinear Control
0
0
0
0
K
X
2
I
d
Xd
1
0
0
c
d
3
T
2
d
T 0
d
T 0
L
1
B
, B
, w
.
0
0
0
1
2
0
e
P
0
c
2
1
c 1
1
0
0
a
T 0
a
T 0
a
T 0
Defining the evaluation signal of dynamic performance as
z
C x D w D u
1
11
12 2
(33)
z
2
C 2 x
21
D w
22
D
2
u
q 14
0
0
0
q
0
0
0
r
r
24
3
7
0
q
0
0
0 q
0
0
r
r
In the equation:
15
C
25
4
8
1
, C
, D
, D
,
0
0
q
2
12
22
16
0
0
0
q
0
r
r
26
5
9
0
0
0
q 17
0
0
0
q 27
6
r
10
r
0 0 0 0
0 0 0 0
11
D
21
D
, C , C ,
q >0( i=1,2; j=4-
0 0 0 0
1
2
11
D , 12
D , 21
D , 22
D are weighting matrix, ij
0 0 0 0
7)and ir >0( i=3-10)weighting coefficient. We can select optimal performance combination
through changing weighting coefficient, including stability of ship power system, voltage
regulation precision and low energy loss of excitation system.
From Eq.(32) and Eq.(33), we can get the augmentation controlled object based on mixed H-
two/H-infinity control theory
A
1
B
2
B
P
C
1
1
D 1
1
D 2
(34)
C
2
2
D 1
2
D 2
For controlled object P , existing H-two/H-infinity state feedback controller:
Efd
U
2
u
F x [ f 1 f 2 f 3 f 4]
f 1 Efd f 2 U f 3
f 4
(35)
That is nonlinear H-two/H-infinity voltage control law of diesel-generator set.
Third step, we design nonlinear robust synthetic controller.
Combining Eq.(28) with Eq.(35), we can get nonlinear robust synthetic controller of diesel-
generator set[11-18]
Robust Control Research of Chaos
Phenomenon for Diesel-Generator Set on Parallel Connection
71
1
T T
T T
T T
T
T
T E U
1 0
1 0
1
1
1
1
q
a
a
b
1
u
L
f 1
f 2(
1)
f 3
f 3 1
c
f 3 L
f 3 sin
K
1
c 2 K 1
c 2 K 1
c 2 K 1
c 2 K 1
K 1
c 2 K 1 Xd
2
2
T U X X
E UT
U T ( X X )
d
q
f sin2
q
1
1
1
cos( 1)
d
q
o
c s2( 1)
(36)
c K 2
3
2 1
Xd q
X
c 2 K 1 Xd
c 2 K 1 Xd q
X
2
u
f 1 Efd f 2 U f 3
f 4
Eq.(36) considers the coupling function of speed and voltage, which controls both
synthetically. It can increase dynamic precision of speed and voltage, improving the stability
of ship power system.
5. Results of computer simulation
The key parameters of diesel-generator set control system in this paper are as follow:
The power of diesel-generator set is 1250kW; the rated speed n =1500r/min; the rotary
inertia of set J=71.822kg·m2; the damping coefficient of set D =5.54;the magnetic pole pair
number of generator p=2; the rated torque of diesel engine 11.9kN·m; the maximum troke of
output axis 10mm.
The rated voltage of synchronous generator is 390V; the rated current 2310A; the power factor
0.8; the rated frequency 50Hz; the exciting voltage of exciter 83V; the exciting current 7.7A.
Designing nonlinear synthetic controller based on mixed H-two/H-infinity control theory,
assuming disturbance signal coefficient of Eq.(23) 1
d =0.1, assuming weighting coefficient of
Eq.(24) q 11 =0.002, q 12 =0.4, q 13 =0.5, 1 r =0.01, q 21 =0.002, q 22 =0.4, q 23 =0.5, 2 r =0.01.
Corresponding matrix are
0 1
0
0
0.002
0
0
0
A 0 0
1
,
1
B
0.1
, C 1 C 2
0
0.4
0
, 12
D
22
D
0
.
0 0 0.0014
0
0
0
0.5
0.01
Using LMI toolbox, we get state feedback controller:
F [ 0
.3582
35.1042
157.7578
]
(37)
Assuming weighting coefficient of Eq.(33) q 14 =0.1, q 15 =2800, q 16 =0.1, q 17 =0.1, q 24 =0.1, q 25 =2800, q 26 =0.1, q 27 =0.1, 3 r = 4 r = 5 r = 6 r =1, 7 r = 8 r = 9 r = 10
r =1.
Corresponding matrix are
0.4545
0
0
0
0
0
0
0
0.0011 0.0011 0.0002 0.2043
0.0021
0
0
0.2032
A
, B
,
0
0
0
1
1
0
0
0
1
?