Method and device for allocating thrust
View Patent ↗Force balance and moment balance associated with thrust of air and water craft equipped with thrust generators are preset in view of non-linear characteristics and dynamic characteristics of thrust generators. A performance index for minimizing thrusts generated by the thrust generators is defined. Using the balance as restricting condition, propeller thrusts of the thrust generators and rudder angles and changing speeds of rudders that minimize the performance index are calculated.
1. A method of allocating thrusts in air and water craft equipped with a plurality of thrust generators that generate thrusts corresponding to manipulated variables, comprising calculating the manipulated variables given to the plurality of thrust generators to allow the air and water craft to run with a given targeted thrust or to be held at a fixed point, wherein
based on force balance and moment balance between the thrusts generated by the thrust generators and a thrust of the air and water craft, which is predetermined based on non-linear characteristics of the thrust generators, and
based on a predetermined performance index associated with state variables relating to states of the thrust generators and/or the thrusts generated by the thrust generators, for minimizing the thrusts generated by the thrust generators,
the manipulated variables of the thrust generators that satisfy balance between the manipulated variables and the targeted thrust and a predetermined condition of the performance index are calculated, the balance being predetermined based on the non-linear characteristics and dynamic characteristics of the thrust generators, wherein the balance is given by formulae (1) to (3):
∑
i
=
1
n
f
xi
=
X
(
1
)
∑
i
=
1
n
f
yi
=
Y
(
2
)
∑
i
=
1
n
(
k
1
i
f
xi
+
k
2
i
f
yi
)
=
N
(
3
)
where X is a longitudinal component of the thrust of the air and water craft,
Y is a lateral component of the thrust of the air and water craft,
N is a thrust moment in a turning direction of the air and water craft,
f xi is a longitudinal component of the thrust generated by an i-th thrust generator,
f yi is a lateral component of the thrust generated by the i-th thrust generator,
k 1i and k 2i are coefficients, and
i is 1 to n (n: natural number); and wherein
thrusts F(t)=[fx 1 . . . fxn fy 1 . . . fyn] T generated by the thrust generators are given by a non-linear equation (4):
F ( t )= h[x ( t ), u ( t ), t] (4)
when the manipulated variables of the thrust generators are represented by u(t)=[u 1 . . . um] T (m: positive integer) of the thrust generators,
where t is time variable, and
x are state variables given by non-linear differential equations (5):
{dot over (x)} ( t )= g[x ( t ), u ( t ), t] (5).
2. The method according to claim 1 , wherein the performance index J is given by a formula (11)
J
=
ϕ
[
x
(
t
+
T
f
)
]
+
∫
t
t
+
T
f
L
[
x
(
t
′
)
,
u
(
t
′
)
]
ⅆ
t
′
(
11
)
where Φ and L are scalar value functions differentiable up to a predetermined order or more, T f is a constant, and
t′ is a variable that satisfies t≦t′≦t+T f , and
the predetermined condition is given to minimize or maximize the value of the performance index J.
3. The method according to claim 2 , wherein the performance index J includes weighting factors relating to the state variables x and/or the manipulated variables u, and
the weighting factors are changed on line.
4. The method according to claim 3 , wherein when a failure occurs in the thrust generator, the weighting factors relating to the state variables x and/or the manipulated variables u of the thrust generator in which the failure occurs are changed.
5. The method according to claim 1 , wherein the manipulated variables u satisfy relationship represented by a formula (6):
| u j ( t )|< u j max (6)
where u jmax is a constant, and
j is 1 to m (m: natural number).
6. The method according to claim 1 , wherein the state variables x satisfy relationship represented by a formula (7)
|x I ( t )< x i max (7)
where X imax is a constant.
7. The method according to claim 1 , wherein the thrust generators are azimuth thrusters and the balance is given by formulae (8) to (10)
∑
i
=
1
n
T
i
(
-
yo
i
cos
θ
i
+
xo
i
sin
θ
i
)
=
N
(
10
)
where T i is a propeller thrust of the i-th thrust generator,
θ i is a turning angle of the i-th thrust generator,
xo i is a position of the i-th thrust generator that is relative to a center of gravity of the air and water craft in a longitudinal direction craft, and
yo i is a position of the i-th thrust generator that is relative to the center of gravity of the air and water craft in a lateral direction of the craft.