复杂机动动作最优航迹控制模型及操纵特性分析
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, :V ,x y ,γ ,h ,χ .
(1)
2
,
(Aircraft Maneuver)
x
:
3
T
D
: (2)
T = uTmax (h, M (h, V )) L nz mg − T sin α D= = K K (2) ,Tmax , ;K
.
(4) ,wi,r ,pi,r i
i r
.
r
,
Fj
,
j +1
[6]
.
Slalom : .
. , .
Jeremy H.Gillula reachable set , , Hamilton-Jacobi , , .
[7]
3
,
(The optimal trajectory control model)
(The equation of motion)
, .
3.1
, , , . , . , . , , . , , , . Niching SSGA , , , . ,
[9,10]
, . , , . . ,
nz u
, ,
[11]
φ
, , .
β =0 , [12] :
◦
˙ = 1 (T cos α − D − mg sin γ ) V m g(nz cosφ − cosγ ) γ ˙ = V gnz sin φ γ ˙ = V cos γ x ˙ = V cos γ cos χ y ˙ = V cos γ sin χ ˙ = V sin γ h
1
(Introduction)
. , , ,
: xxxx−xx−xx; : xxxx−xx−xx. . E-mail: liuying204@sohu.com; Tel.:+86 13302192801. : (61074152).
: , , ,
, . ,
; : . , , , ,
,
[1-2]
. . .Mellinger[3] .
p3,3 =
α−12 αmax −12◦ 10◦ −α 10◦ −αmin
1
1 , , . γ, : , j = 1, 2, · · · , 36 (10) t , ,
n
.
m−1
min (ω
i=1
Wi Pi (X ) + (1 − ω )
j =1
Fnz ,j )
s.t Xj,t = g(Xj,t−1 , nzj,t−1 , ∆t) αmin ≤ α ≤ αmax Vmin ≤ Vj,t ≤ Vmax hmin ≤ hj,t ≤ hmax nzmin ≤ nz ≤ nzmax nzj,t = nzj,t−1 + fnz ,j ∆t ψj = |γj,t − γjf | ≤ δ γjf = j ×10 ,n = 6, ,m = 36 , 36 ∆t = 0.05s, g(·) . . 6 , 36 (11)
,
, fω,j , ∈ [−1, 1.5] j = 1, 2, · · · , 37 , fω,j ∈ [−5◦ , 5◦ ] j = 2, · · · , 37. , fnz ,j , 10◦ fnz ,j fω,j . , , , , 36
7 , 2
φ
, [0◦ , 360◦ ], 37
1 2 3 4 5 6 7
, . Niching SSGA , , . ; ; , ,
, ,
The Optimal Trajectory Control Model of the Aircraft Maneuver and the operation characteristic analysis
LIU Ying12 , LI Min-qiang2
xx xxxx
x x
Control Theory & Applications
Vol. xx No. x Xxx. xxxx
DOI: 10.7641/CTA.201x.xxxxx
12 † (1. 2. 95927 ,
,
,
1 300072; 061036)
: , . , . , : ; : V328.3 ; :A ,
n
i
, . .
,
Wi=1.
i=1
nzj,t = nzj,t−1 + fnz ,j ∆t φj,t = φj,t−1 + (ωj,t−1 + fω,j ∆t)∆t u = u j,t j,t−1 + fu,j ∆t
(8) . ,nzj,t
(9)
t j
,∆ t
φj,t uj,t ,fnz ,j fω,j
,
u
10◦ 6 , 1
. .
36
φ=0 ,
◦
2
(30◦ ≤ γ ≤ 40◦ )
4.5 ≤ nz ≤ 5.5
p2,1 =
0
4.5−nz 4.5−nzmin nz −5.5 nzmax −5.5
ψj = |γj,t − γjf | ≤ δ γ , j,t γ , jf δ j 0.1◦ . j
x
:
5
3.4
(The optimal trajectory control model of the barrel roll) , , , , . , , fnz ,j ϑ . φ∈
2
. , nz fnz,j fnz ,j φ, fω,j ,
(6)
(7)
; , (3) .
m− 1
:
ψj = |Xj,t − Xjf | ≤ δ , j = 1, 2, · · · , n
(3) (7) ,Xj,t ,Xjf j .
(8)
j
t
,δ :
J = min(ω Wi Pi (X ) + (1 − ω )
j =1
Fi )
(3) ,n .ω . Wi
,
,m ω > 0.5,
Fmax
.
h
, , , . ,
, .
, α
V
nzmin
f
.
, nz ≤ nz ≤ nzmax . , . fnzmin ≤ fnz ≤ fnzmax fωmin ≤ fω ≤ fωmax f umin ≤ fu ≤ fumax .
αmin ≤ α ≤ αmax Vmin ≤ V ≤ Vmax h min ≤ h ≤ hmax
(1. College of Management and Economics, Tianjin University, Tianjin 300072, China; 2. 95927unit, Hebei,Cangzhou 061036, China)
Abstract: To improve the control ability of the maneuver and reduce the flight risk from the view of operation of the pilots, optimal trajectory control model of the maneuver, taking the control rate of change as the optimization parameters, is proposed. The maneuver has been divided into different trajectory primitives. If the maneuver is divided reasonably, each of the trajectory primitives has the identical control rate of change. The control rate of change not only provides the control input of the maneuver, but also reflects the pilots’ control condition of the maneuver. Niching steady-state genetic algorithm (Niching SSGA) is adopted to solve the optimal control model and the optimal control sequences of the maneuver are obtained. The control inputs of the maneuver corresponding to the optimal control sequences are able to drive the aircraft to complete the optimal maneuver. The optimal maneuver control model is used to analyze the characteristic vertical and lateral maneuvers, i.e. loop and barrel roll. The optimal control sequences of the maneuvers are obtained respectively and the operation characteristics of maneuvers are analyzed. Key words: maneuver; optimal trajectory control; Niching steady-state genetic algorithm; loop maneuver; barrel roll maneuver
j
,
3.2
(The optimal trajectory control model of the maneuver)
, . , , , , , , , . , , , , , . , : , .
n i=1
, ∆fj = |fj+1 − fj |,Fj 0 if 0 ≤ ∆fj ≤ Fmin ∆f − F j min Fj = (5) if Fmin < ∆fj < Fmax F − Fmin max 1 if ∆fj ≥ Fmax (5) ,Fmin , .
†
2
xx
,
, , .Emilio (maneuver , Maneuver , . .
[5]
. , .
[8]
Frazzoli (trim primitive) primitive), Automaton
[4]
.
, . , , .
360◦
, , , , , ,
inverse simulation . , , . , . ,
nz ≥ 4 nzmin ≤ nz < 4 nz < nzmin 10◦ ≤ α ≤ 12◦ 12◦ < α ≤ αmax αmin ≤ α < 10◦ α > αmax or α < αmin
3 (γ = 90◦ )
nz ≥ 4
p3,2 =
1 0
◦
if if if if if if if
10◦ ≤ α ≤ 12◦
1 0
650−v 650−vmin
Байду номын сангаас
v ≥ 650km/h
p3,1 =
1 0
4−nz 4−nzmin
if 4.5 ≤ nz ≤ 5.5 if nzmin ≤ nz < 4.5 if 5.5 < nz ≤ nzmax if nz < nzmax or nz > nzmin if v ≥ 650 if vmin ≤ V < 650 if v < vmin
γ = 0◦ ϑ = 12◦ φ = 30◦ φ = 90◦ φ = 180◦ φ = 270◦ φ = 360◦
.
n i =1
min (ω Wi Pi (X )+ (1 − ω )( s.t Xj,t = g(Xj,t−1 , nzj,t−1 , ∆t) αmin ≤ α ≤ αmax : Vmin ≤ Vj,t ≤ Vmax hmin ≤ hj,t ≤ hmax , nzmin ≤ nz ≤ nzmax nzj,t = nzj,t−1 + fnz ,j ∆t
.
j fu,j
Pi (X ) ,
i
:
3.3
r
Pi (X ) =
wi,r pi,r
(4)
(The optimal trajectory control model of the loop maneuver)
,
4
xx
, , , . , , , ,
1
. ,
nz u. , fnz , fnz ,j ∈[−1, 1, 5] j = 1, 2, · · · , n,fnz (9) .
m −1 j=1
Fnz ,j +
m −1 j=2
Fω,j ))
2 2 2 ,
, ;
, 1 7 , ◦ φ=0 , 3 7 , 3 .
(1)
2
,
(Aircraft Maneuver)
x
:
3
T
D
: (2)
T = uTmax (h, M (h, V )) L nz mg − T sin α D= = K K (2) ,Tmax , ;K
.
(4) ,wi,r ,pi,r i
i r
.
r
,
Fj
,
j +1
[6]
.
Slalom : .
. , .
Jeremy H.Gillula reachable set , , Hamilton-Jacobi , , .
[7]
3
,
(The optimal trajectory control model)
(The equation of motion)
, .
3.1
, , , . , . , . , , . , , , . Niching SSGA , , , . ,
[9,10]
, . , , . . ,
nz u
, ,
[11]
φ
, , .
β =0 , [12] :
◦
˙ = 1 (T cos α − D − mg sin γ ) V m g(nz cosφ − cosγ ) γ ˙ = V gnz sin φ γ ˙ = V cos γ x ˙ = V cos γ cos χ y ˙ = V cos γ sin χ ˙ = V sin γ h
1
(Introduction)
. , , ,
: xxxx−xx−xx; : xxxx−xx−xx. . E-mail: liuying204@sohu.com; Tel.:+86 13302192801. : (61074152).
: , , ,
, . ,
; : . , , , ,
,
[1-2]
. . .Mellinger[3] .
p3,3 =
α−12 αmax −12◦ 10◦ −α 10◦ −αmin
1
1 , , . γ, : , j = 1, 2, · · · , 36 (10) t , ,
n
.
m−1
min (ω
i=1
Wi Pi (X ) + (1 − ω )
j =1
Fnz ,j )
s.t Xj,t = g(Xj,t−1 , nzj,t−1 , ∆t) αmin ≤ α ≤ αmax Vmin ≤ Vj,t ≤ Vmax hmin ≤ hj,t ≤ hmax nzmin ≤ nz ≤ nzmax nzj,t = nzj,t−1 + fnz ,j ∆t ψj = |γj,t − γjf | ≤ δ γjf = j ×10 ,n = 6, ,m = 36 , 36 ∆t = 0.05s, g(·) . . 6 , 36 (11)
,
, fω,j , ∈ [−1, 1.5] j = 1, 2, · · · , 37 , fω,j ∈ [−5◦ , 5◦ ] j = 2, · · · , 37. , fnz ,j , 10◦ fnz ,j fω,j . , , , , 36
7 , 2
φ
, [0◦ , 360◦ ], 37
1 2 3 4 5 6 7
, . Niching SSGA , , . ; ; , ,
, ,
The Optimal Trajectory Control Model of the Aircraft Maneuver and the operation characteristic analysis
LIU Ying12 , LI Min-qiang2
xx xxxx
x x
Control Theory & Applications
Vol. xx No. x Xxx. xxxx
DOI: 10.7641/CTA.201x.xxxxx
12 † (1. 2. 95927 ,
,
,
1 300072; 061036)
: , . , . , : ; : V328.3 ; :A ,
n
i
, . .
,
Wi=1.
i=1
nzj,t = nzj,t−1 + fnz ,j ∆t φj,t = φj,t−1 + (ωj,t−1 + fω,j ∆t)∆t u = u j,t j,t−1 + fu,j ∆t
(8) . ,nzj,t
(9)
t j
,∆ t
φj,t uj,t ,fnz ,j fω,j
,
u
10◦ 6 , 1
. .
36
φ=0 ,
◦
2
(30◦ ≤ γ ≤ 40◦ )
4.5 ≤ nz ≤ 5.5
p2,1 =
0
4.5−nz 4.5−nzmin nz −5.5 nzmax −5.5
ψj = |γj,t − γjf | ≤ δ γ , j,t γ , jf δ j 0.1◦ . j
x
:
5
3.4
(The optimal trajectory control model of the barrel roll) , , , , . , , fnz ,j ϑ . φ∈
2
. , nz fnz,j fnz ,j φ, fω,j ,
(6)
(7)
; , (3) .
m− 1
:
ψj = |Xj,t − Xjf | ≤ δ , j = 1, 2, · · · , n
(3) (7) ,Xj,t ,Xjf j .
(8)
j
t
,δ :
J = min(ω Wi Pi (X ) + (1 − ω )
j =1
Fi )
(3) ,n .ω . Wi
,
,m ω > 0.5,
Fmax
.
h
, , , . ,
, .
, α
V
nzmin
f
.
, nz ≤ nz ≤ nzmax . , . fnzmin ≤ fnz ≤ fnzmax fωmin ≤ fω ≤ fωmax f umin ≤ fu ≤ fumax .
αmin ≤ α ≤ αmax Vmin ≤ V ≤ Vmax h min ≤ h ≤ hmax
(1. College of Management and Economics, Tianjin University, Tianjin 300072, China; 2. 95927unit, Hebei,Cangzhou 061036, China)
Abstract: To improve the control ability of the maneuver and reduce the flight risk from the view of operation of the pilots, optimal trajectory control model of the maneuver, taking the control rate of change as the optimization parameters, is proposed. The maneuver has been divided into different trajectory primitives. If the maneuver is divided reasonably, each of the trajectory primitives has the identical control rate of change. The control rate of change not only provides the control input of the maneuver, but also reflects the pilots’ control condition of the maneuver. Niching steady-state genetic algorithm (Niching SSGA) is adopted to solve the optimal control model and the optimal control sequences of the maneuver are obtained. The control inputs of the maneuver corresponding to the optimal control sequences are able to drive the aircraft to complete the optimal maneuver. The optimal maneuver control model is used to analyze the characteristic vertical and lateral maneuvers, i.e. loop and barrel roll. The optimal control sequences of the maneuvers are obtained respectively and the operation characteristics of maneuvers are analyzed. Key words: maneuver; optimal trajectory control; Niching steady-state genetic algorithm; loop maneuver; barrel roll maneuver
j
,
3.2
(The optimal trajectory control model of the maneuver)
, . , , , , , , , . , , , , , . , : , .
n i=1
, ∆fj = |fj+1 − fj |,Fj 0 if 0 ≤ ∆fj ≤ Fmin ∆f − F j min Fj = (5) if Fmin < ∆fj < Fmax F − Fmin max 1 if ∆fj ≥ Fmax (5) ,Fmin , .
†
2
xx
,
, , .Emilio (maneuver , Maneuver , . .
[5]
. , .
[8]
Frazzoli (trim primitive) primitive), Automaton
[4]
.
, . , , .
360◦
, , , , , ,
inverse simulation . , , . , . ,
nz ≥ 4 nzmin ≤ nz < 4 nz < nzmin 10◦ ≤ α ≤ 12◦ 12◦ < α ≤ αmax αmin ≤ α < 10◦ α > αmax or α < αmin
3 (γ = 90◦ )
nz ≥ 4
p3,2 =
1 0
◦
if if if if if if if
10◦ ≤ α ≤ 12◦
1 0
650−v 650−vmin
Байду номын сангаас
v ≥ 650km/h
p3,1 =
1 0
4−nz 4−nzmin
if 4.5 ≤ nz ≤ 5.5 if nzmin ≤ nz < 4.5 if 5.5 < nz ≤ nzmax if nz < nzmax or nz > nzmin if v ≥ 650 if vmin ≤ V < 650 if v < vmin
γ = 0◦ ϑ = 12◦ φ = 30◦ φ = 90◦ φ = 180◦ φ = 270◦ φ = 360◦
.
n i =1
min (ω Wi Pi (X )+ (1 − ω )( s.t Xj,t = g(Xj,t−1 , nzj,t−1 , ∆t) αmin ≤ α ≤ αmax : Vmin ≤ Vj,t ≤ Vmax hmin ≤ hj,t ≤ hmax , nzmin ≤ nz ≤ nzmax nzj,t = nzj,t−1 + fnz ,j ∆t
.
j fu,j
Pi (X ) ,
i
:
3.3
r
Pi (X ) =
wi,r pi,r
(4)
(The optimal trajectory control model of the loop maneuver)
,
4
xx
, , , . , , , ,
1
. ,
nz u. , fnz , fnz ,j ∈[−1, 1, 5] j = 1, 2, · · · , n,fnz (9) .
m −1 j=1
Fnz ,j +
m −1 j=2
Fω,j ))
2 2 2 ,
, ;
, 1 7 , ◦ φ=0 , 3 7 , 3 .