D
cos x
sin x
cos x
5 4 6 x 5 x
5 5 D x ;
x1 x2
x x M 2
x M l 4
3 3 3
2776
g
cos x5 ; h
cos x5 sin x5 。
J。 Cent。 South Univ。 (2012) 19: 2774−2781
3
Mx3
Mx3
Thus, the bridge crane system was pided into three coupled subsystems: the positioning subsystem, lifting rope subsystem and anti-swing subsystem。
The control object of the bridge crane was to move the trolley to its destination and complement anti-swing of the load at the same time when the system model exists uncertainty and disturbance (for example, winds and different payloads)。 In order to decouple the system, four sliding mode functions were defined for the three subsystems with sliding surface, sx=cxe1+e2, sθ=cθe5+e6, sl=cle3+e4, s=αsx+sθ。
Take the index reaching law as
s1 sgn(s) k1s
sl 2 sgn(sl ) k2 sl
(5)
(6)
Fig。 2 Fuzzy neural network structure
where cx, cl, cθ, α, ε1, k1, ε2 and k2 are positive numbers。 Then, according to Eqs。 (4)−(6), the following equations can be introduced。
u1 [h2 f1 (h1 h3 ) f2 h2 f3 h2cxe2
(h3 h1 )(cle4 lsgn(s ) k s )
1)
Input layer
Each node in this layer is connected with the input vector。 The error and its change rate are the network inputs, which is corresponding to the j-th node in the input−output and can be expressed as
(1)
h2 xd c e6 h2 1h2 sgn(s) k1h2 s]/
wij 1
(g2h3 g1h2 g3h2 g2h1 )
(7)
I (1) w(1) x(1) x(1)
(9)
j ij i i
(1) (1) (1) (1)
u cl e4 f2 ld 2 sgn(sl ) k2 sl g2u1
h2
(8)
Oj
f j
(I j
) I j
where (1) (1)
x1 e(t) , x2
e(t)。
However, f1, h1, f2, g2, h2, f3, g3, and h3 are generally
unknown in the actual system, therefore, the control law is difficult to implement。
4 Fuzzy neural network
2)
Membership layer
In this layer, input variables are defuzzied, Gaussian membership function is chosen。
w(2) 1
4。1Fuzzy neural network structure
ij
I (2) w(2) (c
,2 )
(I (2) cij )2
(10)
As the actual system control law is difficult to 桥式起重机智能防摆控制英文文献和中文翻译(4):http://www.youerw.com/fanyi/lunwen_97253.html