where

Kq = flow-gain soeffisient  and KS  = flow-prexxure soeffisient。

The movement of the piston, the change of the oil volume due to  compressibility

Fig。 2。 Non-linear and asymmetric dead zone。

Z。 Knohl, 5。 Unbehauen ] Wechatvonicz 10 (2000) 127−143 l3l

and the leakage oil flow determine the total oil flow QL  as

Q A 5˙ Vt  P˙ f P   , 2

L  =   p    ‡ 4þ L ‡  (  L) ( )

where Vt is the total compressed oil volume, Ap the surface area of the piston, 。 the velocity of the piston, þe the eRective bulk-modulus (compressibility) and f(PL) the non-linear influence of the internal and external oil leakage。 Here, it is assumed that the rod and the head-side areas of the piston are equal。 If the leakage function is approximated by a linear relation, Eq。 (2) can be rewritten as

4þewhere Ctp is the total leakage coeAcient of the piston。 The balance of forces at the sliding carriage leads to

YG  = ApPL  = Wt5¨ ‡ Bp5˙ ‡ K5, (4)

where YG is the force generated by the piston, Wt the total mass of the piston and the load, Bp the damping coeAcient of the piston and the load and K the load spring gradient。 Neglecting the non-linear eRects of dry and adhesive friction, combining Eqs。 (l), (3) and (4) and applying the Laplace transformation to the resulting third-order diRerential equation results in the transfer function

V¯ (z) = z(a2z2 ‡ alz ‡ aO) (  )

where the abbreviations 4þe

are used。 In Eq。 (5), the load force caused by the external spring is considered as an external disturbance。 The parameters of the linear model of the hydraulic system given by Eq。 (6), which depend on the constants derived by linearization,

are all of varying nature。 Variation of the load mass and the damping coeAcient can also be interpreted as parameter changes of the linear model。

To take the large dead zone of the actuating valve into account, a static non- linear dead zone that is portrayed in Fig。 2 and described by

, fl(1)    1 > Ul  > O

is added to the input of the linear model。 Discretization and identification of the real plant gives the transfer function

V¯ (z—l) = l — O。8898z—l — O。l472z—2 ‡ O。O4l4z—3 (

in a series with the static input non-linearity given by Eq。 (7)。 In conclusion, the hydraulic system, as given in Fig。 l, can be described as a serial connection of a nonlinear dead zone, an integrator and a second-order linear system。 Using the model that is given by Eqs。 (8) and (7), the design of the ANNNA controller is studied in the next section。摘要：本文主要介绍的是利用人工神经网络系统（ANN-1）自适应特性进行液压系统位置的控制。被调查的液压系统由一个4 / 3的比例阀，液压缸组成且载荷为变载荷。变载荷为一个阻尼弹性系统产生。这样的配置的主要问题是阀的死区较大。假设液压缸和负载力可以线性建模为一个二阶积分系统，液压系统的动态模型可以被描述为非线性的静态输入（死区）和线性系统的串联连接。为了控制这样的液压系统，通常提出的方案，利用输入一个非线性函数逆向补偿和线性系统自适应控制。我们提出一个新的方案，利用一个人工神经网络系统代替一个通常固定非线性函数逆向输入。此方案的一个重要特点是人工神经网络可以描述几种类型的非线性函数而自身的结构不发生变化。利用可调节的LQ控制器控制系统的线性部分。文献综述