Abstrast This paper is concerned with adaptive position control using artificial neural networks (ANNs)。 The hydraulic system to be investigated consists of a 4]3 way proportional valve, a diRerential cylinder and a variable load force。 This force results from a mass-spring- damper system。 The main problem in this configuration is the large dead zone in the valve。 Assuming that the cylinder and the load force can be linearly modelled as a second-order system and an integrator, the dynamic model of the hydraulic system can be described as a series connection of a static input non-linearity (dead zone) and a linear system。 For the control of such a Hammerstein system, it is proposed to use an inverse of the input non- linearity for compensation and a linear adaptive controller for the resulting system。 In our new scheme, we use an ANN instead of a fixed inverse non-linearity。 A key feature of this approach is that the ANN can describe several types of non-linear functions without structural changes。 To control the linear part of the system, an adaptive LQ controller is used。 g l999 Elsevier Science Ltd。 All rights reserved。83333

Ke5wovdz„ Artificial neural networks; Non-linear adaptive control; Hydraulic drive

1。Introdustion

Hydraulic drives are widely used in industry, since they can produce large

O957-4l58]OO]$ - see front matter g l999 Elsevier Science Ltd。 All rights reserved。 PII„ S O 9 5 7 - 4 l 5 8 ( 9 9 ) O O O 5 4 - 9

l28 Z。 Knohl, 5。 Unbehauen ] Wechatvonicz 10 (2000) 127−143

torques, high-speed responses with fast motions and speed reversals。 Low-power electrical command inputs are converted into the movement of valve magnetic coils to control a high-power hydraulic actuator。 Compared to electro-magnetical drives, the modelling of these systems is much more complicated。 Laminar and turbulent flows, channel geometry and friction results in system equations that are highly non-linear。 The parameters of hydraulic systems, depending on the relation between flow velocity and pressure and oil viscosity, vary heavily。 Because a normal proportional valve, which incorporates a large dead zone, is used, the non- linearity of the control system, is distinctly marked, hence, highly sophisticated controllers, as, for instance, presented in this paper, are required to handle the dead zone problem。 Classical approaches, like P or PD regulators for positioning of hydraulic drives, do not give satisfactory performance。 For this reason, adaptive control techniques are used。 To compensate for the parameter variations of the hydraulic system with a nearly linear servo valve, a model-reference adaptive controller can be used [l,2]。 But the large dead zone of the 4]3 way proportional valve requires special attention in the control design。 Dead zones have a number of possible adverse eRects on control systems„ the most common one is the decrease of control accuracy。 They may also cause limit cycles or system instability。

For control of non-linear systems, a large number of control schemes exist, where ANNs are used to train the system inverse [3,4]。 These schemes work well for various kinds of systems without a priori knowledge。 But if one wants to control one particular system for which a priori knowledge is available, using this knowledge leads to smaller ANNs, which are easier to configure and train。

Thus, assuming that the valve can be described by a dead zone and the rest of the hydraulic system can be satisfactorily approximated using a linear model, a series connection of a dead zone and a linear system is used to describe the whole plant。 Many adaptive controllers have been proposed to deal with this kind of Hammerstein system。 For instance, in [5,6] control schemes for systems with pre- load non-linearities and a dead zone are described。 Other advanced control approaches in adaptive control systems with input or output non-linearities have been proposed to address these problems [7−ll]。 Because the authors use a standard model reference adaptive controller (MRAC), the controlled system must have a stable inverse。 In [l2], two schemes are proposed to eliminate the eRect of an unknown dead zone on the closed-loop control system, and their convergence and robustness properties are discussed。 The authors assume that the input and the output of the dead zone are measured。