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This paper deals with the high performance adaptive robust motion control of electrohydraulic servo system driven by dual vane hydraulic rotary actuator. The recently developed adaptive robust control theory is used to handle the nonlinearities and modelling uncertainties in hydraulic systems. Aside from the difficulty of handling parametric variations, the traditional adaptive robust controller (ARC) is also a little complicated in practice. To address these challenging issues, a simplified adaptive robust control with varying boundary discontinuous projection is developed to enhance the robustness of the closed-loop system, based on the features of hydraulic rotary actuator. Compared with previous ARC controller, the resulting controller has a simple algorithm for more suitable implementation and can handle parametric variations via nonlinear robust design. The controller theoretically achieves a guaranteed transient performance and final tracking accuracy in the presence of both parametric uncertainties and uncertain nonlinearities. Extensive simulation results are obtained for a hydraulic rotary actuator to verify the high performance nature of proposed control strategy.

Hydraulic systems have been used in industry in a wide number of applications by virtue of their small size-to-power ratios and the ability to apply very large forces and torques, for example electrohydraulic positioning systems [

In the past, lots of research works in control of hydraulic systems have used linear control theory and feedback linearization techniques [

During the past two decades, a mathematically rigorous nonlinear adaptive robust control (ARC) approach has been proposed for high performance robust control of uncertain nonlinear systems in the presence of both parametric uncertainties and uncertain nonlinearities [

For the hydraulic system, its relative degree is normally larger than one and also has nonsmooth nonlinearities, such as frictions [

In this paper, a simplified adaptive robust control with varying boundary discontinuous projection strategy is proposed. In contrast to the previous ARC controllers, in order to improve the operability, the simplified ARC approach reduces the relative degree of hydraulic servo system to one by utilizing the feature that hydraulic rotary actuator typically has larger leakage characteristics, which can help to avoid carrying out the complicated backstepping design. Moreover, the varying boundary discontinuous projection will be used to handle the estimation process of varying parameters via differential pressure signal. As a result, the resulting controller becomes simpler and the parameter adaptation process is more comprehensive in the presence of varying parameters.

To test the proposed simplified ARC strategy with varying boundary discontinuous projection, extensive comparative simulation results have been obtained for the motion control of a hydraulic rotary actuator. These results verify the high-performance nature of the proposed approach as same as traditional ARC method, but have more simple structure and flexible parametric adaptation.

The remainder of this paper is organized as follows. Problem formulation and system models are given in Section

The system under consideration is depicted in Figure

Hydraulic motion servo system and rotary actuator.

Given the desired motion trajectory

From [

To begin the controller design, some practical and reasonable assumptions and simplifications have to be made. For simplicity, the dynamic (

Also, combined with load flow equation (

Regarding the discontinuous nonlinearity due to the directional change of valve opening,

As in [

In the above scaling expressions,

In general, the system (

The state space equation (

For most applications, the extent of the parametric uncertainties and uncertain nonlinearities is known. Thus the following practical assumption is made.

Parametric uncertainties and uncertain nonlinearities satisfy

In (

In the following, a varying boundary discontinuous projection based ARC controller will be presented to achieve high performance of hydraulic servo system. To this end, the following notations are introduced.

Let

By using an adaptation law given by

Properties (P1) and (P2) imply that the parameter estimations are always within the known bounded set

Property (P4) shows that a better estimation performance can be given by using the varying boundary discontinuous projection, compared to the traditional discontinuous projection so long as the given varying boundary is reasonable.

Noting that the first equation of (

With the projection type adaptive law (

The robust control function

One example of a smooth

With the control law

With the projection type adaptation law (

In general, all signals are bounded. Furthermore, the positive definite function

is bounded above by

where

If after a finite time

Based on (

Results in (A) of Theorem

To illustrate above designs, simulation results are obtained for the hydraulic system discussed in Section ^{2}, ^{3}/rad, ^{5}, ^{5}/(N·s), ^{4}/(s·V·

In general, hydraulic motion servo system usually suffers from significant external disturbance, which could degrade the performance of hydraulic motion servo system. As an example of varying boundary discontinuous projection, ignoring the minor factor of unmodeled friction torques, that is, assume

In implementation, as an alternative, a pragmatic approach [

The following three controllers are compared.

ARC

DCARC: the desired compensation adaptive robust control with traditional discontinuous projection and the controller parameters are the same as in ARC

Motion controller: the proportional-integral-derivative (PID) controller, which is widely used in industrial control. The tuned gains are

To test the normal tracking performance of each controller, simulations are first run for the ideal case only with parametric uncertainties (i.e.,

Tracking error in the presence of parametric uncertainty only.

To test the robustness against performance of the proposed schemes, a large varying external disturbance sinusoidal

ARCs’ tracking errors in the presence of parametric uncertainty and uncertain nonlinearities.

Parameter adaptation in the presence of uncertain nonlinearities.

The simulation is also run for fast desired trajectory and similar results have been obtained. For example, for a 2 Hz desired trajectory given by ^{2}. The tracking errors are shown in Figures

Tracking errors for a fast sinusoidal curve in the presence of parametric uncertainties only.

Tracking errors for a fast sinusoidal curve in the presence of parametric uncertainties and uncertain nonlinearities.

Scaled ARCs’ tracking errors for a fast sinusoidal curve in the presence of parametric uncertainties and uncertain nonlinearities.

Point to point motion trajectory profile.

Tracking errors in point to point motion in the presence of parametric uncertainty only.

Scaled ARCs’ tracking errors in point to point motion in the presence of parametric uncertainty only.

Tracking errors in point to point motion in the presence of parametric uncertainty and uncertain nonlinearities.

Scaled ARCs’ tracking errors in point to point motion in the presence of parametric uncertainty and uncertain nonlinearities.

In this paper, a varying boundary discontinuous projection based adaptive robust controller is proposed for the high performance robust motion control of an electrohydraulic servo system driven by dual vane hydraulic rotary actuator, to enhance the robustness against parameter variations and disturbances. And some significant modifications and simplifications have been made by using differential pressure signal according to the internal leakage feature of the considered hydraulic rotary actuator. Based on a simplified system model and varying boundary discontinuous projection, a desired compensation ARC controller is constructed. The controller takes into account the particular nonlinearities associated with hydraulic dynamics and parametric uncertainties due to variations of inertia load and lumped damping coefficient as well as uncertain nonlinearities coming from external disturbance. Comparative simulation results show that the proposed scheme has a more robust parameter adaptation process and is more suitable for implementation. As future works, it is very interesting to investigate the adaptive and robust design of hydraulic systems with potential hydraulic faults [

The authors declare that there is no conflict of interests regarding the publication of this paper.