Real-Time Simulation of Fluid Power Systems Containing Small Oil Volumes, Using the Method of Multiple Scales

Abstract

Machinery devices often consist of mechanical mechanisms that are actuated by fluid power systems. In many applications, the mechanical system can be modelled and analysed in terms of the multibody system dynamics. Fluid power systems, in turn, can be analysed via the lumped-fluid theory, with which simulation of fluid power systems requires smaller integration time steps than needed by multi-body solvers. This leaves simulation of the entire machinery device beyond reach for a real-time framework, with the main reason for the very small time steps in modelling of fluid power systems being the presence of a small hydraulic volume, which creates a numerical stiffness problem. The stiffness issue may arise from numerical singularity emerging in the fluid power system, which implies that solving the governing equations involves different time scales-small and large. To resolve the numerical singularity in hydraulic circuits, the authors developed a perturbed model to alleviate the stiffness problem demonstrated that it can increase the integration time step by an order of magnitude. Since the perturbed model does necessitate a correction factor for the volumetric flow rate, the method of multiple scales is applied to compute the pressure within the small volume to second-order accuracy, O(ε 2), in comparison with the perturbed model's O(ε). The results reveal that if the correction parameter is not set, the perturbed model's cumulative error leads to considerable deviation in piston position with respect to the reference model, whereas the multiple-scale model eliminates the issue of cumulative error without demanding any flow-rate correction factor. INDEX TERMS fluid power system, real-time simulation, singular perturbed model, small volumes.

A Hybrid Model for Fast and Efficient Simulation of Fluid Power Circuits With Small Volumes Utilizing a Recurrent Neural Network

“…To overcome the error, a special corrector factor for the model should be used. To solve this problem and allow the simulation without a corrector factor definition, a novel method based on the combined singular perturbation theory and Method of multiple scales (MMS) was proposed by Kiani-Oshtorjani et al [19]. This robust method allows the elimination of the accumulative error and makes the simulation faster and more accurate than the original method based on the singular perturbation theory.…”

Estimating the Characteristic Curve of a Directional Control Valve in a Combined Multibody and Hydraulic System Using an Augmented Discrete Extended Kalman Filter

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