Hybrid models for hardware-in-the-loop simulation of hydraulic systems Part 1: Theory

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Physical modelling of hydraulic systems results in systems of differential and algebraic equations (DAEs) that are normally stiff. This is because they often include multiple temporal scales and present complex and non-linear behaviour. The simulation of these stiff DAEs in real time demands small time steps, in order to achieve algorithm stability, because explicit fixed step solvers are usually applied. Modelling some fast dynamics as instantaneous changes in order to reduce the model's stiffness has been an area of research in the last few years. The description of the dynamic behaviour as piecewise continuous modes, interspersed with discrete transitions, together with the reduction in the model complexity, facilitates the use of fixed time step integration methods and thus allows real-time simulation. The main goal of this work was to obtain not too complex models in order to allow the models to be used in hardware-in-the-loop experiments. This paper proposes the use of the statecharts formalism to describe hybrid behaviour in hydraulic systems and presents semiempirical models of a valve controlled hydraulic cylinder intended to test real controller performance on a hardware-in-the-loop setup. These semiempirical models require less computing power, and it is easier to adjust the model parameters.