Combining model-based and model-free approaches for the control of an electro-hydraulic system

Model-free control, as introduced by Fliess and Join, is a compelling feedback control method for complex systems that can only be modelled with considerable effort. However, systematic parametrisation techniques, the concrete implementation, and the analysis of the approaches deserve further investigations. The present paper serves to propose a systematic way to parameterise a model-free controller for a system approximated by a first-order differential equation with unknown parts. Furthermore, model-based and model-free approaches are combined to efficiently control a hydraulic piston (model-based) actuated by four pilot-operated proportional valves (model-free) as a practical example of a typical electro-hydraulic system. Only pressure measurements and the position signal of the piston are used. No measurement of hydraulic flows or spool positions are required. The effects of the different parameters of the model-free controller are investigated and the implementation is discussed in detail. Several experiments on a test bed are carried out, showing a high positioning accuracy for a wide range of piston velocities and a behaviour robust against leakages. An open-access toolbox is used for the design of advanced differentiators to estimate unmeasured quantities required in the controller. This contribution shows that with the right tools, it is possible to design an efficient model-free controller and benefit from its advantages.