Model-free control of a magnetically supported plate

Abstract

Established model-based methods often use a combination of state feedback and observer to control complex systems. They rely on detailed mathematical models that are often hard to derive. Nonetheless, such methods may achieve a high level of accuracy, which justifies the cumbersome modelling. An alternative approach is model-free control, in a form introduced by Fliess and Join, where the system is approximated in a short time interval by a low-order differential equation with unknown parts, a so-called ultra-local model. This control method is a powerful tool, but the parametrisation and the concrete implementation may require time, effort, and experience. The present paper investigates the systematic tuning of a model-free controller for a magnetically supported plate that is modelled as an unstable multiple-input multiple-output system. Furthermore, the incorporation of model information into the model-free controller is investigated. These adaptations ultimately improve results by simplifying parameter tuning and interpretation of estimates. Several experiments are carried out on a test bed to show the capabilities of the proposed algorithms for set point stabilisation and trajectory tracking. The effects of the different parameters in the model-free controllers are addressed, and excellent robustness with respect to actuator faults is demonstrated. Filters for estimating derivatives and unknown quantities are designed using an open-source toolbox.