Lyapunov-based self-tuning of sliding surfaces — methodology and application to hydraulic valves

This publication discusses the topic of sliding mode control and its practical application to position control of a hydraulic directional valve. The main issue relies on the design of an adaptive sliding function, to achieve optimal closed loop performance. For this, a Lyapunov-based stability proof for a second order sliding mode controller is presented. To obtain adaption functionality, it is extended by considering the sliding function parameters. This achieves a stable adaption of the closed loop dynamics. Further, the advantages of nonlinear sliding functions in comparison to linear ones are discussed and an approach based on the idea of dynamical pole placement is extended by the newly introduced self-tuning process. To discuss the features of the proposed adaption law, the application of sliding mode control of a hydraulic valve is considered, where no prior parameter optimization is carried out before. The proposed adaption law achieves a high closed loop performance within a short period of time without any need of parameter optimization. Additionally it is shown, that the use of a nonlinear sliding function increases the closed loop performance, compared to a linear formulation.