Second order sliding control with state dependent gain and its application to a hydraulic drive

The application of sliding modes for control of hydraulic drives appear promising due to strong robustness toward plant uncertainties and disturbances. Especially high order sliding modes may be successfully implemented avoiding the discontinuous control seen in first order sliding controls. However, the very feature of switching about the control target may be undesirable due to finite sampling time and actuator dynamics, and may cause oscillating flow line pressures. This paper discusses a second order sliding controller based on the so-called prescribed convergence algorithm, when used for chattering elimination in hydraulic drive control applications. For this usage the algorithm suffers from poor convergence properties unless a high control gain is chosen, which in turn increases pressure oscillations. To negotiate the combined challenge the controller is extended with a proportional term for improved convergence speed, and the gain of the discontinuous control is made variable according to the control target itself. It is shown that the control error and its derivative are globally convergent to a vicinity of the target via Lyapunov arguments, with accuracy dependent on control parameters, and finite time convergence properties are considered via homogeneity reasoning. Results demonstrate improved control operation compared to the basic algorithm when implemented for position tracking control of a hydraulic drive.