An Approach for Second Order Control With Finite Time Convergence for Electro-Hydraulic Drives

Being a second order sliding algorithm, the super twisting algorithm is highly attractive for application in control of hydraulic drives and mechanical systems in general, as it utilizes only the control error while driving the control error as well as its derivative to zero for properly chosen algorithm parameters. However a discontinuous term internally in the control structure may excite pressures of transmission lines in hydraulic drives as the control structure strives to maintain the control error and its derivative equal to zero. In this paper a modified version of a controller based on the super twisting algorithm is proposed, with the focus of eliminating the discontinuous term in order to achieve a more smooth control operation. The convergence properties of the proposed controller are analyzed via a conservative phase plane analysis. Furthermore, homogeneity considerations imply finite time convergence of states to the origin under certain model assumptions. Results demonstrate the smooth control operation compared to the direct super twisting control approach while maintaining robustness properties in relation to position tracking of a hydraulic drive, under parameter perturbations, uncertainties and un-modeled dynamics.