Adaptive Control of a Differential Hydraulic Cylinder with Dynamic Friction Model

Servo valve controlled hydraulic differential cylinders are non-linear, strongly coupled multivariable electromechanical systems. When the piston’s velocity with respect to the cylinder is in the vicinity of zero the effect of adhesion is a significant effect due to which decreasing absolute value of velocity results in increasing stiction force. Furthermore, when the motion is initiated from equilibrium state of zero initial velocity adhesion can compensate arbitrary forces within certain limits keeping the piston almost fixed. This regime of friction can be modeled by some elastic deformation the deformable elements of which become disconnected over certain force limits. In the paper a concise application of the dynamic LuGre Model of friction is reported in which the effects of the elastic deformation, adhesion, and viscosity are combined with each other. To compensate the effect of the imprecisely known system parameters and unknown external forces an adaptive control is developed in which varying fractional order derivatives are used to reduce the hectic behavior of friction in the case of ‘critical’ trajectories that asymptotically converge to a fixed position and zero velocity. Simulation results made by INRIA’s Scilab are presented. It is concluded that the combined application of the two adaptive techniques can result in accurate control if the LuGre model satisfactorily describes the reality.