Dynamic model of a non-linear servo control system using transmission line modelling technique

The modelling and simulation of a test rig based on the transmission line modelling technique is presented in this paper. The studied test rig is a non-linear servo control system and represents a CNC machine tool feed drive where the controller commands the movement of worktable linked to a motor through a ball-screw. The transmission line modelling technique has been successfully applied until now for hydraulic systems, electromagnetic, acoustics and several mechanical applications (not much emphasis on digital controllers). The paper presents a novel application of this method for modelling the interaction between the position loop controller, servo system and the worktable mechanism. It addresses the modelling of the non-linearities (Coulomb and viscous friction, backlash) and axial and torsional forces applied on the ball-screw nut during its linear movement. The simulation results generated by the MATLAB program compare well with the measured data when same stimuli are applied to the test rig. So this numerical method is successfully applied for accurate modelling of non-linear and dynamic behaviour of CNC machine tools feed drives