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.